TSTP Solution File: SYO325^5 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SYO325^5 : TPTP v7.5.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Tue Mar 29 00:51:09 EDT 2022
% Result : Timeout 291.94s 292.30s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SYO325^5 : TPTP v7.5.0. Released v4.0.0.
% 0.03/0.12 % Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n024.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPUModel : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % RAMPerCPU : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % DateTime : Sat Mar 12 03:49:04 EST 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.12/0.34 Python 2.7.5
% 1.51/1.77 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox2/benchmark/', '/export/starexec/sandbox2/benchmark/']
% 1.51/1.77 FOF formula (<kernel.Constant object at 0x228e638>, <kernel.Type object at 0x228e9e0>) of role type named a_type
% 1.51/1.77 Using role type
% 1.51/1.77 Declaring a:Type
% 1.51/1.77 FOF formula (<kernel.Constant object at 0x2292ef0>, <kernel.DependentProduct object at 0x228e7e8>) of role type named cK
% 1.51/1.77 Using role type
% 1.51/1.77 Declaring cK:((a->Prop)->(a->Prop))
% 1.51/1.77 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), (((cK (fun (Xx0:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))) Xx)->((cK (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_1SS
% 1.51/1.77 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), (((cK (fun (Xx0:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))) Xx)->((cK (cK (fun (Xx0:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))))) Xx)))):Prop
% 1.51/1.77 Parameter a_DUMMY:a.
% 1.51/1.77 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), (((cK (fun (Xx0:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))) Xx)->((cK (cK (fun (Xx0:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))))) Xx))))']
% 1.51/1.77 Parameter a:Type.
% 1.51/1.77 Parameter cK:((a->Prop)->(a->Prop)).
% 1.51/1.77 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), (((cK (fun (Xx0:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))) Xx)->((cK (cK (fun (Xx0:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))))) Xx))))
% 1.51/1.77 Found x0:((cK (fun (Xx0:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))) Xx)
% 1.51/1.77 Instantiate: X:=(fun (Xx0:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))):(a->Prop)
% 1.51/1.77 Found x0 as proof of ((cK X) Xx)
% 1.51/1.77 Found x2:(X Xx0)
% 1.51/1.77 Found x2 as proof of ((cK (fun (Xx00:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx00)))))) Xx0)
% 1.51/1.77 Found (fun (x2:(X Xx0))=> x2) as proof of ((cK (fun (Xx00:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx00)))))) Xx0)
% 1.51/1.77 Found (fun (Xx0:a) (x2:(X Xx0))=> x2) as proof of ((X Xx0)->((cK (fun (Xx00:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx00)))))) Xx0))
% 1.51/1.77 Found (fun (Xx0:a) (x2:(X Xx0))=> x2) as proof of (forall (Xx:a), ((X Xx)->((cK (fun (Xx0:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))) Xx)))
% 1.51/1.77 Found x4:(X0 Xx1)
% 1.51/1.77 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx10:a), ((S Xx10)->((cK S) Xx10)))) (S Xx1))))
% 1.51/1.77 Found (fun (x4:(X0 Xx1))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx10:a), ((S Xx10)->((cK S) Xx10)))) (S Xx1))))
% 1.51/1.77 Found (fun (Xx1:a) (x4:(X0 Xx1))=> x4) as proof of ((X0 Xx1)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx10:a), ((S Xx10)->((cK S) Xx10)))) (S Xx1)))))
% 1.51/1.77 Found (fun (Xx1:a) (x4:(X0 Xx1))=> x4) as proof of (forall (Xx:a), ((X0 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% 1.51/1.77 Found x6:(X0 Xx1)
% 1.51/1.77 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx10:a), ((S Xx10)->((cK S) Xx10)))) (S Xx1))))
% 1.51/1.77 Found (fun (x6:(X0 Xx1))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx10:a), ((S Xx10)->((cK S) Xx10)))) (S Xx1))))
% 2.51/2.75 Found (fun (Xx1:a) (x6:(X0 Xx1))=> x6) as proof of ((X0 Xx1)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx10:a), ((S Xx10)->((cK S) Xx10)))) (S Xx1)))))
% 2.51/2.75 Found (fun (Xx1:a) (x6:(X0 Xx1))=> x6) as proof of (forall (Xx:a), ((X0 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% 2.51/2.75 Found x60:=(x6 Xx0):((x3 Xx0)->((cK x3) Xx0))
% 2.51/2.75 Found (x6 Xx0) as proof of ((x3 Xx0)->((cK X0) Xx0))
% 2.51/2.75 Found (x6 Xx0) as proof of ((x3 Xx0)->((cK X0) Xx0))
% 2.51/2.75 Found (fun (x6:(forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1))))=> (x6 Xx0)) as proof of ((x3 Xx0)->((cK X0) Xx0))
% 2.51/2.75 Found (fun (x6:(forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1)))->((x3 Xx0)->((cK X0) Xx0)))
% 2.51/2.75 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1))))=> (x6 Xx0))) as proof of ((cK X0) Xx0)
% 2.51/2.75 Found ((and_rect0 ((cK X0) Xx0)) (fun (x6:(forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1))))=> (x6 Xx0))) as proof of ((cK X0) Xx0)
% 2.51/2.75 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1)))->((x3 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1)))) (x3 Xx0)) P) x6) x4)) ((cK X0) Xx0)) (fun (x6:(forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1))))=> (x6 Xx0))) as proof of ((cK X0) Xx0)
% 2.51/2.75 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1)))->((x3 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1)))) (x3 Xx0)) P) x6) x4)) ((cK X0) Xx0)) (fun (x6:(forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1))))=> (x6 Xx0))) as proof of ((cK X0) Xx0)
% 2.51/2.75 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 2.51/2.75 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X0) Xx0))
% 2.51/2.75 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X0) Xx0))
% 2.51/2.75 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X0) Xx0))
% 2.51/2.75 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X0) Xx0)))
% 2.51/2.75 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X0) Xx0)
% 2.51/2.75 Found ((and_rect0 ((cK X0) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X0) Xx0)
% 2.51/2.75 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X0) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X0) Xx0)
% 2.51/2.75 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X0) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X0) Xx0)
% 2.51/2.75 Found x8:(X0 Xx1)
% 2.51/2.75 Found x8 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx10:a), ((S Xx10)->((cK S) Xx10)))) (S Xx1))))
% 2.51/2.75 Found (fun (x8:(X0 Xx1))=> x8) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx10:a), ((S Xx10)->((cK S) Xx10)))) (S Xx1))))
% 2.51/2.75 Found (fun (Xx1:a) (x8:(X0 Xx1))=> x8) as proof of ((X0 Xx1)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx10:a), ((S Xx10)->((cK S) Xx10)))) (S Xx1)))))
% 2.51/2.75 Found (fun (Xx1:a) (x8:(X0 Xx1))=> x8) as proof of (forall (Xx:a), ((X0 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% 2.51/2.75 Found x500:=(x50 x6):((cK x3) Xx0)
% 2.51/2.75 Found (x50 x6) as proof of ((cK X0) Xx0)
% 2.51/2.75 Found ((x5 Xx0) x6) as proof of ((cK X0) Xx0)
% 2.51/2.75 Found ((x5 Xx0) x6) as proof of ((cK X0) Xx0)
% 2.51/2.75 Found ((x5 Xx0) x6) as proof of ((cK X0) Xx0)
% 2.51/2.75 Found x4:(X00 Xx1)
% 2.51/2.75 Found x4 as proof of (X0 Xx1)
% 2.51/2.75 Found (fun (x4:(X00 Xx1))=> x4) as proof of (X0 Xx1)
% 2.51/2.75 Found (fun (Xx1:a) (x4:(X00 Xx1))=> x4) as proof of ((X00 Xx1)->(X0 Xx1))
% 2.51/2.75 Found (fun (Xx1:a) (x4:(X00 Xx1))=> x4) as proof of (forall (Xx:a), ((X00 Xx)->(X0 Xx)))
% 2.51/2.75 Found x6:(X00 Xx1)
% 2.51/2.75 Found x6 as proof of (X0 Xx1)
% 2.51/2.75 Found (fun (x6:(X00 Xx1))=> x6) as proof of (X0 Xx1)
% 2.51/2.75 Found (fun (Xx1:a) (x6:(X00 Xx1))=> x6) as proof of ((X00 Xx1)->(X0 Xx1))
% 3.09/3.36 Found (fun (Xx1:a) (x6:(X00 Xx1))=> x6) as proof of (forall (Xx:a), ((X00 Xx)->(X0 Xx)))
% 3.09/3.36 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 3.09/3.36 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X00) Xx0))
% 3.09/3.36 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X00) Xx0))
% 3.09/3.36 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X00) Xx0))
% 3.09/3.36 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X00) Xx0)))
% 3.09/3.36 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X00) Xx0)
% 3.09/3.36 Found ((and_rect0 ((cK X00) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X00) Xx0)
% 3.09/3.36 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X00) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X00) Xx0)
% 3.09/3.36 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X00) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X00) Xx0)
% 3.09/3.36 Found x6:(X00 Xx1)
% 3.09/3.36 Found x6 as proof of (X0 Xx1)
% 3.09/3.36 Found (fun (x6:(X00 Xx1))=> x6) as proof of (X0 Xx1)
% 3.09/3.36 Found (fun (Xx1:a) (x6:(X00 Xx1))=> x6) as proof of ((X00 Xx1)->(X0 Xx1))
% 3.09/3.36 Found (fun (Xx1:a) (x6:(X00 Xx1))=> x6) as proof of (forall (Xx:a), ((X00 Xx)->(X0 Xx)))
% 3.09/3.36 Found x60:=(x6 Xx0):((x3 Xx0)->((cK x3) Xx0))
% 3.09/3.36 Found (x6 Xx0) as proof of ((x3 Xx0)->((cK X00) Xx0))
% 3.09/3.36 Found (x6 Xx0) as proof of ((x3 Xx0)->((cK X00) Xx0))
% 3.09/3.36 Found (fun (x6:(forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1))))=> (x6 Xx0)) as proof of ((x3 Xx0)->((cK X00) Xx0))
% 3.09/3.36 Found (fun (x6:(forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1)))->((x3 Xx0)->((cK X00) Xx0)))
% 3.09/3.36 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1))))=> (x6 Xx0))) as proof of ((cK X00) Xx0)
% 3.09/3.36 Found ((and_rect0 ((cK X00) Xx0)) (fun (x6:(forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1))))=> (x6 Xx0))) as proof of ((cK X00) Xx0)
% 3.09/3.36 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1)))->((x3 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1)))) (x3 Xx0)) P) x6) x4)) ((cK X00) Xx0)) (fun (x6:(forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1))))=> (x6 Xx0))) as proof of ((cK X00) Xx0)
% 3.09/3.36 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1)))->((x3 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1)))) (x3 Xx0)) P) x6) x4)) ((cK X00) Xx0)) (fun (x6:(forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1))))=> (x6 Xx0))) as proof of ((cK X00) Xx0)
% 3.09/3.36 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 3.09/3.36 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X00) Xx0))
% 3.09/3.36 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X00) Xx0))
% 3.09/3.36 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X00) Xx0))
% 3.09/3.36 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X00) Xx0)))
% 3.09/3.36 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X00) Xx0)
% 3.09/3.36 Found ((and_rect0 ((cK X00) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X00) Xx0)
% 3.09/3.36 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X00) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X00) Xx0)
% 3.09/3.36 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X00) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X00) Xx0)
% 3.58/3.75 Found x8:(X00 Xx1)
% 3.58/3.75 Found x8 as proof of (X0 Xx1)
% 3.58/3.75 Found (fun (x8:(X00 Xx1))=> x8) as proof of (X0 Xx1)
% 3.58/3.75 Found (fun (Xx1:a) (x8:(X00 Xx1))=> x8) as proof of ((X00 Xx1)->(X0 Xx1))
% 3.58/3.75 Found (fun (Xx1:a) (x8:(X00 Xx1))=> x8) as proof of (forall (Xx:a), ((X00 Xx)->(X0 Xx)))
% 3.58/3.75 Found x600:=(x60 x7):((cK x3) Xx0)
% 3.58/3.75 Found (x60 x7) as proof of ((cK X00) Xx0)
% 3.58/3.75 Found ((x6 Xx0) x7) as proof of ((cK X00) Xx0)
% 3.58/3.75 Found ((x6 Xx0) x7) as proof of ((cK X00) Xx0)
% 3.58/3.75 Found ((x6 Xx0) x7) as proof of ((cK X00) Xx0)
% 3.58/3.75 Found x8:(X00 Xx1)
% 3.58/3.75 Found x8 as proof of (X0 Xx1)
% 3.58/3.75 Found (fun (x8:(X00 Xx1))=> x8) as proof of (X0 Xx1)
% 3.58/3.75 Found (fun (Xx1:a) (x8:(X00 Xx1))=> x8) as proof of ((X00 Xx1)->(X0 Xx1))
% 3.58/3.75 Found (fun (Xx1:a) (x8:(X00 Xx1))=> x8) as proof of (forall (Xx:a), ((X00 Xx)->(X0 Xx)))
% 3.58/3.75 Found x600:=(x60 x7):((cK x4) Xx0)
% 3.58/3.75 Found (x60 x7) as proof of ((cK X00) Xx0)
% 3.58/3.75 Found ((x6 Xx0) x7) as proof of ((cK X00) Xx0)
% 3.58/3.75 Found ((x6 Xx0) x7) as proof of ((cK X00) Xx0)
% 3.58/3.75 Found ((x6 Xx0) x7) as proof of ((cK X00) Xx0)
% 3.58/3.75 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 3.58/3.75 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X00) Xx0))
% 3.58/3.75 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X00) Xx0))
% 3.58/3.75 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X00) Xx0))
% 3.58/3.75 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X00) Xx0)))
% 3.58/3.75 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X00) Xx0)
% 3.58/3.75 Found ((and_rect0 ((cK X00) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X00) Xx0)
% 3.58/3.75 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X00) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X00) Xx0)
% 3.58/3.75 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X00) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X00) Xx0)
% 3.58/3.75 Found x6:(X00 Xx1)
% 3.58/3.75 Instantiate: X0:=X00:(a->Prop)
% 3.58/3.75 Found (fun (x6:(X00 Xx1))=> x6) as proof of (X0 Xx1)
% 3.58/3.75 Found (fun (Xx1:a) (x6:(X00 Xx1))=> x6) as proof of ((X00 Xx1)->(X0 Xx1))
% 3.58/3.75 Found (fun (Xx1:a) (x6:(X00 Xx1))=> x6) as proof of (forall (Xx:a), ((X00 Xx)->(X0 Xx)))
% 3.58/3.75 Found ((x310 (fun (Xx1:a) (x6:(X00 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X00) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X0) Xx0)
% 3.58/3.75 Found (((x31 X0) (fun (Xx1:a) (x6:(X00 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X00) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X0) Xx0)
% 3.58/3.75 Found ((((x3 x4) X0) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X0) Xx0)
% 3.58/3.75 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> ((((x3 x4) X0) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))))) as proof of ((cK X0) Xx0)
% 3.58/3.75 Found x8:(X00 Xx1)
% 3.58/3.75 Found x8 as proof of (X0 Xx1)
% 3.58/3.75 Found (fun (x8:(X00 Xx1))=> x8) as proof of (X0 Xx1)
% 3.58/3.75 Found (fun (Xx1:a) (x8:(X00 Xx1))=> x8) as proof of ((X00 Xx1)->(X0 Xx1))
% 3.58/3.75 Found (fun (Xx1:a) (x8:(X00 Xx1))=> x8) as proof of (forall (Xx:a), ((X00 Xx)->(X0 Xx)))
% 3.86/4.04 Found x500:=(x50 x6):((cK x3) Xx0)
% 3.86/4.04 Found (x50 x6) as proof of ((cK X00) Xx0)
% 3.86/4.04 Found ((x5 Xx0) x6) as proof of ((cK X00) Xx0)
% 3.86/4.04 Found ((x5 Xx0) x6) as proof of ((cK X00) Xx0)
% 3.86/4.04 Found ((x5 Xx0) x6) as proof of ((cK X00) Xx0)
% 3.86/4.04 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 3.86/4.04 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X00) Xx0))
% 3.86/4.04 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X00) Xx0))
% 3.86/4.04 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X00) Xx0))
% 3.86/4.04 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X00) Xx0)))
% 3.86/4.04 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X00) Xx0)
% 3.86/4.04 Found ((and_rect0 ((cK X00) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X00) Xx0)
% 3.86/4.04 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X00) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X00) Xx0)
% 3.86/4.04 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X00) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X00) Xx0)
% 3.86/4.04 Found x4:(X00 Xx1)
% 3.86/4.04 Instantiate: X00:=(cK x5):(a->Prop)
% 3.86/4.04 Found x4 as proof of (X0 Xx1)
% 3.86/4.04 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X0 Xx1)
% 3.86/4.04 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X0 Xx1))
% 3.86/4.04 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X0 Xx1)))
% 3.86/4.04 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X0 Xx1)
% 3.86/4.04 Found ((and_rect0 (X0 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X0 Xx1)
% 3.86/4.04 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X0 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X0 Xx1)
% 3.86/4.04 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X0 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X0 Xx1)
% 3.86/4.04 Found x4:(X00 Xx1)
% 3.86/4.04 Found x4 as proof of (X0 Xx1)
% 3.86/4.04 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X0 Xx1)
% 3.86/4.04 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X0 Xx1))
% 3.86/4.04 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X0 Xx1)))
% 3.86/4.04 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X0 Xx1)
% 3.86/4.04 Found ((and_rect0 (X0 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X0 Xx1)
% 3.86/4.04 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X0 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X0 Xx1)
% 3.86/4.04 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X0 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X0 Xx1)
% 6.08/6.28 Found x4:(X01 Xx1)
% 6.08/6.28 Found x4 as proof of (X00 Xx1)
% 6.08/6.28 Found (fun (x4:(X01 Xx1))=> x4) as proof of (X00 Xx1)
% 6.08/6.28 Found (fun (Xx1:a) (x4:(X01 Xx1))=> x4) as proof of ((X01 Xx1)->(X00 Xx1))
% 6.08/6.28 Found (fun (Xx1:a) (x4:(X01 Xx1))=> x4) as proof of (forall (Xx:a), ((X01 Xx)->(X00 Xx)))
% 6.08/6.28 Found x6:(X01 Xx1)
% 6.08/6.28 Found x6 as proof of (X00 Xx1)
% 6.08/6.28 Found (fun (x6:(X01 Xx1))=> x6) as proof of (X00 Xx1)
% 6.08/6.28 Found (fun (Xx1:a) (x6:(X01 Xx1))=> x6) as proof of ((X01 Xx1)->(X00 Xx1))
% 6.08/6.28 Found (fun (Xx1:a) (x6:(X01 Xx1))=> x6) as proof of (forall (Xx:a), ((X01 Xx)->(X00 Xx)))
% 6.08/6.28 Found x6:(X01 Xx1)
% 6.08/6.28 Found x6 as proof of (X00 Xx1)
% 6.08/6.28 Found (fun (x6:(X01 Xx1))=> x6) as proof of (X00 Xx1)
% 6.08/6.28 Found (fun (Xx1:a) (x6:(X01 Xx1))=> x6) as proof of ((X01 Xx1)->(X00 Xx1))
% 6.08/6.28 Found (fun (Xx1:a) (x6:(X01 Xx1))=> x6) as proof of (forall (Xx:a), ((X01 Xx)->(X00 Xx)))
% 6.08/6.28 Found x6:(X01 Xx1)
% 6.08/6.28 Found x6 as proof of (X00 Xx1)
% 6.08/6.28 Found (fun (x6:(X01 Xx1))=> x6) as proof of (X00 Xx1)
% 6.08/6.28 Found (fun (Xx1:a) (x6:(X01 Xx1))=> x6) as proof of ((X01 Xx1)->(X00 Xx1))
% 6.08/6.28 Found (fun (Xx1:a) (x6:(X01 Xx1))=> x6) as proof of (forall (Xx:a), ((X01 Xx)->(X00 Xx)))
% 6.08/6.28 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 6.08/6.28 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X01) Xx0))
% 6.08/6.28 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X01) Xx0))
% 6.08/6.28 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X01) Xx0))
% 6.08/6.28 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X01) Xx0)))
% 6.08/6.28 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X01) Xx0)
% 6.08/6.28 Found ((and_rect0 ((cK X01) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X01) Xx0)
% 6.08/6.28 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X01) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X01) Xx0)
% 6.08/6.28 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X01) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X01) Xx0)
% 6.08/6.28 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 6.08/6.28 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X01) Xx0))
% 6.08/6.28 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X01) Xx0))
% 6.08/6.28 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X01) Xx0))
% 6.08/6.28 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X01) Xx0)))
% 6.08/6.28 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X01) Xx0)
% 6.08/6.28 Found ((and_rect0 ((cK X01) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X01) Xx0)
% 6.08/6.28 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X01) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X01) Xx0)
% 6.08/6.28 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X01) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X01) Xx0)
% 6.08/6.28 Found x60:=(x6 Xx0):((x3 Xx0)->((cK x3) Xx0))
% 6.08/6.28 Found (x6 Xx0) as proof of ((x3 Xx0)->((cK X01) Xx0))
% 6.08/6.28 Found (x6 Xx0) as proof of ((x3 Xx0)->((cK X01) Xx0))
% 6.08/6.28 Found (fun (x6:(forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1))))=> (x6 Xx0)) as proof of ((x3 Xx0)->((cK X01) Xx0))
% 6.08/6.28 Found (fun (x6:(forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1)))->((x3 Xx0)->((cK X01) Xx0)))
% 6.08/6.28 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1))))=> (x6 Xx0))) as proof of ((cK X01) Xx0)
% 6.64/6.81 Found ((and_rect0 ((cK X01) Xx0)) (fun (x6:(forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1))))=> (x6 Xx0))) as proof of ((cK X01) Xx0)
% 6.64/6.81 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1)))->((x3 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1)))) (x3 Xx0)) P) x6) x4)) ((cK X01) Xx0)) (fun (x6:(forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1))))=> (x6 Xx0))) as proof of ((cK X01) Xx0)
% 6.64/6.81 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1)))->((x3 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1)))) (x3 Xx0)) P) x6) x4)) ((cK X01) Xx0)) (fun (x6:(forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1))))=> (x6 Xx0))) as proof of ((cK X01) Xx0)
% 6.64/6.81 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 6.64/6.81 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X01) Xx0))
% 6.64/6.81 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X01) Xx0))
% 6.64/6.81 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X01) Xx0))
% 6.64/6.81 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X01) Xx0)))
% 6.64/6.81 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X01) Xx0)
% 6.64/6.81 Found ((and_rect0 ((cK X01) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X01) Xx0)
% 6.64/6.81 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X01) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X01) Xx0)
% 6.64/6.81 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X01) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X01) Xx0)
% 6.64/6.81 Found x8:(X01 Xx1)
% 6.64/6.81 Found x8 as proof of (X00 Xx1)
% 6.64/6.81 Found (fun (x8:(X01 Xx1))=> x8) as proof of (X00 Xx1)
% 6.64/6.81 Found (fun (Xx1:a) (x8:(X01 Xx1))=> x8) as proof of ((X01 Xx1)->(X00 Xx1))
% 6.64/6.81 Found (fun (Xx1:a) (x8:(X01 Xx1))=> x8) as proof of (forall (Xx:a), ((X01 Xx)->(X00 Xx)))
% 6.64/6.81 Found x600:=(x60 x7):((cK x4) Xx0)
% 6.64/6.81 Found (x60 x7) as proof of ((cK X01) Xx0)
% 6.64/6.81 Found ((x6 Xx0) x7) as proof of ((cK X01) Xx0)
% 6.64/6.81 Found ((x6 Xx0) x7) as proof of ((cK X01) Xx0)
% 6.64/6.81 Found ((x6 Xx0) x7) as proof of ((cK X01) Xx0)
% 6.64/6.81 Found x8:(X01 Xx1)
% 6.64/6.81 Found x8 as proof of (X00 Xx1)
% 6.64/6.81 Found (fun (x8:(X01 Xx1))=> x8) as proof of (X00 Xx1)
% 6.64/6.81 Found (fun (Xx1:a) (x8:(X01 Xx1))=> x8) as proof of ((X01 Xx1)->(X00 Xx1))
% 6.64/6.81 Found (fun (Xx1:a) (x8:(X01 Xx1))=> x8) as proof of (forall (Xx:a), ((X01 Xx)->(X00 Xx)))
% 6.64/6.81 Found x600:=(x60 x7):((cK x3) Xx0)
% 6.64/6.81 Found (x60 x7) as proof of ((cK X01) Xx0)
% 6.64/6.81 Found ((x6 Xx0) x7) as proof of ((cK X01) Xx0)
% 6.64/6.81 Found ((x6 Xx0) x7) as proof of ((cK X01) Xx0)
% 6.64/6.81 Found ((x6 Xx0) x7) as proof of ((cK X01) Xx0)
% 6.64/6.81 Found x8:(X01 Xx1)
% 6.64/6.81 Found x8 as proof of (X00 Xx1)
% 6.64/6.81 Found (fun (x8:(X01 Xx1))=> x8) as proof of (X00 Xx1)
% 6.64/6.81 Found (fun (Xx1:a) (x8:(X01 Xx1))=> x8) as proof of ((X01 Xx1)->(X00 Xx1))
% 6.64/6.81 Found (fun (Xx1:a) (x8:(X01 Xx1))=> x8) as proof of (forall (Xx:a), ((X01 Xx)->(X00 Xx)))
% 6.64/6.81 Found x600:=(x60 x7):((cK x4) Xx0)
% 6.64/6.81 Found (x60 x7) as proof of ((cK X01) Xx0)
% 6.64/6.81 Found ((x6 Xx0) x7) as proof of ((cK X01) Xx0)
% 6.64/6.81 Found ((x6 Xx0) x7) as proof of ((cK X01) Xx0)
% 6.64/6.81 Found ((x6 Xx0) x7) as proof of ((cK X01) Xx0)
% 6.64/6.81 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 6.64/6.81 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X01) Xx0))
% 6.64/6.81 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X01) Xx0))
% 6.64/6.81 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X01) Xx0))
% 6.64/6.81 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X01) Xx0)))
% 6.64/6.81 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X01) Xx0)
% 6.64/6.81 Found ((and_rect0 ((cK X01) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X01) Xx0)
% 7.07/7.25 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X01) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X01) Xx0)
% 7.07/7.25 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X01) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X01) Xx0)
% 7.07/7.25 Found x6:(X01 Xx1)
% 7.07/7.25 Instantiate: X00:=X01:(a->Prop)
% 7.07/7.25 Found (fun (x6:(X01 Xx1))=> x6) as proof of (X00 Xx1)
% 7.07/7.25 Found (fun (Xx1:a) (x6:(X01 Xx1))=> x6) as proof of ((X01 Xx1)->(X00 Xx1))
% 7.07/7.25 Found (fun (Xx1:a) (x6:(X01 Xx1))=> x6) as proof of (forall (Xx:a), ((X01 Xx)->(X00 Xx)))
% 7.07/7.25 Found ((x320 (fun (Xx1:a) (x6:(X01 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X01) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X00) Xx0)
% 7.07/7.25 Found (((x32 X00) (fun (Xx1:a) (x6:(X01 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X01) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X00) Xx0)
% 7.07/7.25 Found ((((x3 x4) X00) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X00) Xx0)
% 7.07/7.25 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> ((((x3 x4) X00) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))))) as proof of ((cK X00) Xx0)
% 7.07/7.25 Found x8:(X01 Xx1)
% 7.07/7.25 Found x8 as proof of (X00 Xx1)
% 7.07/7.25 Found (fun (x8:(X01 Xx1))=> x8) as proof of (X00 Xx1)
% 7.07/7.25 Found (fun (Xx1:a) (x8:(X01 Xx1))=> x8) as proof of ((X01 Xx1)->(X00 Xx1))
% 7.07/7.25 Found (fun (Xx1:a) (x8:(X01 Xx1))=> x8) as proof of (forall (Xx:a), ((X01 Xx)->(X00 Xx)))
% 7.07/7.25 Found x600:=(x60 x7):((cK x3) Xx0)
% 7.07/7.25 Found (x60 x7) as proof of ((cK X01) Xx0)
% 7.07/7.25 Found ((x6 Xx0) x7) as proof of ((cK X01) Xx0)
% 7.07/7.25 Found ((x6 Xx0) x7) as proof of ((cK X01) Xx0)
% 7.07/7.25 Found ((x6 Xx0) x7) as proof of ((cK X01) Xx0)
% 7.07/7.25 Found x8:(X01 Xx1)
% 7.07/7.25 Found x8 as proof of (X00 Xx1)
% 7.07/7.25 Found (fun (x8:(X01 Xx1))=> x8) as proof of (X00 Xx1)
% 7.07/7.25 Found (fun (Xx1:a) (x8:(X01 Xx1))=> x8) as proof of ((X01 Xx1)->(X00 Xx1))
% 7.07/7.25 Found (fun (Xx1:a) (x8:(X01 Xx1))=> x8) as proof of (forall (Xx:a), ((X01 Xx)->(X00 Xx)))
% 7.07/7.25 Found x600:=(x60 x7):((cK x4) Xx0)
% 7.07/7.25 Found (x60 x7) as proof of ((cK X01) Xx0)
% 7.07/7.25 Found ((x6 Xx0) x7) as proof of ((cK X01) Xx0)
% 7.07/7.25 Found ((x6 Xx0) x7) as proof of ((cK X01) Xx0)
% 7.07/7.25 Found ((x6 Xx0) x7) as proof of ((cK X01) Xx0)
% 7.07/7.25 Found x8:(X01 Xx1)
% 7.07/7.25 Found x8 as proof of (X00 Xx1)
% 7.07/7.25 Found (fun (x8:(X01 Xx1))=> x8) as proof of (X00 Xx1)
% 7.07/7.25 Found (fun (Xx1:a) (x8:(X01 Xx1))=> x8) as proof of ((X01 Xx1)->(X00 Xx1))
% 7.07/7.25 Found (fun (Xx1:a) (x8:(X01 Xx1))=> x8) as proof of (forall (Xx:a), ((X01 Xx)->(X00 Xx)))
% 7.07/7.25 Found x500:=(x50 x6):((cK x3) Xx0)
% 7.07/7.25 Found (x50 x6) as proof of ((cK X01) Xx0)
% 7.07/7.25 Found ((x5 Xx0) x6) as proof of ((cK X01) Xx0)
% 7.07/7.25 Found ((x5 Xx0) x6) as proof of ((cK X01) Xx0)
% 7.07/7.25 Found ((x5 Xx0) x6) as proof of ((cK X01) Xx0)
% 7.07/7.25 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 7.07/7.25 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X01) Xx0))
% 7.07/7.25 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X01) Xx0))
% 7.07/7.25 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X01) Xx0))
% 7.07/7.25 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X01) Xx0)))
% 7.40/7.63 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X01) Xx0)
% 7.40/7.63 Found ((and_rect0 ((cK X01) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X01) Xx0)
% 7.40/7.63 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X01) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X01) Xx0)
% 7.40/7.63 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X01) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X01) Xx0)
% 7.40/7.63 Found x4:(X01 Xx1)
% 7.40/7.63 Instantiate: X01:=(cK x5):(a->Prop)
% 7.40/7.63 Found x4 as proof of (X00 Xx1)
% 7.40/7.63 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X00 Xx1)
% 7.40/7.63 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X00 Xx1))
% 7.40/7.63 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X00 Xx1)))
% 7.40/7.63 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X00 Xx1)
% 7.40/7.63 Found ((and_rect0 (X00 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X00 Xx1)
% 7.40/7.63 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X00 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X00 Xx1)
% 7.40/7.63 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X00 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X00 Xx1)
% 7.40/7.63 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 7.40/7.63 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X01) Xx0))
% 7.40/7.63 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X01) Xx0))
% 7.40/7.63 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X01) Xx0))
% 7.40/7.63 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X01) Xx0)))
% 7.40/7.63 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X01) Xx0)
% 7.40/7.63 Found ((and_rect0 ((cK X01) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X01) Xx0)
% 7.40/7.63 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X01) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X01) Xx0)
% 7.40/7.63 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X01) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X01) Xx0)
% 7.40/7.63 Found x6:(X01 Xx1)
% 7.40/7.63 Instantiate: X00:=X01:(a->Prop)
% 7.40/7.63 Found (fun (x6:(X01 Xx1))=> x6) as proof of (X00 Xx1)
% 7.40/7.63 Found (fun (Xx1:a) (x6:(X01 Xx1))=> x6) as proof of ((X01 Xx1)->(X00 Xx1))
% 7.40/7.63 Found (fun (Xx1:a) (x6:(X01 Xx1))=> x6) as proof of (forall (Xx:a), ((X01 Xx)->(X00 Xx)))
% 7.40/7.63 Found ((x320 (fun (Xx1:a) (x6:(X01 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X01) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X00) Xx0)
% 7.40/7.63 Found (((x32 X00) (fun (Xx1:a) (x6:(X01 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X01) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X00) Xx0)
% 7.71/7.95 Found ((((x3 x4) X00) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X00) Xx0)
% 7.71/7.95 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> ((((x3 x4) X00) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))))) as proof of ((cK X00) Xx0)
% 7.71/7.95 Found x4:(X01 Xx1)
% 7.71/7.95 Found x4 as proof of (X00 Xx1)
% 7.71/7.95 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X00 Xx1)
% 7.71/7.95 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X00 Xx1))
% 7.71/7.95 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X00 Xx1)))
% 7.71/7.95 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X00 Xx1)
% 7.71/7.95 Found ((and_rect0 (X00 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X00 Xx1)
% 7.71/7.95 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X00 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X00 Xx1)
% 7.71/7.95 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X00 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X00 Xx1)
% 7.71/7.95 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 7.71/7.95 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X01) Xx0))
% 7.71/7.95 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X01) Xx0))
% 7.71/7.95 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X01) Xx0))
% 7.71/7.95 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X01) Xx0)))
% 7.71/7.95 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X01) Xx0)
% 7.71/7.95 Found ((and_rect0 ((cK X01) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X01) Xx0)
% 7.71/7.95 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X01) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X01) Xx0)
% 7.71/7.95 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X01) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X01) Xx0)
% 7.71/7.95 Found x4:(X01 Xx1)
% 7.71/7.95 Instantiate: X01:=(cK x5):(a->Prop)
% 7.71/7.95 Found x4 as proof of (X00 Xx1)
% 7.71/7.95 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X00 Xx1)
% 7.71/7.95 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X00 Xx1))
% 7.71/7.95 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X00 Xx1)))
% 7.71/7.95 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X00 Xx1)
% 10.21/10.39 Found ((and_rect0 (X00 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X00 Xx1)
% 10.21/10.39 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X00 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X00 Xx1)
% 10.21/10.39 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X00 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X00 Xx1)
% 10.21/10.39 Found x4:(X01 Xx1)
% 10.21/10.39 Found x4 as proof of (X00 Xx1)
% 10.21/10.39 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X00 Xx1)
% 10.21/10.39 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X00 Xx1))
% 10.21/10.39 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X00 Xx1)))
% 10.21/10.39 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X00 Xx1)
% 10.21/10.39 Found ((and_rect0 (X00 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X00 Xx1)
% 10.21/10.39 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X00 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X00 Xx1)
% 10.21/10.39 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X00 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X00 Xx1)
% 10.21/10.39 Found x4:(X02 Xx1)
% 10.21/10.39 Found x4 as proof of (X01 Xx1)
% 10.21/10.39 Found (fun (x4:(X02 Xx1))=> x4) as proof of (X01 Xx1)
% 10.21/10.39 Found (fun (Xx1:a) (x4:(X02 Xx1))=> x4) as proof of ((X02 Xx1)->(X01 Xx1))
% 10.21/10.39 Found (fun (Xx1:a) (x4:(X02 Xx1))=> x4) as proof of (forall (Xx:a), ((X02 Xx)->(X01 Xx)))
% 10.21/10.39 Found x6:(X02 Xx1)
% 10.21/10.39 Found x6 as proof of (X01 Xx1)
% 10.21/10.39 Found (fun (x6:(X02 Xx1))=> x6) as proof of (X01 Xx1)
% 10.21/10.39 Found (fun (Xx1:a) (x6:(X02 Xx1))=> x6) as proof of ((X02 Xx1)->(X01 Xx1))
% 10.21/10.39 Found (fun (Xx1:a) (x6:(X02 Xx1))=> x6) as proof of (forall (Xx:a), ((X02 Xx)->(X01 Xx)))
% 10.21/10.39 Found x6:(X02 Xx1)
% 10.21/10.39 Found x6 as proof of (X01 Xx1)
% 10.21/10.39 Found (fun (x6:(X02 Xx1))=> x6) as proof of (X01 Xx1)
% 10.21/10.39 Found (fun (Xx1:a) (x6:(X02 Xx1))=> x6) as proof of ((X02 Xx1)->(X01 Xx1))
% 10.21/10.39 Found (fun (Xx1:a) (x6:(X02 Xx1))=> x6) as proof of (forall (Xx:a), ((X02 Xx)->(X01 Xx)))
% 10.21/10.39 Found x6:(X02 Xx1)
% 10.21/10.39 Found x6 as proof of (X01 Xx1)
% 10.21/10.39 Found (fun (x6:(X02 Xx1))=> x6) as proof of (X01 Xx1)
% 10.21/10.39 Found (fun (Xx1:a) (x6:(X02 Xx1))=> x6) as proof of ((X02 Xx1)->(X01 Xx1))
% 10.21/10.39 Found (fun (Xx1:a) (x6:(X02 Xx1))=> x6) as proof of (forall (Xx:a), ((X02 Xx)->(X01 Xx)))
% 10.21/10.39 Found x6:(X02 Xx1)
% 10.21/10.39 Found x6 as proof of (X01 Xx1)
% 10.21/10.39 Found (fun (x6:(X02 Xx1))=> x6) as proof of (X01 Xx1)
% 10.21/10.39 Found (fun (Xx1:a) (x6:(X02 Xx1))=> x6) as proof of ((X02 Xx1)->(X01 Xx1))
% 10.21/10.39 Found (fun (Xx1:a) (x6:(X02 Xx1))=> x6) as proof of (forall (Xx:a), ((X02 Xx)->(X01 Xx)))
% 10.21/10.39 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 10.21/10.39 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X02) Xx0))
% 10.21/10.39 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X02) Xx0))
% 10.21/10.39 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X02) Xx0))
% 10.21/10.39 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X02) Xx0)))
% 10.21/10.39 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X02) Xx0)
% 10.21/10.39 Found ((and_rect0 ((cK X02) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X02) Xx0)
% 11.34/11.52 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X02) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X02) Xx0)
% 11.34/11.52 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X02) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X02) Xx0)
% 11.34/11.52 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 11.34/11.52 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X02) Xx0))
% 11.34/11.52 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X02) Xx0))
% 11.34/11.52 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X02) Xx0))
% 11.34/11.52 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X02) Xx0)))
% 11.34/11.52 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X02) Xx0)
% 11.34/11.52 Found ((and_rect0 ((cK X02) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X02) Xx0)
% 11.34/11.52 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X02) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X02) Xx0)
% 11.34/11.52 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X02) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X02) Xx0)
% 11.34/11.52 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 11.34/11.52 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X02) Xx0))
% 11.34/11.52 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X02) Xx0))
% 11.34/11.52 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X02) Xx0))
% 11.34/11.52 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X02) Xx0)))
% 11.34/11.52 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X02) Xx0)
% 11.34/11.52 Found ((and_rect0 ((cK X02) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X02) Xx0)
% 11.34/11.52 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X02) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X02) Xx0)
% 11.34/11.52 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X02) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X02) Xx0)
% 11.34/11.52 Found x8:(X02 Xx1)
% 11.34/11.52 Found x8 as proof of (X01 Xx1)
% 11.34/11.52 Found (fun (x8:(X02 Xx1))=> x8) as proof of (X01 Xx1)
% 11.34/11.52 Found (fun (Xx1:a) (x8:(X02 Xx1))=> x8) as proof of ((X02 Xx1)->(X01 Xx1))
% 11.34/11.52 Found (fun (Xx1:a) (x8:(X02 Xx1))=> x8) as proof of (forall (Xx:a), ((X02 Xx)->(X01 Xx)))
% 11.34/11.52 Found x600:=(x60 x7):((cK x4) Xx0)
% 11.34/11.52 Found (x60 x7) as proof of ((cK X02) Xx0)
% 11.34/11.52 Found ((x6 Xx0) x7) as proof of ((cK X02) Xx0)
% 11.34/11.52 Found ((x6 Xx0) x7) as proof of ((cK X02) Xx0)
% 11.34/11.52 Found ((x6 Xx0) x7) as proof of ((cK X02) Xx0)
% 11.34/11.52 Found x60:=(x6 Xx0):((x3 Xx0)->((cK x3) Xx0))
% 11.34/11.52 Found (x6 Xx0) as proof of ((x3 Xx0)->((cK X02) Xx0))
% 11.34/11.52 Found (x6 Xx0) as proof of ((x3 Xx0)->((cK X02) Xx0))
% 11.34/11.52 Found (fun (x6:(forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1))))=> (x6 Xx0)) as proof of ((x3 Xx0)->((cK X02) Xx0))
% 11.34/11.52 Found (fun (x6:(forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1)))->((x3 Xx0)->((cK X02) Xx0)))
% 11.34/11.52 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1))))=> (x6 Xx0))) as proof of ((cK X02) Xx0)
% 11.85/12.09 Found ((and_rect0 ((cK X02) Xx0)) (fun (x6:(forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1))))=> (x6 Xx0))) as proof of ((cK X02) Xx0)
% 11.85/12.09 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1)))->((x3 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1)))) (x3 Xx0)) P) x6) x4)) ((cK X02) Xx0)) (fun (x6:(forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1))))=> (x6 Xx0))) as proof of ((cK X02) Xx0)
% 11.85/12.09 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1)))->((x3 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1)))) (x3 Xx0)) P) x6) x4)) ((cK X02) Xx0)) (fun (x6:(forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1))))=> (x6 Xx0))) as proof of ((cK X02) Xx0)
% 11.85/12.09 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 11.85/12.09 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X02) Xx0))
% 11.85/12.09 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X02) Xx0))
% 11.85/12.09 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X02) Xx0))
% 11.85/12.09 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X02) Xx0)))
% 11.85/12.09 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X02) Xx0)
% 11.85/12.09 Found ((and_rect0 ((cK X02) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X02) Xx0)
% 11.85/12.09 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X02) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X02) Xx0)
% 11.85/12.09 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X02) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X02) Xx0)
% 11.85/12.09 Found x8:(X02 Xx1)
% 11.85/12.09 Found x8 as proof of (X01 Xx1)
% 11.85/12.09 Found (fun (x8:(X02 Xx1))=> x8) as proof of (X01 Xx1)
% 11.85/12.09 Found (fun (Xx1:a) (x8:(X02 Xx1))=> x8) as proof of ((X02 Xx1)->(X01 Xx1))
% 11.85/12.09 Found (fun (Xx1:a) (x8:(X02 Xx1))=> x8) as proof of (forall (Xx:a), ((X02 Xx)->(X01 Xx)))
% 11.85/12.09 Found x600:=(x60 x7):((cK x4) Xx0)
% 11.85/12.09 Found (x60 x7) as proof of ((cK X02) Xx0)
% 11.85/12.09 Found ((x6 Xx0) x7) as proof of ((cK X02) Xx0)
% 11.85/12.09 Found ((x6 Xx0) x7) as proof of ((cK X02) Xx0)
% 11.85/12.09 Found ((x6 Xx0) x7) as proof of ((cK X02) Xx0)
% 11.85/12.09 Found x8:(X02 Xx1)
% 11.85/12.09 Found x8 as proof of (X01 Xx1)
% 11.85/12.09 Found (fun (x8:(X02 Xx1))=> x8) as proof of (X01 Xx1)
% 11.85/12.09 Found (fun (Xx1:a) (x8:(X02 Xx1))=> x8) as proof of ((X02 Xx1)->(X01 Xx1))
% 11.85/12.09 Found (fun (Xx1:a) (x8:(X02 Xx1))=> x8) as proof of (forall (Xx:a), ((X02 Xx)->(X01 Xx)))
% 11.85/12.09 Found x600:=(x60 x7):((cK x4) Xx0)
% 11.85/12.09 Found (x60 x7) as proof of ((cK X02) Xx0)
% 11.85/12.09 Found ((x6 Xx0) x7) as proof of ((cK X02) Xx0)
% 11.85/12.09 Found ((x6 Xx0) x7) as proof of ((cK X02) Xx0)
% 11.85/12.09 Found ((x6 Xx0) x7) as proof of ((cK X02) Xx0)
% 11.85/12.09 Found x8:(X02 Xx1)
% 11.85/12.09 Found x8 as proof of (X01 Xx1)
% 11.85/12.09 Found (fun (x8:(X02 Xx1))=> x8) as proof of (X01 Xx1)
% 11.85/12.09 Found (fun (Xx1:a) (x8:(X02 Xx1))=> x8) as proof of ((X02 Xx1)->(X01 Xx1))
% 11.85/12.09 Found (fun (Xx1:a) (x8:(X02 Xx1))=> x8) as proof of (forall (Xx:a), ((X02 Xx)->(X01 Xx)))
% 11.85/12.09 Found x600:=(x60 x7):((cK x3) Xx0)
% 11.85/12.09 Found (x60 x7) as proof of ((cK X02) Xx0)
% 11.85/12.09 Found ((x6 Xx0) x7) as proof of ((cK X02) Xx0)
% 11.85/12.09 Found ((x6 Xx0) x7) as proof of ((cK X02) Xx0)
% 11.85/12.09 Found ((x6 Xx0) x7) as proof of ((cK X02) Xx0)
% 11.85/12.09 Found x8:(X02 Xx1)
% 11.85/12.09 Found x8 as proof of (X01 Xx1)
% 11.85/12.09 Found (fun (x8:(X02 Xx1))=> x8) as proof of (X01 Xx1)
% 11.85/12.09 Found (fun (Xx1:a) (x8:(X02 Xx1))=> x8) as proof of ((X02 Xx1)->(X01 Xx1))
% 11.85/12.09 Found (fun (Xx1:a) (x8:(X02 Xx1))=> x8) as proof of (forall (Xx:a), ((X02 Xx)->(X01 Xx)))
% 11.85/12.09 Found x600:=(x60 x7):((cK x4) Xx0)
% 11.85/12.09 Found (x60 x7) as proof of ((cK X02) Xx0)
% 11.85/12.09 Found ((x6 Xx0) x7) as proof of ((cK X02) Xx0)
% 11.85/12.09 Found ((x6 Xx0) x7) as proof of ((cK X02) Xx0)
% 11.85/12.09 Found ((x6 Xx0) x7) as proof of ((cK X02) Xx0)
% 11.85/12.09 Found x8:(X02 Xx1)
% 11.85/12.09 Found x8 as proof of (X01 Xx1)
% 11.85/12.09 Found (fun (x8:(X02 Xx1))=> x8) as proof of (X01 Xx1)
% 11.85/12.09 Found (fun (Xx1:a) (x8:(X02 Xx1))=> x8) as proof of ((X02 Xx1)->(X01 Xx1))
% 12.13/12.32 Found (fun (Xx1:a) (x8:(X02 Xx1))=> x8) as proof of (forall (Xx:a), ((X02 Xx)->(X01 Xx)))
% 12.13/12.32 Found x600:=(x60 x7):((cK x3) Xx0)
% 12.13/12.32 Found (x60 x7) as proof of ((cK X02) Xx0)
% 12.13/12.32 Found ((x6 Xx0) x7) as proof of ((cK X02) Xx0)
% 12.13/12.32 Found ((x6 Xx0) x7) as proof of ((cK X02) Xx0)
% 12.13/12.32 Found ((x6 Xx0) x7) as proof of ((cK X02) Xx0)
% 12.13/12.32 Found x8:(X02 Xx1)
% 12.13/12.32 Found x8 as proof of (X01 Xx1)
% 12.13/12.32 Found (fun (x8:(X02 Xx1))=> x8) as proof of (X01 Xx1)
% 12.13/12.32 Found (fun (Xx1:a) (x8:(X02 Xx1))=> x8) as proof of ((X02 Xx1)->(X01 Xx1))
% 12.13/12.32 Found (fun (Xx1:a) (x8:(X02 Xx1))=> x8) as proof of (forall (Xx:a), ((X02 Xx)->(X01 Xx)))
% 12.13/12.32 Found x600:=(x60 x7):((cK x4) Xx0)
% 12.13/12.32 Found (x60 x7) as proof of ((cK X02) Xx0)
% 12.13/12.32 Found ((x6 Xx0) x7) as proof of ((cK X02) Xx0)
% 12.13/12.32 Found ((x6 Xx0) x7) as proof of ((cK X02) Xx0)
% 12.13/12.32 Found ((x6 Xx0) x7) as proof of ((cK X02) Xx0)
% 12.13/12.32 Found x8:(X02 Xx1)
% 12.13/12.32 Found x8 as proof of (X01 Xx1)
% 12.13/12.32 Found (fun (x8:(X02 Xx1))=> x8) as proof of (X01 Xx1)
% 12.13/12.32 Found (fun (Xx1:a) (x8:(X02 Xx1))=> x8) as proof of ((X02 Xx1)->(X01 Xx1))
% 12.13/12.32 Found (fun (Xx1:a) (x8:(X02 Xx1))=> x8) as proof of (forall (Xx:a), ((X02 Xx)->(X01 Xx)))
% 12.13/12.32 Found x500:=(x50 x6):((cK x3) Xx0)
% 12.13/12.32 Found (x50 x6) as proof of ((cK X02) Xx0)
% 12.13/12.32 Found ((x5 Xx0) x6) as proof of ((cK X02) Xx0)
% 12.13/12.32 Found ((x5 Xx0) x6) as proof of ((cK X02) Xx0)
% 12.13/12.32 Found ((x5 Xx0) x6) as proof of ((cK X02) Xx0)
% 12.13/12.32 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 12.13/12.32 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X02) Xx0))
% 12.13/12.32 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X02) Xx0))
% 12.13/12.32 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X02) Xx0))
% 12.13/12.32 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X02) Xx0)))
% 12.13/12.32 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X02) Xx0)
% 12.13/12.32 Found ((and_rect0 ((cK X02) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X02) Xx0)
% 12.13/12.32 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X02) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X02) Xx0)
% 12.13/12.32 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X02) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X02) Xx0)
% 12.13/12.32 Found x6:(X02 Xx1)
% 12.13/12.32 Instantiate: X01:=X02:(a->Prop)
% 12.13/12.32 Found (fun (x6:(X02 Xx1))=> x6) as proof of (X01 Xx1)
% 12.13/12.32 Found (fun (Xx1:a) (x6:(X02 Xx1))=> x6) as proof of ((X02 Xx1)->(X01 Xx1))
% 12.13/12.32 Found (fun (Xx1:a) (x6:(X02 Xx1))=> x6) as proof of (forall (Xx:a), ((X02 Xx)->(X01 Xx)))
% 12.13/12.32 Found ((x330 (fun (Xx1:a) (x6:(X02 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X02) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X01) Xx0)
% 12.13/12.32 Found (((x33 X01) (fun (Xx1:a) (x6:(X02 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X02) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X01) Xx0)
% 12.13/12.32 Found ((((x3 x4) X01) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X01) Xx0)
% 12.13/12.32 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> ((((x3 x4) X01) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))))) as proof of ((cK X01) Xx0)
% 13.12/13.29 Found x8:(X02 Xx1)
% 13.12/13.29 Found x8 as proof of (X01 Xx1)
% 13.12/13.29 Found (fun (x8:(X02 Xx1))=> x8) as proof of (X01 Xx1)
% 13.12/13.29 Found (fun (Xx1:a) (x8:(X02 Xx1))=> x8) as proof of ((X02 Xx1)->(X01 Xx1))
% 13.12/13.29 Found (fun (Xx1:a) (x8:(X02 Xx1))=> x8) as proof of (forall (Xx:a), ((X02 Xx)->(X01 Xx)))
% 13.12/13.29 Found x600:=(x60 x7):((cK x3) Xx0)
% 13.12/13.29 Found (x60 x7) as proof of ((cK X02) Xx0)
% 13.12/13.29 Found ((x6 Xx0) x7) as proof of ((cK X02) Xx0)
% 13.12/13.29 Found ((x6 Xx0) x7) as proof of ((cK X02) Xx0)
% 13.12/13.29 Found ((x6 Xx0) x7) as proof of ((cK X02) Xx0)
% 13.12/13.29 Found x8:(X02 Xx1)
% 13.12/13.29 Found x8 as proof of (X01 Xx1)
% 13.12/13.29 Found (fun (x8:(X02 Xx1))=> x8) as proof of (X01 Xx1)
% 13.12/13.29 Found (fun (Xx1:a) (x8:(X02 Xx1))=> x8) as proof of ((X02 Xx1)->(X01 Xx1))
% 13.12/13.29 Found (fun (Xx1:a) (x8:(X02 Xx1))=> x8) as proof of (forall (Xx:a), ((X02 Xx)->(X01 Xx)))
% 13.12/13.29 Found x600:=(x60 x7):((cK x4) Xx0)
% 13.12/13.29 Found (x60 x7) as proof of ((cK X02) Xx0)
% 13.12/13.29 Found ((x6 Xx0) x7) as proof of ((cK X02) Xx0)
% 13.12/13.29 Found ((x6 Xx0) x7) as proof of ((cK X02) Xx0)
% 13.12/13.29 Found ((x6 Xx0) x7) as proof of ((cK X02) Xx0)
% 13.12/13.29 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 13.12/13.29 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X02) Xx0))
% 13.12/13.29 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X02) Xx0))
% 13.12/13.29 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X02) Xx0))
% 13.12/13.29 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X02) Xx0)))
% 13.12/13.29 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X02) Xx0)
% 13.12/13.29 Found ((and_rect0 ((cK X02) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X02) Xx0)
% 13.12/13.29 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X02) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X02) Xx0)
% 13.12/13.29 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X02) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X02) Xx0)
% 13.12/13.29 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 13.12/13.29 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X02) Xx0))
% 13.12/13.29 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X02) Xx0))
% 13.12/13.29 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X02) Xx0))
% 13.12/13.29 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X02) Xx0)))
% 13.12/13.29 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X02) Xx0)
% 13.12/13.29 Found ((and_rect0 ((cK X02) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X02) Xx0)
% 13.12/13.29 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X02) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X02) Xx0)
% 13.12/13.29 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X02) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X02) Xx0)
% 13.12/13.29 Found x6:(X02 Xx1)
% 13.12/13.29 Instantiate: X01:=X02:(a->Prop)
% 13.12/13.29 Found (fun (x6:(X02 Xx1))=> x6) as proof of (X01 Xx1)
% 13.12/13.29 Found (fun (Xx1:a) (x6:(X02 Xx1))=> x6) as proof of ((X02 Xx1)->(X01 Xx1))
% 13.12/13.29 Found (fun (Xx1:a) (x6:(X02 Xx1))=> x6) as proof of (forall (Xx:a), ((X02 Xx)->(X01 Xx)))
% 13.12/13.29 Found ((x330 (fun (Xx1:a) (x6:(X02 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X02) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X01) Xx0)
% 13.44/13.62 Found (((x33 X01) (fun (Xx1:a) (x6:(X02 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X02) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X01) Xx0)
% 13.44/13.62 Found ((((x3 x4) X01) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X01) Xx0)
% 13.44/13.62 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> ((((x3 x4) X01) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))))) as proof of ((cK X01) Xx0)
% 13.44/13.62 Found x4:(X02 Xx1)
% 13.44/13.62 Instantiate: X02:=(cK x5):(a->Prop)
% 13.44/13.62 Found x4 as proof of (X01 Xx1)
% 13.44/13.62 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X01 Xx1)
% 13.44/13.62 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X01 Xx1))
% 13.44/13.62 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X01 Xx1)))
% 13.44/13.62 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X01 Xx1)
% 13.44/13.62 Found ((and_rect0 (X01 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X01 Xx1)
% 13.44/13.62 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X01 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X01 Xx1)
% 13.44/13.62 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X01 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X01 Xx1)
% 13.44/13.62 Found x4:(X02 Xx1)
% 13.44/13.62 Found x4 as proof of (X01 Xx1)
% 13.44/13.62 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X01 Xx1)
% 13.44/13.62 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X01 Xx1))
% 13.44/13.62 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X01 Xx1)))
% 13.44/13.62 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X01 Xx1)
% 13.44/13.62 Found ((and_rect0 (X01 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X01 Xx1)
% 13.44/13.62 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X01 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X01 Xx1)
% 13.44/13.62 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X01 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X01 Xx1)
% 13.44/13.62 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 13.44/13.62 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X02) Xx0))
% 13.44/13.62 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X02) Xx0))
% 13.44/13.62 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X02) Xx0))
% 13.44/13.62 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X02) Xx0)))
% 13.91/14.09 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X02) Xx0)
% 13.91/14.09 Found ((and_rect0 ((cK X02) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X02) Xx0)
% 13.91/14.09 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X02) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X02) Xx0)
% 13.91/14.09 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X02) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X02) Xx0)
% 13.91/14.09 Found x4:(X02 Xx1)
% 13.91/14.09 Instantiate: X02:=(cK x5):(a->Prop)
% 13.91/14.09 Found x4 as proof of (X01 Xx1)
% 13.91/14.09 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X01 Xx1)
% 13.91/14.09 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X01 Xx1))
% 13.91/14.09 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X01 Xx1)))
% 13.91/14.09 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X01 Xx1)
% 13.91/14.09 Found ((and_rect0 (X01 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X01 Xx1)
% 13.91/14.09 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X01 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X01 Xx1)
% 13.91/14.09 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X01 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X01 Xx1)
% 13.91/14.09 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 13.91/14.09 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X02) Xx0))
% 13.91/14.09 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X02) Xx0))
% 13.91/14.09 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X02) Xx0))
% 13.91/14.09 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X02) Xx0)))
% 13.91/14.09 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X02) Xx0)
% 13.91/14.09 Found ((and_rect0 ((cK X02) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X02) Xx0)
% 13.91/14.09 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X02) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X02) Xx0)
% 13.91/14.09 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X02) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X02) Xx0)
% 13.91/14.09 Found x6:(X02 Xx1)
% 13.91/14.09 Instantiate: X01:=X02:(a->Prop)
% 13.91/14.09 Found (fun (x6:(X02 Xx1))=> x6) as proof of (X01 Xx1)
% 13.91/14.09 Found (fun (Xx1:a) (x6:(X02 Xx1))=> x6) as proof of ((X02 Xx1)->(X01 Xx1))
% 13.91/14.09 Found (fun (Xx1:a) (x6:(X02 Xx1))=> x6) as proof of (forall (Xx:a), ((X02 Xx)->(X01 Xx)))
% 13.91/14.09 Found ((x330 (fun (Xx1:a) (x6:(X02 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X02) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X01) Xx0)
% 14.09/14.30 Found (((x33 X01) (fun (Xx1:a) (x6:(X02 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X02) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X01) Xx0)
% 14.09/14.30 Found ((((x3 x4) X01) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X01) Xx0)
% 14.09/14.30 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> ((((x3 x4) X01) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))))) as proof of ((cK X01) Xx0)
% 14.09/14.30 Found x4:(X02 Xx1)
% 14.09/14.30 Found x4 as proof of (X01 Xx1)
% 14.09/14.30 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X01 Xx1)
% 14.09/14.30 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X01 Xx1))
% 14.09/14.30 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X01 Xx1)))
% 14.09/14.30 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X01 Xx1)
% 14.09/14.30 Found ((and_rect0 (X01 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X01 Xx1)
% 14.09/14.30 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X01 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X01 Xx1)
% 14.09/14.30 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X01 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X01 Xx1)
% 14.09/14.30 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 14.09/14.30 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X02) Xx0))
% 14.09/14.30 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X02) Xx0))
% 14.09/14.30 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X02) Xx0))
% 14.09/14.30 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X02) Xx0)))
% 14.09/14.30 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X02) Xx0)
% 14.09/14.30 Found ((and_rect0 ((cK X02) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X02) Xx0)
% 14.09/14.30 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X02) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X02) Xx0)
% 14.09/14.30 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X02) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X02) Xx0)
% 14.09/14.30 Found x4:(X02 Xx1)
% 14.09/14.30 Instantiate: X02:=(cK x5):(a->Prop)
% 14.09/14.30 Found x4 as proof of (X01 Xx1)
% 14.09/14.30 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X01 Xx1)
% 14.09/14.30 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X01 Xx1))
% 14.09/14.30 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X01 Xx1)))
% 14.09/14.30 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X01 Xx1)
% 17.79/18.02 Found ((and_rect0 (X01 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X01 Xx1)
% 17.79/18.02 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X01 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X01 Xx1)
% 17.79/18.02 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X01 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X01 Xx1)
% 17.79/18.02 Found x4:(X02 Xx1)
% 17.79/18.02 Found x4 as proof of (X01 Xx1)
% 17.79/18.02 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X01 Xx1)
% 17.79/18.02 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X01 Xx1))
% 17.79/18.02 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X01 Xx1)))
% 17.79/18.02 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X01 Xx1)
% 17.79/18.02 Found ((and_rect0 (X01 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X01 Xx1)
% 17.79/18.02 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X01 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X01 Xx1)
% 17.79/18.02 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X01 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X01 Xx1)
% 17.79/18.02 Found x4:(X03 Xx1)
% 17.79/18.02 Found x4 as proof of (X02 Xx1)
% 17.79/18.02 Found (fun (x4:(X03 Xx1))=> x4) as proof of (X02 Xx1)
% 17.79/18.02 Found (fun (Xx1:a) (x4:(X03 Xx1))=> x4) as proof of ((X03 Xx1)->(X02 Xx1))
% 17.79/18.02 Found (fun (Xx1:a) (x4:(X03 Xx1))=> x4) as proof of (forall (Xx:a), ((X03 Xx)->(X02 Xx)))
% 17.79/18.02 Found x6:(X03 Xx1)
% 17.79/18.02 Found x6 as proof of (X02 Xx1)
% 17.79/18.02 Found (fun (x6:(X03 Xx1))=> x6) as proof of (X02 Xx1)
% 17.79/18.02 Found (fun (Xx1:a) (x6:(X03 Xx1))=> x6) as proof of ((X03 Xx1)->(X02 Xx1))
% 17.79/18.02 Found (fun (Xx1:a) (x6:(X03 Xx1))=> x6) as proof of (forall (Xx:a), ((X03 Xx)->(X02 Xx)))
% 17.79/18.02 Found x6:(X03 Xx1)
% 17.79/18.02 Found x6 as proof of (X02 Xx1)
% 17.79/18.02 Found (fun (x6:(X03 Xx1))=> x6) as proof of (X02 Xx1)
% 17.79/18.02 Found (fun (Xx1:a) (x6:(X03 Xx1))=> x6) as proof of ((X03 Xx1)->(X02 Xx1))
% 17.79/18.02 Found (fun (Xx1:a) (x6:(X03 Xx1))=> x6) as proof of (forall (Xx:a), ((X03 Xx)->(X02 Xx)))
% 17.79/18.02 Found x6:(X03 Xx1)
% 17.79/18.02 Found x6 as proof of (X02 Xx1)
% 17.79/18.02 Found (fun (x6:(X03 Xx1))=> x6) as proof of (X02 Xx1)
% 17.79/18.02 Found (fun (Xx1:a) (x6:(X03 Xx1))=> x6) as proof of ((X03 Xx1)->(X02 Xx1))
% 17.79/18.02 Found (fun (Xx1:a) (x6:(X03 Xx1))=> x6) as proof of (forall (Xx:a), ((X03 Xx)->(X02 Xx)))
% 17.79/18.02 Found x6:(X03 Xx1)
% 17.79/18.02 Found x6 as proof of (X02 Xx1)
% 17.79/18.02 Found (fun (x6:(X03 Xx1))=> x6) as proof of (X02 Xx1)
% 17.79/18.02 Found (fun (Xx1:a) (x6:(X03 Xx1))=> x6) as proof of ((X03 Xx1)->(X02 Xx1))
% 17.79/18.02 Found (fun (Xx1:a) (x6:(X03 Xx1))=> x6) as proof of (forall (Xx:a), ((X03 Xx)->(X02 Xx)))
% 17.79/18.02 Found x6:(X03 Xx1)
% 17.79/18.02 Found x6 as proof of (X02 Xx1)
% 17.79/18.02 Found (fun (x6:(X03 Xx1))=> x6) as proof of (X02 Xx1)
% 17.79/18.02 Found (fun (Xx1:a) (x6:(X03 Xx1))=> x6) as proof of ((X03 Xx1)->(X02 Xx1))
% 17.79/18.02 Found (fun (Xx1:a) (x6:(X03 Xx1))=> x6) as proof of (forall (Xx:a), ((X03 Xx)->(X02 Xx)))
% 17.79/18.02 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 17.79/18.02 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X03) Xx0))
% 17.79/18.02 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X03) Xx0))
% 17.79/18.02 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X03) Xx0))
% 17.79/18.02 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X03) Xx0)))
% 18.06/18.24 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X03) Xx0)
% 18.06/18.24 Found ((and_rect0 ((cK X03) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X03) Xx0)
% 18.06/18.24 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X03) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X03) Xx0)
% 18.06/18.24 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X03) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X03) Xx0)
% 18.06/18.24 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 18.06/18.24 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X03) Xx0))
% 18.06/18.24 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X03) Xx0))
% 18.06/18.24 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X03) Xx0))
% 18.06/18.24 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X03) Xx0)))
% 18.06/18.24 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X03) Xx0)
% 18.06/18.24 Found ((and_rect0 ((cK X03) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X03) Xx0)
% 18.06/18.24 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X03) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X03) Xx0)
% 18.06/18.24 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X03) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X03) Xx0)
% 18.06/18.24 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 18.06/18.24 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X03) Xx0))
% 18.06/18.24 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X03) Xx0))
% 18.06/18.24 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X03) Xx0))
% 18.06/18.24 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X03) Xx0)))
% 18.06/18.24 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X03) Xx0)
% 18.06/18.24 Found ((and_rect0 ((cK X03) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X03) Xx0)
% 18.06/18.24 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X03) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X03) Xx0)
% 18.06/18.24 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X03) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X03) Xx0)
% 18.06/18.24 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 18.06/18.24 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X03) Xx0))
% 18.06/18.24 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X03) Xx0))
% 18.06/18.24 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X03) Xx0))
% 18.06/18.24 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X03) Xx0)))
% 18.06/18.24 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X03) Xx0)
% 18.06/18.24 Found ((and_rect0 ((cK X03) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X03) Xx0)
% 18.06/18.24 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X03) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X03) Xx0)
% 19.50/19.70 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X03) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X03) Xx0)
% 19.50/19.70 Found x8:(X03 Xx1)
% 19.50/19.70 Found x8 as proof of (X02 Xx1)
% 19.50/19.70 Found (fun (x8:(X03 Xx1))=> x8) as proof of (X02 Xx1)
% 19.50/19.70 Found (fun (Xx1:a) (x8:(X03 Xx1))=> x8) as proof of ((X03 Xx1)->(X02 Xx1))
% 19.50/19.70 Found (fun (Xx1:a) (x8:(X03 Xx1))=> x8) as proof of (forall (Xx:a), ((X03 Xx)->(X02 Xx)))
% 19.50/19.70 Found x600:=(x60 x7):((cK x4) Xx0)
% 19.50/19.70 Found (x60 x7) as proof of ((cK X03) Xx0)
% 19.50/19.70 Found ((x6 Xx0) x7) as proof of ((cK X03) Xx0)
% 19.50/19.70 Found ((x6 Xx0) x7) as proof of ((cK X03) Xx0)
% 19.50/19.70 Found ((x6 Xx0) x7) as proof of ((cK X03) Xx0)
% 19.50/19.70 Found x60:=(x6 Xx0):((x3 Xx0)->((cK x3) Xx0))
% 19.50/19.70 Found (x6 Xx0) as proof of ((x3 Xx0)->((cK X03) Xx0))
% 19.50/19.70 Found (x6 Xx0) as proof of ((x3 Xx0)->((cK X03) Xx0))
% 19.50/19.70 Found (fun (x6:(forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1))))=> (x6 Xx0)) as proof of ((x3 Xx0)->((cK X03) Xx0))
% 19.50/19.70 Found (fun (x6:(forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1)))->((x3 Xx0)->((cK X03) Xx0)))
% 19.50/19.70 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1))))=> (x6 Xx0))) as proof of ((cK X03) Xx0)
% 19.50/19.70 Found ((and_rect0 ((cK X03) Xx0)) (fun (x6:(forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1))))=> (x6 Xx0))) as proof of ((cK X03) Xx0)
% 19.50/19.70 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1)))->((x3 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1)))) (x3 Xx0)) P) x6) x4)) ((cK X03) Xx0)) (fun (x6:(forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1))))=> (x6 Xx0))) as proof of ((cK X03) Xx0)
% 19.50/19.70 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1)))->((x3 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1)))) (x3 Xx0)) P) x6) x4)) ((cK X03) Xx0)) (fun (x6:(forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1))))=> (x6 Xx0))) as proof of ((cK X03) Xx0)
% 19.50/19.70 Found x8:(X03 Xx1)
% 19.50/19.70 Found x8 as proof of (X02 Xx1)
% 19.50/19.70 Found (fun (x8:(X03 Xx1))=> x8) as proof of (X02 Xx1)
% 19.50/19.70 Found (fun (Xx1:a) (x8:(X03 Xx1))=> x8) as proof of ((X03 Xx1)->(X02 Xx1))
% 19.50/19.70 Found (fun (Xx1:a) (x8:(X03 Xx1))=> x8) as proof of (forall (Xx:a), ((X03 Xx)->(X02 Xx)))
% 19.50/19.70 Found x600:=(x60 x7):((cK x4) Xx0)
% 19.50/19.70 Found (x60 x7) as proof of ((cK X03) Xx0)
% 19.50/19.70 Found ((x6 Xx0) x7) as proof of ((cK X03) Xx0)
% 19.50/19.70 Found ((x6 Xx0) x7) as proof of ((cK X03) Xx0)
% 19.50/19.70 Found ((x6 Xx0) x7) as proof of ((cK X03) Xx0)
% 19.50/19.70 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 19.50/19.70 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X03) Xx0))
% 19.50/19.70 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X03) Xx0))
% 19.50/19.70 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X03) Xx0))
% 19.50/19.70 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X03) Xx0)))
% 19.50/19.70 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X03) Xx0)
% 19.50/19.70 Found ((and_rect0 ((cK X03) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X03) Xx0)
% 19.50/19.70 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X03) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X03) Xx0)
% 19.50/19.70 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X03) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X03) Xx0)
% 19.50/19.70 Found x8:(X03 Xx1)
% 19.50/19.70 Found x8 as proof of (X02 Xx1)
% 19.50/19.70 Found (fun (x8:(X03 Xx1))=> x8) as proof of (X02 Xx1)
% 20.28/20.46 Found (fun (Xx1:a) (x8:(X03 Xx1))=> x8) as proof of ((X03 Xx1)->(X02 Xx1))
% 20.28/20.46 Found (fun (Xx1:a) (x8:(X03 Xx1))=> x8) as proof of (forall (Xx:a), ((X03 Xx)->(X02 Xx)))
% 20.28/20.46 Found x600:=(x60 x7):((cK x4) Xx0)
% 20.28/20.46 Found (x60 x7) as proof of ((cK X03) Xx0)
% 20.28/20.46 Found ((x6 Xx0) x7) as proof of ((cK X03) Xx0)
% 20.28/20.46 Found ((x6 Xx0) x7) as proof of ((cK X03) Xx0)
% 20.28/20.46 Found ((x6 Xx0) x7) as proof of ((cK X03) Xx0)
% 20.28/20.46 Found x8:(X03 Xx1)
% 20.28/20.46 Found x8 as proof of (X02 Xx1)
% 20.28/20.46 Found (fun (x8:(X03 Xx1))=> x8) as proof of (X02 Xx1)
% 20.28/20.46 Found (fun (Xx1:a) (x8:(X03 Xx1))=> x8) as proof of ((X03 Xx1)->(X02 Xx1))
% 20.28/20.46 Found (fun (Xx1:a) (x8:(X03 Xx1))=> x8) as proof of (forall (Xx:a), ((X03 Xx)->(X02 Xx)))
% 20.28/20.46 Found x600:=(x60 x7):((cK x3) Xx0)
% 20.28/20.46 Found (x60 x7) as proof of ((cK X03) Xx0)
% 20.28/20.46 Found ((x6 Xx0) x7) as proof of ((cK X03) Xx0)
% 20.28/20.46 Found ((x6 Xx0) x7) as proof of ((cK X03) Xx0)
% 20.28/20.46 Found ((x6 Xx0) x7) as proof of ((cK X03) Xx0)
% 20.28/20.46 Found x8:(X03 Xx1)
% 20.28/20.46 Found x8 as proof of (X02 Xx1)
% 20.28/20.46 Found (fun (x8:(X03 Xx1))=> x8) as proof of (X02 Xx1)
% 20.28/20.46 Found (fun (Xx1:a) (x8:(X03 Xx1))=> x8) as proof of ((X03 Xx1)->(X02 Xx1))
% 20.28/20.46 Found (fun (Xx1:a) (x8:(X03 Xx1))=> x8) as proof of (forall (Xx:a), ((X03 Xx)->(X02 Xx)))
% 20.28/20.46 Found x600:=(x60 x7):((cK x4) Xx0)
% 20.28/20.46 Found (x60 x7) as proof of ((cK X03) Xx0)
% 20.28/20.46 Found ((x6 Xx0) x7) as proof of ((cK X03) Xx0)
% 20.28/20.46 Found ((x6 Xx0) x7) as proof of ((cK X03) Xx0)
% 20.28/20.46 Found ((x6 Xx0) x7) as proof of ((cK X03) Xx0)
% 20.28/20.46 Found x8:(X03 Xx1)
% 20.28/20.46 Found x8 as proof of (X02 Xx1)
% 20.28/20.46 Found (fun (x8:(X03 Xx1))=> x8) as proof of (X02 Xx1)
% 20.28/20.46 Found (fun (Xx1:a) (x8:(X03 Xx1))=> x8) as proof of ((X03 Xx1)->(X02 Xx1))
% 20.28/20.46 Found (fun (Xx1:a) (x8:(X03 Xx1))=> x8) as proof of (forall (Xx:a), ((X03 Xx)->(X02 Xx)))
% 20.28/20.46 Found x600:=(x60 x7):((cK x4) Xx0)
% 20.28/20.46 Found (x60 x7) as proof of ((cK X03) Xx0)
% 20.28/20.46 Found ((x6 Xx0) x7) as proof of ((cK X03) Xx0)
% 20.28/20.46 Found ((x6 Xx0) x7) as proof of ((cK X03) Xx0)
% 20.28/20.46 Found ((x6 Xx0) x7) as proof of ((cK X03) Xx0)
% 20.28/20.46 Found x8:(X03 Xx1)
% 20.28/20.46 Found x8 as proof of (X02 Xx1)
% 20.28/20.46 Found (fun (x8:(X03 Xx1))=> x8) as proof of (X02 Xx1)
% 20.28/20.46 Found (fun (Xx1:a) (x8:(X03 Xx1))=> x8) as proof of ((X03 Xx1)->(X02 Xx1))
% 20.28/20.46 Found (fun (Xx1:a) (x8:(X03 Xx1))=> x8) as proof of (forall (Xx:a), ((X03 Xx)->(X02 Xx)))
% 20.28/20.46 Found x600:=(x60 x7):((cK x4) Xx0)
% 20.28/20.46 Found (x60 x7) as proof of ((cK X03) Xx0)
% 20.28/20.46 Found ((x6 Xx0) x7) as proof of ((cK X03) Xx0)
% 20.28/20.46 Found ((x6 Xx0) x7) as proof of ((cK X03) Xx0)
% 20.28/20.46 Found ((x6 Xx0) x7) as proof of ((cK X03) Xx0)
% 20.28/20.46 Found x8:(X03 Xx1)
% 20.28/20.46 Found x8 as proof of (X02 Xx1)
% 20.28/20.46 Found (fun (x8:(X03 Xx1))=> x8) as proof of (X02 Xx1)
% 20.28/20.46 Found (fun (Xx1:a) (x8:(X03 Xx1))=> x8) as proof of ((X03 Xx1)->(X02 Xx1))
% 20.28/20.46 Found (fun (Xx1:a) (x8:(X03 Xx1))=> x8) as proof of (forall (Xx:a), ((X03 Xx)->(X02 Xx)))
% 20.28/20.46 Found x600:=(x60 x7):((cK x4) Xx0)
% 20.28/20.46 Found (x60 x7) as proof of ((cK X03) Xx0)
% 20.28/20.46 Found ((x6 Xx0) x7) as proof of ((cK X03) Xx0)
% 20.28/20.46 Found ((x6 Xx0) x7) as proof of ((cK X03) Xx0)
% 20.28/20.46 Found ((x6 Xx0) x7) as proof of ((cK X03) Xx0)
% 20.28/20.46 Found x8:(X03 Xx1)
% 20.28/20.46 Found x8 as proof of (X02 Xx1)
% 20.28/20.46 Found (fun (x8:(X03 Xx1))=> x8) as proof of (X02 Xx1)
% 20.28/20.46 Found (fun (Xx1:a) (x8:(X03 Xx1))=> x8) as proof of ((X03 Xx1)->(X02 Xx1))
% 20.28/20.46 Found (fun (Xx1:a) (x8:(X03 Xx1))=> x8) as proof of (forall (Xx:a), ((X03 Xx)->(X02 Xx)))
% 20.28/20.46 Found x600:=(x60 x7):((cK x3) Xx0)
% 20.28/20.46 Found (x60 x7) as proof of ((cK X03) Xx0)
% 20.28/20.46 Found ((x6 Xx0) x7) as proof of ((cK X03) Xx0)
% 20.28/20.46 Found ((x6 Xx0) x7) as proof of ((cK X03) Xx0)
% 20.28/20.46 Found ((x6 Xx0) x7) as proof of ((cK X03) Xx0)
% 20.28/20.46 Found x8:(X03 Xx1)
% 20.28/20.46 Found x8 as proof of (X02 Xx1)
% 20.28/20.46 Found (fun (x8:(X03 Xx1))=> x8) as proof of (X02 Xx1)
% 20.28/20.46 Found (fun (Xx1:a) (x8:(X03 Xx1))=> x8) as proof of ((X03 Xx1)->(X02 Xx1))
% 20.28/20.46 Found (fun (Xx1:a) (x8:(X03 Xx1))=> x8) as proof of (forall (Xx:a), ((X03 Xx)->(X02 Xx)))
% 20.28/20.46 Found x600:=(x60 x7):((cK x4) Xx0)
% 20.28/20.46 Found (x60 x7) as proof of ((cK X03) Xx0)
% 20.28/20.46 Found ((x6 Xx0) x7) as proof of ((cK X03) Xx0)
% 20.28/20.46 Found ((x6 Xx0) x7) as proof of ((cK X03) Xx0)
% 20.28/20.46 Found ((x6 Xx0) x7) as proof of ((cK X03) Xx0)
% 20.28/20.46 Found x8:(X03 Xx1)
% 20.28/20.46 Found x8 as proof of (X02 Xx1)
% 20.28/20.46 Found (fun (x8:(X03 Xx1))=> x8) as proof of (X02 Xx1)
% 20.28/20.46 Found (fun (Xx1:a) (x8:(X03 Xx1))=> x8) as proof of ((X03 Xx1)->(X02 Xx1))
% 20.28/20.46 Found (fun (Xx1:a) (x8:(X03 Xx1))=> x8) as proof of (forall (Xx:a), ((X03 Xx)->(X02 Xx)))
% 20.28/20.46 Found x500:=(x50 x6):((cK x3) Xx0)
% 20.53/20.72 Found (x50 x6) as proof of ((cK X03) Xx0)
% 20.53/20.72 Found ((x5 Xx0) x6) as proof of ((cK X03) Xx0)
% 20.53/20.72 Found ((x5 Xx0) x6) as proof of ((cK X03) Xx0)
% 20.53/20.72 Found ((x5 Xx0) x6) as proof of ((cK X03) Xx0)
% 20.53/20.72 Found x8:(X03 Xx1)
% 20.53/20.72 Found x8 as proof of (X02 Xx1)
% 20.53/20.72 Found (fun (x8:(X03 Xx1))=> x8) as proof of (X02 Xx1)
% 20.53/20.72 Found (fun (Xx1:a) (x8:(X03 Xx1))=> x8) as proof of ((X03 Xx1)->(X02 Xx1))
% 20.53/20.72 Found (fun (Xx1:a) (x8:(X03 Xx1))=> x8) as proof of (forall (Xx:a), ((X03 Xx)->(X02 Xx)))
% 20.53/20.72 Found x600:=(x60 x7):((cK x3) Xx0)
% 20.53/20.72 Found (x60 x7) as proof of ((cK X03) Xx0)
% 20.53/20.72 Found ((x6 Xx0) x7) as proof of ((cK X03) Xx0)
% 20.53/20.72 Found ((x6 Xx0) x7) as proof of ((cK X03) Xx0)
% 20.53/20.72 Found ((x6 Xx0) x7) as proof of ((cK X03) Xx0)
% 20.53/20.72 Found x8:(X03 Xx1)
% 20.53/20.72 Found x8 as proof of (X02 Xx1)
% 20.53/20.72 Found (fun (x8:(X03 Xx1))=> x8) as proof of (X02 Xx1)
% 20.53/20.72 Found (fun (Xx1:a) (x8:(X03 Xx1))=> x8) as proof of ((X03 Xx1)->(X02 Xx1))
% 20.53/20.72 Found (fun (Xx1:a) (x8:(X03 Xx1))=> x8) as proof of (forall (Xx:a), ((X03 Xx)->(X02 Xx)))
% 20.53/20.72 Found x600:=(x60 x7):((cK x4) Xx0)
% 20.53/20.72 Found (x60 x7) as proof of ((cK X03) Xx0)
% 20.53/20.72 Found ((x6 Xx0) x7) as proof of ((cK X03) Xx0)
% 20.53/20.72 Found ((x6 Xx0) x7) as proof of ((cK X03) Xx0)
% 20.53/20.72 Found ((x6 Xx0) x7) as proof of ((cK X03) Xx0)
% 20.53/20.72 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 20.53/20.72 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X03) Xx0))
% 20.53/20.72 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X03) Xx0))
% 20.53/20.72 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X03) Xx0))
% 20.53/20.72 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X03) Xx0)))
% 20.53/20.72 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X03) Xx0)
% 20.53/20.72 Found ((and_rect0 ((cK X03) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X03) Xx0)
% 20.53/20.72 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X03) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X03) Xx0)
% 20.53/20.72 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X03) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X03) Xx0)
% 20.53/20.72 Found x6:(X03 Xx1)
% 20.53/20.72 Instantiate: X02:=X03:(a->Prop)
% 20.53/20.72 Found (fun (x6:(X03 Xx1))=> x6) as proof of (X02 Xx1)
% 20.53/20.72 Found (fun (Xx1:a) (x6:(X03 Xx1))=> x6) as proof of ((X03 Xx1)->(X02 Xx1))
% 20.53/20.72 Found (fun (Xx1:a) (x6:(X03 Xx1))=> x6) as proof of (forall (Xx:a), ((X03 Xx)->(X02 Xx)))
% 20.53/20.72 Found ((x340 (fun (Xx1:a) (x6:(X03 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X03) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X02) Xx0)
% 20.53/20.72 Found (((x34 X02) (fun (Xx1:a) (x6:(X03 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X03) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X02) Xx0)
% 20.53/20.72 Found ((((x3 x4) X02) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X02) Xx0)
% 20.53/20.72 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> ((((x3 x4) X02) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))))) as proof of ((cK X02) Xx0)
% 20.53/20.72 Found x8:(X03 Xx1)
% 20.53/20.72 Found x8 as proof of (X02 Xx1)
% 21.68/21.87 Found (fun (x8:(X03 Xx1))=> x8) as proof of (X02 Xx1)
% 21.68/21.87 Found (fun (Xx1:a) (x8:(X03 Xx1))=> x8) as proof of ((X03 Xx1)->(X02 Xx1))
% 21.68/21.87 Found (fun (Xx1:a) (x8:(X03 Xx1))=> x8) as proof of (forall (Xx:a), ((X03 Xx)->(X02 Xx)))
% 21.68/21.87 Found x600:=(x60 x7):((cK x3) Xx0)
% 21.68/21.87 Found (x60 x7) as proof of ((cK X03) Xx0)
% 21.68/21.87 Found ((x6 Xx0) x7) as proof of ((cK X03) Xx0)
% 21.68/21.87 Found ((x6 Xx0) x7) as proof of ((cK X03) Xx0)
% 21.68/21.87 Found ((x6 Xx0) x7) as proof of ((cK X03) Xx0)
% 21.68/21.87 Found x8:(X03 Xx1)
% 21.68/21.87 Found x8 as proof of (X02 Xx1)
% 21.68/21.87 Found (fun (x8:(X03 Xx1))=> x8) as proof of (X02 Xx1)
% 21.68/21.87 Found (fun (Xx1:a) (x8:(X03 Xx1))=> x8) as proof of ((X03 Xx1)->(X02 Xx1))
% 21.68/21.87 Found (fun (Xx1:a) (x8:(X03 Xx1))=> x8) as proof of (forall (Xx:a), ((X03 Xx)->(X02 Xx)))
% 21.68/21.87 Found x600:=(x60 x7):((cK x4) Xx0)
% 21.68/21.87 Found (x60 x7) as proof of ((cK X03) Xx0)
% 21.68/21.87 Found ((x6 Xx0) x7) as proof of ((cK X03) Xx0)
% 21.68/21.87 Found ((x6 Xx0) x7) as proof of ((cK X03) Xx0)
% 21.68/21.87 Found ((x6 Xx0) x7) as proof of ((cK X03) Xx0)
% 21.68/21.87 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 21.68/21.87 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X03) Xx0))
% 21.68/21.87 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X03) Xx0))
% 21.68/21.87 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X03) Xx0))
% 21.68/21.87 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X03) Xx0)))
% 21.68/21.87 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X03) Xx0)
% 21.68/21.87 Found ((and_rect0 ((cK X03) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X03) Xx0)
% 21.68/21.87 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X03) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X03) Xx0)
% 21.68/21.87 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X03) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X03) Xx0)
% 21.68/21.87 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 21.68/21.87 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X03) Xx0))
% 21.68/21.87 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X03) Xx0))
% 21.68/21.87 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X03) Xx0))
% 21.68/21.87 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X03) Xx0)))
% 21.68/21.87 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X03) Xx0)
% 21.68/21.87 Found ((and_rect0 ((cK X03) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X03) Xx0)
% 21.68/21.87 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X03) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X03) Xx0)
% 21.68/21.87 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X03) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X03) Xx0)
% 21.68/21.87 Found x6:(X03 Xx1)
% 21.68/21.87 Instantiate: X02:=X03:(a->Prop)
% 21.68/21.87 Found (fun (x6:(X03 Xx1))=> x6) as proof of (X02 Xx1)
% 21.68/21.87 Found (fun (Xx1:a) (x6:(X03 Xx1))=> x6) as proof of ((X03 Xx1)->(X02 Xx1))
% 21.68/21.87 Found (fun (Xx1:a) (x6:(X03 Xx1))=> x6) as proof of (forall (Xx:a), ((X03 Xx)->(X02 Xx)))
% 21.68/21.87 Found ((x340 (fun (Xx1:a) (x6:(X03 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X03) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X02) Xx0)
% 21.68/21.87 Found (((x34 X02) (fun (Xx1:a) (x6:(X03 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X03) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X02) Xx0)
% 22.05/22.26 Found ((((x3 x4) X02) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X02) Xx0)
% 22.05/22.26 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> ((((x3 x4) X02) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))))) as proof of ((cK X02) Xx0)
% 22.05/22.26 Found x4:(X03 Xx1)
% 22.05/22.26 Instantiate: X03:=(cK x5):(a->Prop)
% 22.05/22.26 Found x4 as proof of (X02 Xx1)
% 22.05/22.26 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X02 Xx1)
% 22.05/22.26 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X02 Xx1))
% 22.05/22.26 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X02 Xx1)))
% 22.05/22.26 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X02 Xx1)
% 22.05/22.26 Found ((and_rect0 (X02 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X02 Xx1)
% 22.05/22.26 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X02 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X02 Xx1)
% 22.05/22.26 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X02 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X02 Xx1)
% 22.05/22.26 Found x4:(X03 Xx1)
% 22.05/22.26 Found x4 as proof of (X02 Xx1)
% 22.05/22.26 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X02 Xx1)
% 22.05/22.26 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X02 Xx1))
% 22.05/22.26 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X02 Xx1)))
% 22.05/22.26 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X02 Xx1)
% 22.05/22.26 Found ((and_rect0 (X02 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X02 Xx1)
% 22.05/22.26 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X02 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X02 Xx1)
% 22.05/22.26 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X02 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X02 Xx1)
% 22.05/22.26 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 22.05/22.26 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X03) Xx0))
% 22.05/22.26 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X03) Xx0))
% 22.05/22.26 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X03) Xx0))
% 22.05/22.26 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X03) Xx0)))
% 22.05/22.26 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X03) Xx0)
% 22.69/22.88 Found ((and_rect0 ((cK X03) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X03) Xx0)
% 22.69/22.88 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X03) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X03) Xx0)
% 22.69/22.88 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X03) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X03) Xx0)
% 22.69/22.88 Found x4:(X03 Xx1)
% 22.69/22.88 Instantiate: X03:=(cK x5):(a->Prop)
% 22.69/22.88 Found x4 as proof of (X02 Xx1)
% 22.69/22.88 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X02 Xx1)
% 22.69/22.88 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X02 Xx1))
% 22.69/22.88 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X02 Xx1)))
% 22.69/22.88 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X02 Xx1)
% 22.69/22.88 Found ((and_rect0 (X02 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X02 Xx1)
% 22.69/22.88 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X02 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X02 Xx1)
% 22.69/22.88 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X02 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X02 Xx1)
% 22.69/22.88 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 22.69/22.88 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X03) Xx0))
% 22.69/22.88 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X03) Xx0))
% 22.69/22.88 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X03) Xx0))
% 22.69/22.88 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X03) Xx0)))
% 22.69/22.88 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X03) Xx0)
% 22.69/22.88 Found ((and_rect0 ((cK X03) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X03) Xx0)
% 22.69/22.88 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X03) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X03) Xx0)
% 22.69/22.88 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X03) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X03) Xx0)
% 22.69/22.88 Found x6:(X03 Xx1)
% 22.69/22.88 Instantiate: X02:=X03:(a->Prop)
% 22.69/22.88 Found (fun (x6:(X03 Xx1))=> x6) as proof of (X02 Xx1)
% 22.69/22.88 Found (fun (Xx1:a) (x6:(X03 Xx1))=> x6) as proof of ((X03 Xx1)->(X02 Xx1))
% 22.69/22.88 Found (fun (Xx1:a) (x6:(X03 Xx1))=> x6) as proof of (forall (Xx:a), ((X03 Xx)->(X02 Xx)))
% 22.69/22.88 Found ((x340 (fun (Xx1:a) (x6:(X03 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X03) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X02) Xx0)
% 22.69/22.88 Found (((x34 X02) (fun (Xx1:a) (x6:(X03 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X03) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X02) Xx0)
% 23.28/23.46 Found ((((x3 x4) X02) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X02) Xx0)
% 23.28/23.46 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> ((((x3 x4) X02) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))))) as proof of ((cK X02) Xx0)
% 23.28/23.46 Found x4:(X03 Xx1)
% 23.28/23.46 Found x4 as proof of (X02 Xx1)
% 23.28/23.46 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X02 Xx1)
% 23.28/23.46 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X02 Xx1))
% 23.28/23.46 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X02 Xx1)))
% 23.28/23.46 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X02 Xx1)
% 23.28/23.46 Found ((and_rect0 (X02 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X02 Xx1)
% 23.28/23.46 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X02 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X02 Xx1)
% 23.28/23.46 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X02 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X02 Xx1)
% 23.28/23.46 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 23.28/23.46 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X03) Xx0))
% 23.28/23.46 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X03) Xx0))
% 23.28/23.46 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X03) Xx0))
% 23.28/23.46 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X03) Xx0)))
% 23.28/23.46 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X03) Xx0)
% 23.28/23.46 Found ((and_rect0 ((cK X03) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X03) Xx0)
% 23.28/23.46 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X03) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X03) Xx0)
% 23.28/23.46 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X03) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X03) Xx0)
% 23.28/23.46 Found x4:(X03 Xx1)
% 23.28/23.46 Instantiate: X03:=(cK x5):(a->Prop)
% 23.28/23.46 Found x4 as proof of (X02 Xx1)
% 23.28/23.46 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X02 Xx1)
% 23.28/23.46 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X02 Xx1))
% 23.28/23.46 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X02 Xx1)))
% 23.28/23.46 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X02 Xx1)
% 23.28/23.46 Found ((and_rect0 (X02 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X02 Xx1)
% 23.37/23.59 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X02 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X02 Xx1)
% 23.37/23.59 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X02 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X02 Xx1)
% 23.37/23.59 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 23.37/23.59 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X03) Xx0))
% 23.37/23.59 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X03) Xx0))
% 23.37/23.59 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X03) Xx0))
% 23.37/23.59 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X03) Xx0)))
% 23.37/23.59 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X03) Xx0)
% 23.37/23.59 Found ((and_rect0 ((cK X03) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X03) Xx0)
% 23.37/23.59 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X03) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X03) Xx0)
% 23.37/23.59 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X03) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X03) Xx0)
% 23.37/23.59 Found x6:(X03 Xx1)
% 23.37/23.59 Instantiate: X02:=X03:(a->Prop)
% 23.37/23.59 Found (fun (x6:(X03 Xx1))=> x6) as proof of (X02 Xx1)
% 23.37/23.59 Found (fun (Xx1:a) (x6:(X03 Xx1))=> x6) as proof of ((X03 Xx1)->(X02 Xx1))
% 23.37/23.59 Found (fun (Xx1:a) (x6:(X03 Xx1))=> x6) as proof of (forall (Xx:a), ((X03 Xx)->(X02 Xx)))
% 23.37/23.59 Found ((x340 (fun (Xx1:a) (x6:(X03 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X03) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X02) Xx0)
% 23.37/23.59 Found (((x34 X02) (fun (Xx1:a) (x6:(X03 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X03) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X02) Xx0)
% 23.37/23.59 Found ((((x3 x4) X02) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X02) Xx0)
% 23.37/23.59 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> ((((x3 x4) X02) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))))) as proof of ((cK X02) Xx0)
% 23.37/23.59 Found x4:(X03 Xx1)
% 23.37/23.59 Found x4 as proof of (X02 Xx1)
% 23.37/23.59 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X02 Xx1)
% 23.37/23.59 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X02 Xx1))
% 23.37/23.59 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X02 Xx1)))
% 23.37/23.59 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X02 Xx1)
% 24.36/24.54 Found ((and_rect0 (X02 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X02 Xx1)
% 24.36/24.54 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X02 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X02 Xx1)
% 24.36/24.54 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X02 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X02 Xx1)
% 24.36/24.54 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 24.36/24.54 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X03) Xx0))
% 24.36/24.54 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X03) Xx0))
% 24.36/24.54 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X03) Xx0))
% 24.36/24.54 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X03) Xx0)))
% 24.36/24.54 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X03) Xx0)
% 24.36/24.54 Found ((and_rect0 ((cK X03) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X03) Xx0)
% 24.36/24.54 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X03) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X03) Xx0)
% 24.36/24.54 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X03) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X03) Xx0)
% 24.36/24.54 Found x4:(X03 Xx1)
% 24.36/24.54 Instantiate: X03:=(cK x5):(a->Prop)
% 24.36/24.54 Found x4 as proof of (X02 Xx1)
% 24.36/24.54 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X02 Xx1)
% 24.36/24.54 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X02 Xx1))
% 24.36/24.54 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X02 Xx1)))
% 24.36/24.54 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X02 Xx1)
% 24.36/24.54 Found ((and_rect0 (X02 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X02 Xx1)
% 24.36/24.54 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X02 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X02 Xx1)
% 24.36/24.54 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X02 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X02 Xx1)
% 24.36/24.54 Found x4:(X04 Xx1)
% 24.36/24.54 Found x4 as proof of (X03 Xx1)
% 24.36/24.54 Found (fun (x4:(X04 Xx1))=> x4) as proof of (X03 Xx1)
% 24.36/24.54 Found (fun (Xx1:a) (x4:(X04 Xx1))=> x4) as proof of ((X04 Xx1)->(X03 Xx1))
% 24.36/24.54 Found (fun (Xx1:a) (x4:(X04 Xx1))=> x4) as proof of (forall (Xx:a), ((X04 Xx)->(X03 Xx)))
% 24.36/24.54 Found x4:(X03 Xx1)
% 24.36/24.54 Found x4 as proof of (X02 Xx1)
% 24.36/24.54 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X02 Xx1)
% 24.36/24.54 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X02 Xx1))
% 24.36/24.54 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X02 Xx1)))
% 29.01/29.23 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X02 Xx1)
% 29.01/29.23 Found ((and_rect0 (X02 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X02 Xx1)
% 29.01/29.23 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X02 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X02 Xx1)
% 29.01/29.23 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X02 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X02 Xx1)
% 29.01/29.23 Found x6:(X04 Xx1)
% 29.01/29.23 Found x6 as proof of (X03 Xx1)
% 29.01/29.23 Found (fun (x6:(X04 Xx1))=> x6) as proof of (X03 Xx1)
% 29.01/29.23 Found (fun (Xx1:a) (x6:(X04 Xx1))=> x6) as proof of ((X04 Xx1)->(X03 Xx1))
% 29.01/29.23 Found (fun (Xx1:a) (x6:(X04 Xx1))=> x6) as proof of (forall (Xx:a), ((X04 Xx)->(X03 Xx)))
% 29.01/29.23 Found x6:(X04 Xx1)
% 29.01/29.23 Found x6 as proof of (X03 Xx1)
% 29.01/29.23 Found (fun (x6:(X04 Xx1))=> x6) as proof of (X03 Xx1)
% 29.01/29.23 Found (fun (Xx1:a) (x6:(X04 Xx1))=> x6) as proof of ((X04 Xx1)->(X03 Xx1))
% 29.01/29.23 Found (fun (Xx1:a) (x6:(X04 Xx1))=> x6) as proof of (forall (Xx:a), ((X04 Xx)->(X03 Xx)))
% 29.01/29.23 Found x6:(X04 Xx1)
% 29.01/29.23 Found x6 as proof of (X03 Xx1)
% 29.01/29.23 Found (fun (x6:(X04 Xx1))=> x6) as proof of (X03 Xx1)
% 29.01/29.23 Found (fun (Xx1:a) (x6:(X04 Xx1))=> x6) as proof of ((X04 Xx1)->(X03 Xx1))
% 29.01/29.23 Found (fun (Xx1:a) (x6:(X04 Xx1))=> x6) as proof of (forall (Xx:a), ((X04 Xx)->(X03 Xx)))
% 29.01/29.23 Found x6:(X04 Xx1)
% 29.01/29.23 Found x6 as proof of (X03 Xx1)
% 29.01/29.23 Found (fun (x6:(X04 Xx1))=> x6) as proof of (X03 Xx1)
% 29.01/29.23 Found (fun (Xx1:a) (x6:(X04 Xx1))=> x6) as proof of ((X04 Xx1)->(X03 Xx1))
% 29.01/29.23 Found (fun (Xx1:a) (x6:(X04 Xx1))=> x6) as proof of (forall (Xx:a), ((X04 Xx)->(X03 Xx)))
% 29.01/29.23 Found x6:(X04 Xx1)
% 29.01/29.23 Found x6 as proof of (X03 Xx1)
% 29.01/29.23 Found (fun (x6:(X04 Xx1))=> x6) as proof of (X03 Xx1)
% 29.01/29.23 Found (fun (Xx1:a) (x6:(X04 Xx1))=> x6) as proof of ((X04 Xx1)->(X03 Xx1))
% 29.01/29.23 Found (fun (Xx1:a) (x6:(X04 Xx1))=> x6) as proof of (forall (Xx:a), ((X04 Xx)->(X03 Xx)))
% 29.01/29.23 Found x6:(X04 Xx1)
% 29.01/29.23 Found x6 as proof of (X03 Xx1)
% 29.01/29.23 Found (fun (x6:(X04 Xx1))=> x6) as proof of (X03 Xx1)
% 29.01/29.23 Found (fun (Xx1:a) (x6:(X04 Xx1))=> x6) as proof of ((X04 Xx1)->(X03 Xx1))
% 29.01/29.23 Found (fun (Xx1:a) (x6:(X04 Xx1))=> x6) as proof of (forall (Xx:a), ((X04 Xx)->(X03 Xx)))
% 29.01/29.23 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 29.01/29.23 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X04) Xx0))
% 29.01/29.23 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X04) Xx0))
% 29.01/29.23 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X04) Xx0))
% 29.01/29.23 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X04) Xx0)))
% 29.01/29.23 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X04) Xx0)
% 29.01/29.23 Found ((and_rect0 ((cK X04) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X04) Xx0)
% 29.01/29.23 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X04) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X04) Xx0)
% 29.01/29.23 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X04) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X04) Xx0)
% 29.01/29.23 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 29.01/29.23 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X04) Xx0))
% 29.01/29.23 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X04) Xx0))
% 29.01/29.23 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X04) Xx0))
% 29.01/29.23 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X04) Xx0)))
% 29.13/29.32 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X04) Xx0)
% 29.13/29.32 Found ((and_rect0 ((cK X04) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X04) Xx0)
% 29.13/29.32 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X04) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X04) Xx0)
% 29.13/29.32 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X04) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X04) Xx0)
% 29.13/29.32 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 29.13/29.32 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X04) Xx0))
% 29.13/29.32 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X04) Xx0))
% 29.13/29.32 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X04) Xx0))
% 29.13/29.32 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X04) Xx0)))
% 29.13/29.32 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X04) Xx0)
% 29.13/29.32 Found ((and_rect0 ((cK X04) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X04) Xx0)
% 29.13/29.32 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X04) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X04) Xx0)
% 29.13/29.32 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X04) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X04) Xx0)
% 29.13/29.32 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 29.13/29.32 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X04) Xx0))
% 29.13/29.32 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X04) Xx0))
% 29.13/29.32 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X04) Xx0))
% 29.13/29.32 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X04) Xx0)))
% 29.13/29.32 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X04) Xx0)
% 29.13/29.32 Found ((and_rect0 ((cK X04) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X04) Xx0)
% 29.13/29.32 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X04) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X04) Xx0)
% 29.13/29.32 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X04) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X04) Xx0)
% 29.13/29.32 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 29.13/29.32 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X04) Xx0))
% 29.13/29.32 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X04) Xx0))
% 29.13/29.32 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X04) Xx0))
% 29.13/29.32 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X04) Xx0)))
% 29.13/29.32 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X04) Xx0)
% 29.13/29.32 Found ((and_rect0 ((cK X04) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X04) Xx0)
% 29.13/29.32 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X04) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X04) Xx0)
% 31.08/31.32 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X04) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X04) Xx0)
% 31.08/31.32 Found x8:(X04 Xx1)
% 31.08/31.32 Found x8 as proof of (X03 Xx1)
% 31.08/31.32 Found (fun (x8:(X04 Xx1))=> x8) as proof of (X03 Xx1)
% 31.08/31.32 Found (fun (Xx1:a) (x8:(X04 Xx1))=> x8) as proof of ((X04 Xx1)->(X03 Xx1))
% 31.08/31.32 Found (fun (Xx1:a) (x8:(X04 Xx1))=> x8) as proof of (forall (Xx:a), ((X04 Xx)->(X03 Xx)))
% 31.08/31.32 Found x600:=(x60 x7):((cK x4) Xx0)
% 31.08/31.32 Found (x60 x7) as proof of ((cK X04) Xx0)
% 31.08/31.32 Found ((x6 Xx0) x7) as proof of ((cK X04) Xx0)
% 31.08/31.32 Found ((x6 Xx0) x7) as proof of ((cK X04) Xx0)
% 31.08/31.32 Found ((x6 Xx0) x7) as proof of ((cK X04) Xx0)
% 31.08/31.32 Found x8:(X04 Xx1)
% 31.08/31.32 Found x8 as proof of (X03 Xx1)
% 31.08/31.32 Found (fun (x8:(X04 Xx1))=> x8) as proof of (X03 Xx1)
% 31.08/31.32 Found (fun (Xx1:a) (x8:(X04 Xx1))=> x8) as proof of ((X04 Xx1)->(X03 Xx1))
% 31.08/31.32 Found (fun (Xx1:a) (x8:(X04 Xx1))=> x8) as proof of (forall (Xx:a), ((X04 Xx)->(X03 Xx)))
% 31.08/31.32 Found x600:=(x60 x7):((cK x4) Xx0)
% 31.08/31.32 Found (x60 x7) as proof of ((cK X04) Xx0)
% 31.08/31.32 Found ((x6 Xx0) x7) as proof of ((cK X04) Xx0)
% 31.08/31.32 Found ((x6 Xx0) x7) as proof of ((cK X04) Xx0)
% 31.08/31.32 Found ((x6 Xx0) x7) as proof of ((cK X04) Xx0)
% 31.08/31.32 Found x8:(X04 Xx1)
% 31.08/31.32 Found x8 as proof of (X03 Xx1)
% 31.08/31.32 Found (fun (x8:(X04 Xx1))=> x8) as proof of (X03 Xx1)
% 31.08/31.32 Found (fun (Xx1:a) (x8:(X04 Xx1))=> x8) as proof of ((X04 Xx1)->(X03 Xx1))
% 31.08/31.32 Found (fun (Xx1:a) (x8:(X04 Xx1))=> x8) as proof of (forall (Xx:a), ((X04 Xx)->(X03 Xx)))
% 31.08/31.32 Found x600:=(x60 x7):((cK x4) Xx0)
% 31.08/31.32 Found (x60 x7) as proof of ((cK X04) Xx0)
% 31.08/31.32 Found ((x6 Xx0) x7) as proof of ((cK X04) Xx0)
% 31.08/31.32 Found ((x6 Xx0) x7) as proof of ((cK X04) Xx0)
% 31.08/31.32 Found ((x6 Xx0) x7) as proof of ((cK X04) Xx0)
% 31.08/31.32 Found x8:(X04 Xx1)
% 31.08/31.32 Found x8 as proof of (X03 Xx1)
% 31.08/31.32 Found (fun (x8:(X04 Xx1))=> x8) as proof of (X03 Xx1)
% 31.08/31.32 Found (fun (Xx1:a) (x8:(X04 Xx1))=> x8) as proof of ((X04 Xx1)->(X03 Xx1))
% 31.08/31.32 Found (fun (Xx1:a) (x8:(X04 Xx1))=> x8) as proof of (forall (Xx:a), ((X04 Xx)->(X03 Xx)))
% 31.08/31.32 Found x600:=(x60 x7):((cK x3) Xx0)
% 31.08/31.32 Found (x60 x7) as proof of ((cK X04) Xx0)
% 31.08/31.32 Found ((x6 Xx0) x7) as proof of ((cK X04) Xx0)
% 31.08/31.32 Found ((x6 Xx0) x7) as proof of ((cK X04) Xx0)
% 31.08/31.32 Found ((x6 Xx0) x7) as proof of ((cK X04) Xx0)
% 31.08/31.32 Found x8:(X04 Xx1)
% 31.08/31.32 Found x8 as proof of (X03 Xx1)
% 31.08/31.32 Found (fun (x8:(X04 Xx1))=> x8) as proof of (X03 Xx1)
% 31.08/31.32 Found (fun (Xx1:a) (x8:(X04 Xx1))=> x8) as proof of ((X04 Xx1)->(X03 Xx1))
% 31.08/31.32 Found (fun (Xx1:a) (x8:(X04 Xx1))=> x8) as proof of (forall (Xx:a), ((X04 Xx)->(X03 Xx)))
% 31.08/31.32 Found x600:=(x60 x7):((cK x4) Xx0)
% 31.08/31.32 Found (x60 x7) as proof of ((cK X04) Xx0)
% 31.08/31.32 Found ((x6 Xx0) x7) as proof of ((cK X04) Xx0)
% 31.08/31.32 Found ((x6 Xx0) x7) as proof of ((cK X04) Xx0)
% 31.08/31.32 Found ((x6 Xx0) x7) as proof of ((cK X04) Xx0)
% 31.08/31.32 Found x60:=(x6 Xx0):((x3 Xx0)->((cK x3) Xx0))
% 31.08/31.32 Found (x6 Xx0) as proof of ((x3 Xx0)->((cK X04) Xx0))
% 31.08/31.32 Found (x6 Xx0) as proof of ((x3 Xx0)->((cK X04) Xx0))
% 31.08/31.32 Found (fun (x6:(forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1))))=> (x6 Xx0)) as proof of ((x3 Xx0)->((cK X04) Xx0))
% 31.08/31.32 Found (fun (x6:(forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1)))->((x3 Xx0)->((cK X04) Xx0)))
% 31.08/31.32 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1))))=> (x6 Xx0))) as proof of ((cK X04) Xx0)
% 31.08/31.32 Found ((and_rect0 ((cK X04) Xx0)) (fun (x6:(forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1))))=> (x6 Xx0))) as proof of ((cK X04) Xx0)
% 31.08/31.32 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1)))->((x3 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1)))) (x3 Xx0)) P) x6) x4)) ((cK X04) Xx0)) (fun (x6:(forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1))))=> (x6 Xx0))) as proof of ((cK X04) Xx0)
% 31.08/31.32 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1)))->((x3 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1)))) (x3 Xx0)) P) x6) x4)) ((cK X04) Xx0)) (fun (x6:(forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1))))=> (x6 Xx0))) as proof of ((cK X04) Xx0)
% 31.79/31.97 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 31.79/31.97 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X04) Xx0))
% 31.79/31.97 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X04) Xx0))
% 31.79/31.97 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X04) Xx0))
% 31.79/31.97 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X04) Xx0)))
% 31.79/31.97 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X04) Xx0)
% 31.79/31.97 Found ((and_rect0 ((cK X04) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X04) Xx0)
% 31.79/31.97 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X04) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X04) Xx0)
% 31.79/31.97 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X04) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X04) Xx0)
% 31.79/31.97 Found x8:(X04 Xx1)
% 31.79/31.97 Found x8 as proof of (X03 Xx1)
% 31.79/31.97 Found (fun (x8:(X04 Xx1))=> x8) as proof of (X03 Xx1)
% 31.79/31.97 Found (fun (Xx1:a) (x8:(X04 Xx1))=> x8) as proof of ((X04 Xx1)->(X03 Xx1))
% 31.79/31.97 Found (fun (Xx1:a) (x8:(X04 Xx1))=> x8) as proof of (forall (Xx:a), ((X04 Xx)->(X03 Xx)))
% 31.79/31.97 Found x600:=(x60 x7):((cK x4) Xx0)
% 31.79/31.97 Found (x60 x7) as proof of ((cK X04) Xx0)
% 31.79/31.97 Found ((x6 Xx0) x7) as proof of ((cK X04) Xx0)
% 31.79/31.97 Found ((x6 Xx0) x7) as proof of ((cK X04) Xx0)
% 31.79/31.97 Found ((x6 Xx0) x7) as proof of ((cK X04) Xx0)
% 31.79/31.97 Found x8:(X04 Xx1)
% 31.79/31.97 Found x8 as proof of (X03 Xx1)
% 31.79/31.97 Found (fun (x8:(X04 Xx1))=> x8) as proof of (X03 Xx1)
% 31.79/31.97 Found (fun (Xx1:a) (x8:(X04 Xx1))=> x8) as proof of ((X04 Xx1)->(X03 Xx1))
% 31.79/31.97 Found (fun (Xx1:a) (x8:(X04 Xx1))=> x8) as proof of (forall (Xx:a), ((X04 Xx)->(X03 Xx)))
% 31.79/31.97 Found x600:=(x60 x7):((cK x4) Xx0)
% 31.79/31.97 Found (x60 x7) as proof of ((cK X04) Xx0)
% 31.79/31.97 Found ((x6 Xx0) x7) as proof of ((cK X04) Xx0)
% 31.79/31.97 Found ((x6 Xx0) x7) as proof of ((cK X04) Xx0)
% 31.79/31.97 Found ((x6 Xx0) x7) as proof of ((cK X04) Xx0)
% 31.79/31.97 Found x8:(X04 Xx1)
% 31.79/31.97 Found x8 as proof of (X03 Xx1)
% 31.79/31.97 Found (fun (x8:(X04 Xx1))=> x8) as proof of (X03 Xx1)
% 31.79/31.97 Found (fun (Xx1:a) (x8:(X04 Xx1))=> x8) as proof of ((X04 Xx1)->(X03 Xx1))
% 31.79/31.97 Found (fun (Xx1:a) (x8:(X04 Xx1))=> x8) as proof of (forall (Xx:a), ((X04 Xx)->(X03 Xx)))
% 31.79/31.97 Found x600:=(x60 x7):((cK x4) Xx0)
% 31.79/31.97 Found (x60 x7) as proof of ((cK X04) Xx0)
% 31.79/31.97 Found ((x6 Xx0) x7) as proof of ((cK X04) Xx0)
% 31.79/31.97 Found ((x6 Xx0) x7) as proof of ((cK X04) Xx0)
% 31.79/31.97 Found ((x6 Xx0) x7) as proof of ((cK X04) Xx0)
% 31.79/31.97 Found x8:(X04 Xx1)
% 31.79/31.97 Found x8 as proof of (X03 Xx1)
% 31.79/31.97 Found (fun (x8:(X04 Xx1))=> x8) as proof of (X03 Xx1)
% 31.79/31.97 Found (fun (Xx1:a) (x8:(X04 Xx1))=> x8) as proof of ((X04 Xx1)->(X03 Xx1))
% 31.79/31.97 Found (fun (Xx1:a) (x8:(X04 Xx1))=> x8) as proof of (forall (Xx:a), ((X04 Xx)->(X03 Xx)))
% 31.79/31.97 Found x600:=(x60 x7):((cK x3) Xx0)
% 31.79/31.97 Found (x60 x7) as proof of ((cK X04) Xx0)
% 31.79/31.97 Found ((x6 Xx0) x7) as proof of ((cK X04) Xx0)
% 31.79/31.97 Found ((x6 Xx0) x7) as proof of ((cK X04) Xx0)
% 31.79/31.97 Found ((x6 Xx0) x7) as proof of ((cK X04) Xx0)
% 31.79/31.97 Found x8:(X04 Xx1)
% 31.79/31.97 Found x8 as proof of (X03 Xx1)
% 31.79/31.97 Found (fun (x8:(X04 Xx1))=> x8) as proof of (X03 Xx1)
% 31.79/31.97 Found (fun (Xx1:a) (x8:(X04 Xx1))=> x8) as proof of ((X04 Xx1)->(X03 Xx1))
% 31.79/31.97 Found (fun (Xx1:a) (x8:(X04 Xx1))=> x8) as proof of (forall (Xx:a), ((X04 Xx)->(X03 Xx)))
% 31.79/31.97 Found x600:=(x60 x7):((cK x4) Xx0)
% 31.79/31.97 Found (x60 x7) as proof of ((cK X04) Xx0)
% 31.79/31.97 Found ((x6 Xx0) x7) as proof of ((cK X04) Xx0)
% 31.79/31.97 Found ((x6 Xx0) x7) as proof of ((cK X04) Xx0)
% 31.79/31.97 Found ((x6 Xx0) x7) as proof of ((cK X04) Xx0)
% 31.79/31.97 Found x8:(X04 Xx1)
% 31.79/31.97 Found x8 as proof of (X03 Xx1)
% 31.79/31.97 Found (fun (x8:(X04 Xx1))=> x8) as proof of (X03 Xx1)
% 31.79/31.97 Found (fun (Xx1:a) (x8:(X04 Xx1))=> x8) as proof of ((X04 Xx1)->(X03 Xx1))
% 31.79/31.97 Found (fun (Xx1:a) (x8:(X04 Xx1))=> x8) as proof of (forall (Xx:a), ((X04 Xx)->(X03 Xx)))
% 31.79/31.97 Found x500:=(x50 x6):((cK x3) Xx0)
% 31.79/31.97 Found (x50 x6) as proof of ((cK X04) Xx0)
% 32.53/32.71 Found ((x5 Xx0) x6) as proof of ((cK X04) Xx0)
% 32.53/32.71 Found ((x5 Xx0) x6) as proof of ((cK X04) Xx0)
% 32.53/32.71 Found ((x5 Xx0) x6) as proof of ((cK X04) Xx0)
% 32.53/32.71 Found x8:(X04 Xx1)
% 32.53/32.71 Found x8 as proof of (X03 Xx1)
% 32.53/32.71 Found (fun (x8:(X04 Xx1))=> x8) as proof of (X03 Xx1)
% 32.53/32.71 Found (fun (Xx1:a) (x8:(X04 Xx1))=> x8) as proof of ((X04 Xx1)->(X03 Xx1))
% 32.53/32.71 Found (fun (Xx1:a) (x8:(X04 Xx1))=> x8) as proof of (forall (Xx:a), ((X04 Xx)->(X03 Xx)))
% 32.53/32.71 Found x600:=(x60 x7):((cK x4) Xx0)
% 32.53/32.71 Found (x60 x7) as proof of ((cK X04) Xx0)
% 32.53/32.71 Found ((x6 Xx0) x7) as proof of ((cK X04) Xx0)
% 32.53/32.71 Found ((x6 Xx0) x7) as proof of ((cK X04) Xx0)
% 32.53/32.71 Found ((x6 Xx0) x7) as proof of ((cK X04) Xx0)
% 32.53/32.71 Found x8:(X04 Xx1)
% 32.53/32.71 Found x8 as proof of (X03 Xx1)
% 32.53/32.71 Found (fun (x8:(X04 Xx1))=> x8) as proof of (X03 Xx1)
% 32.53/32.71 Found (fun (Xx1:a) (x8:(X04 Xx1))=> x8) as proof of ((X04 Xx1)->(X03 Xx1))
% 32.53/32.71 Found (fun (Xx1:a) (x8:(X04 Xx1))=> x8) as proof of (forall (Xx:a), ((X04 Xx)->(X03 Xx)))
% 32.53/32.71 Found x600:=(x60 x7):((cK x4) Xx0)
% 32.53/32.71 Found (x60 x7) as proof of ((cK X04) Xx0)
% 32.53/32.71 Found ((x6 Xx0) x7) as proof of ((cK X04) Xx0)
% 32.53/32.71 Found ((x6 Xx0) x7) as proof of ((cK X04) Xx0)
% 32.53/32.71 Found ((x6 Xx0) x7) as proof of ((cK X04) Xx0)
% 32.53/32.71 Found x8:(X04 Xx1)
% 32.53/32.71 Found x8 as proof of (X03 Xx1)
% 32.53/32.71 Found (fun (x8:(X04 Xx1))=> x8) as proof of (X03 Xx1)
% 32.53/32.71 Found (fun (Xx1:a) (x8:(X04 Xx1))=> x8) as proof of ((X04 Xx1)->(X03 Xx1))
% 32.53/32.71 Found (fun (Xx1:a) (x8:(X04 Xx1))=> x8) as proof of (forall (Xx:a), ((X04 Xx)->(X03 Xx)))
% 32.53/32.71 Found x600:=(x60 x7):((cK x4) Xx0)
% 32.53/32.71 Found (x60 x7) as proof of ((cK X04) Xx0)
% 32.53/32.71 Found ((x6 Xx0) x7) as proof of ((cK X04) Xx0)
% 32.53/32.71 Found ((x6 Xx0) x7) as proof of ((cK X04) Xx0)
% 32.53/32.71 Found ((x6 Xx0) x7) as proof of ((cK X04) Xx0)
% 32.53/32.71 Found x8:(X04 Xx1)
% 32.53/32.71 Found x8 as proof of (X03 Xx1)
% 32.53/32.71 Found (fun (x8:(X04 Xx1))=> x8) as proof of (X03 Xx1)
% 32.53/32.71 Found (fun (Xx1:a) (x8:(X04 Xx1))=> x8) as proof of ((X04 Xx1)->(X03 Xx1))
% 32.53/32.71 Found (fun (Xx1:a) (x8:(X04 Xx1))=> x8) as proof of (forall (Xx:a), ((X04 Xx)->(X03 Xx)))
% 32.53/32.71 Found x600:=(x60 x7):((cK x4) Xx0)
% 32.53/32.71 Found (x60 x7) as proof of ((cK X04) Xx0)
% 32.53/32.71 Found ((x6 Xx0) x7) as proof of ((cK X04) Xx0)
% 32.53/32.71 Found ((x6 Xx0) x7) as proof of ((cK X04) Xx0)
% 32.53/32.71 Found ((x6 Xx0) x7) as proof of ((cK X04) Xx0)
% 32.53/32.71 Found x8:(X04 Xx1)
% 32.53/32.71 Found x8 as proof of (X03 Xx1)
% 32.53/32.71 Found (fun (x8:(X04 Xx1))=> x8) as proof of (X03 Xx1)
% 32.53/32.71 Found (fun (Xx1:a) (x8:(X04 Xx1))=> x8) as proof of ((X04 Xx1)->(X03 Xx1))
% 32.53/32.71 Found (fun (Xx1:a) (x8:(X04 Xx1))=> x8) as proof of (forall (Xx:a), ((X04 Xx)->(X03 Xx)))
% 32.53/32.71 Found x600:=(x60 x7):((cK x3) Xx0)
% 32.53/32.71 Found (x60 x7) as proof of ((cK X04) Xx0)
% 32.53/32.71 Found ((x6 Xx0) x7) as proof of ((cK X04) Xx0)
% 32.53/32.71 Found ((x6 Xx0) x7) as proof of ((cK X04) Xx0)
% 32.53/32.71 Found ((x6 Xx0) x7) as proof of ((cK X04) Xx0)
% 32.53/32.71 Found x8:(X04 Xx1)
% 32.53/32.71 Found x8 as proof of (X03 Xx1)
% 32.53/32.71 Found (fun (x8:(X04 Xx1))=> x8) as proof of (X03 Xx1)
% 32.53/32.71 Found (fun (Xx1:a) (x8:(X04 Xx1))=> x8) as proof of ((X04 Xx1)->(X03 Xx1))
% 32.53/32.71 Found (fun (Xx1:a) (x8:(X04 Xx1))=> x8) as proof of (forall (Xx:a), ((X04 Xx)->(X03 Xx)))
% 32.53/32.71 Found x600:=(x60 x7):((cK x4) Xx0)
% 32.53/32.71 Found (x60 x7) as proof of ((cK X04) Xx0)
% 32.53/32.71 Found ((x6 Xx0) x7) as proof of ((cK X04) Xx0)
% 32.53/32.71 Found ((x6 Xx0) x7) as proof of ((cK X04) Xx0)
% 32.53/32.71 Found ((x6 Xx0) x7) as proof of ((cK X04) Xx0)
% 32.53/32.71 Found x8:(X04 Xx1)
% 32.53/32.71 Found x8 as proof of (X03 Xx1)
% 32.53/32.71 Found (fun (x8:(X04 Xx1))=> x8) as proof of (X03 Xx1)
% 32.53/32.71 Found (fun (Xx1:a) (x8:(X04 Xx1))=> x8) as proof of ((X04 Xx1)->(X03 Xx1))
% 32.53/32.71 Found (fun (Xx1:a) (x8:(X04 Xx1))=> x8) as proof of (forall (Xx:a), ((X04 Xx)->(X03 Xx)))
% 32.53/32.71 Found x600:=(x60 x7):((cK x3) Xx0)
% 32.53/32.71 Found (x60 x7) as proof of ((cK X04) Xx0)
% 32.53/32.71 Found ((x6 Xx0) x7) as proof of ((cK X04) Xx0)
% 32.53/32.71 Found ((x6 Xx0) x7) as proof of ((cK X04) Xx0)
% 32.53/32.71 Found ((x6 Xx0) x7) as proof of ((cK X04) Xx0)
% 32.53/32.71 Found x8:(X04 Xx1)
% 32.53/32.71 Found x8 as proof of (X03 Xx1)
% 32.53/32.71 Found (fun (x8:(X04 Xx1))=> x8) as proof of (X03 Xx1)
% 32.53/32.71 Found (fun (Xx1:a) (x8:(X04 Xx1))=> x8) as proof of ((X04 Xx1)->(X03 Xx1))
% 32.53/32.71 Found (fun (Xx1:a) (x8:(X04 Xx1))=> x8) as proof of (forall (Xx:a), ((X04 Xx)->(X03 Xx)))
% 32.53/32.71 Found x600:=(x60 x7):((cK x4) Xx0)
% 32.53/32.71 Found (x60 x7) as proof of ((cK X04) Xx0)
% 32.53/32.71 Found ((x6 Xx0) x7) as proof of ((cK X04) Xx0)
% 32.53/32.71 Found ((x6 Xx0) x7) as proof of ((cK X04) Xx0)
% 32.53/32.71 Found ((x6 Xx0) x7) as proof of ((cK X04) Xx0)
% 32.53/32.71 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 32.53/32.71 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X04) Xx0))
% 33.27/33.44 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X04) Xx0))
% 33.27/33.44 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X04) Xx0))
% 33.27/33.44 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X04) Xx0)))
% 33.27/33.44 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X04) Xx0)
% 33.27/33.44 Found ((and_rect0 ((cK X04) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X04) Xx0)
% 33.27/33.44 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X04) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X04) Xx0)
% 33.27/33.44 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X04) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X04) Xx0)
% 33.27/33.44 Found x6:(X04 Xx1)
% 33.27/33.44 Instantiate: X03:=X04:(a->Prop)
% 33.27/33.44 Found (fun (x6:(X04 Xx1))=> x6) as proof of (X03 Xx1)
% 33.27/33.44 Found (fun (Xx1:a) (x6:(X04 Xx1))=> x6) as proof of ((X04 Xx1)->(X03 Xx1))
% 33.27/33.44 Found (fun (Xx1:a) (x6:(X04 Xx1))=> x6) as proof of (forall (Xx:a), ((X04 Xx)->(X03 Xx)))
% 33.27/33.44 Found ((x350 (fun (Xx1:a) (x6:(X04 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X04) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X03) Xx0)
% 33.27/33.44 Found (((x35 X03) (fun (Xx1:a) (x6:(X04 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X04) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X03) Xx0)
% 33.27/33.44 Found ((((x3 x4) X03) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X03) Xx0)
% 33.27/33.44 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> ((((x3 x4) X03) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))))) as proof of ((cK X03) Xx0)
% 33.27/33.44 Found x8:(X04 Xx1)
% 33.27/33.44 Found x8 as proof of (X03 Xx1)
% 33.27/33.44 Found (fun (x8:(X04 Xx1))=> x8) as proof of (X03 Xx1)
% 33.27/33.44 Found (fun (Xx1:a) (x8:(X04 Xx1))=> x8) as proof of ((X04 Xx1)->(X03 Xx1))
% 33.27/33.44 Found (fun (Xx1:a) (x8:(X04 Xx1))=> x8) as proof of (forall (Xx:a), ((X04 Xx)->(X03 Xx)))
% 33.27/33.44 Found x600:=(x60 x7):((cK x3) Xx0)
% 33.27/33.44 Found (x60 x7) as proof of ((cK X04) Xx0)
% 33.27/33.44 Found ((x6 Xx0) x7) as proof of ((cK X04) Xx0)
% 33.27/33.44 Found ((x6 Xx0) x7) as proof of ((cK X04) Xx0)
% 33.27/33.44 Found ((x6 Xx0) x7) as proof of ((cK X04) Xx0)
% 33.27/33.44 Found x8:(X04 Xx1)
% 33.27/33.44 Found x8 as proof of (X03 Xx1)
% 33.27/33.44 Found (fun (x8:(X04 Xx1))=> x8) as proof of (X03 Xx1)
% 33.27/33.44 Found (fun (Xx1:a) (x8:(X04 Xx1))=> x8) as proof of ((X04 Xx1)->(X03 Xx1))
% 33.27/33.44 Found (fun (Xx1:a) (x8:(X04 Xx1))=> x8) as proof of (forall (Xx:a), ((X04 Xx)->(X03 Xx)))
% 33.27/33.44 Found x600:=(x60 x7):((cK x4) Xx0)
% 33.27/33.44 Found (x60 x7) as proof of ((cK X04) Xx0)
% 33.27/33.44 Found ((x6 Xx0) x7) as proof of ((cK X04) Xx0)
% 33.27/33.44 Found ((x6 Xx0) x7) as proof of ((cK X04) Xx0)
% 33.27/33.44 Found ((x6 Xx0) x7) as proof of ((cK X04) Xx0)
% 33.27/33.44 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 33.27/33.44 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X04) Xx0))
% 33.27/33.44 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X04) Xx0))
% 33.27/33.44 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X04) Xx0))
% 33.27/33.44 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X04) Xx0)))
% 33.88/34.10 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X04) Xx0)
% 33.88/34.10 Found ((and_rect0 ((cK X04) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X04) Xx0)
% 33.88/34.10 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X04) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X04) Xx0)
% 33.88/34.10 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X04) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X04) Xx0)
% 33.88/34.10 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 33.88/34.10 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X04) Xx0))
% 33.88/34.10 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X04) Xx0))
% 33.88/34.10 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X04) Xx0))
% 33.88/34.10 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X04) Xx0)))
% 33.88/34.10 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X04) Xx0)
% 33.88/34.10 Found ((and_rect0 ((cK X04) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X04) Xx0)
% 33.88/34.10 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X04) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X04) Xx0)
% 33.88/34.10 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X04) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X04) Xx0)
% 33.88/34.10 Found x6:(X04 Xx1)
% 33.88/34.10 Instantiate: X03:=X04:(a->Prop)
% 33.88/34.10 Found (fun (x6:(X04 Xx1))=> x6) as proof of (X03 Xx1)
% 33.88/34.10 Found (fun (Xx1:a) (x6:(X04 Xx1))=> x6) as proof of ((X04 Xx1)->(X03 Xx1))
% 33.88/34.10 Found (fun (Xx1:a) (x6:(X04 Xx1))=> x6) as proof of (forall (Xx:a), ((X04 Xx)->(X03 Xx)))
% 33.88/34.10 Found ((x350 (fun (Xx1:a) (x6:(X04 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X04) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X03) Xx0)
% 33.88/34.10 Found (((x35 X03) (fun (Xx1:a) (x6:(X04 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X04) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X03) Xx0)
% 33.88/34.10 Found ((((x3 x4) X03) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X03) Xx0)
% 33.88/34.10 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> ((((x3 x4) X03) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))))) as proof of ((cK X03) Xx0)
% 33.88/34.10 Found x4:(X04 Xx1)
% 33.88/34.10 Instantiate: X04:=(cK x5):(a->Prop)
% 33.88/34.10 Found x4 as proof of (X03 Xx1)
% 33.88/34.10 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X03 Xx1)
% 33.88/34.10 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X03 Xx1))
% 34.92/35.14 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X03 Xx1)))
% 34.92/35.14 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X03 Xx1)
% 34.92/35.14 Found ((and_rect0 (X03 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X03 Xx1)
% 34.92/35.14 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X03 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X03 Xx1)
% 34.92/35.14 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X03 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X03 Xx1)
% 34.92/35.14 Found x4:(X04 Xx1)
% 34.92/35.14 Found x4 as proof of (X03 Xx1)
% 34.92/35.14 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X03 Xx1)
% 34.92/35.14 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X03 Xx1))
% 34.92/35.14 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X03 Xx1)))
% 34.92/35.14 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X03 Xx1)
% 34.92/35.14 Found ((and_rect0 (X03 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X03 Xx1)
% 34.92/35.14 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X03 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X03 Xx1)
% 34.92/35.14 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X03 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X03 Xx1)
% 34.92/35.14 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 34.92/35.14 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X04) Xx0))
% 34.92/35.14 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X04) Xx0))
% 34.92/35.14 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X04) Xx0))
% 34.92/35.14 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X04) Xx0)))
% 34.92/35.14 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X04) Xx0)
% 34.92/35.14 Found ((and_rect0 ((cK X04) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X04) Xx0)
% 34.92/35.14 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X04) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X04) Xx0)
% 34.92/35.14 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X04) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X04) Xx0)
% 34.92/35.14 Found x4:(X04 Xx1)
% 34.92/35.14 Instantiate: X04:=(cK x5):(a->Prop)
% 34.92/35.14 Found x4 as proof of (X03 Xx1)
% 34.92/35.14 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X03 Xx1)
% 34.92/35.14 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X03 Xx1))
% 34.92/35.14 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X03 Xx1)))
% 35.20/35.42 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X03 Xx1)
% 35.20/35.42 Found ((and_rect0 (X03 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X03 Xx1)
% 35.20/35.42 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X03 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X03 Xx1)
% 35.20/35.42 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X03 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X03 Xx1)
% 35.20/35.42 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 35.20/35.42 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X04) Xx0))
% 35.20/35.42 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X04) Xx0))
% 35.20/35.42 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X04) Xx0))
% 35.20/35.42 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X04) Xx0)))
% 35.20/35.42 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X04) Xx0)
% 35.20/35.42 Found ((and_rect0 ((cK X04) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X04) Xx0)
% 35.20/35.42 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X04) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X04) Xx0)
% 35.20/35.42 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X04) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X04) Xx0)
% 35.20/35.42 Found x6:(X04 Xx1)
% 35.20/35.42 Instantiate: X03:=X04:(a->Prop)
% 35.20/35.42 Found (fun (x6:(X04 Xx1))=> x6) as proof of (X03 Xx1)
% 35.20/35.42 Found (fun (Xx1:a) (x6:(X04 Xx1))=> x6) as proof of ((X04 Xx1)->(X03 Xx1))
% 35.20/35.42 Found (fun (Xx1:a) (x6:(X04 Xx1))=> x6) as proof of (forall (Xx:a), ((X04 Xx)->(X03 Xx)))
% 35.20/35.42 Found ((x350 (fun (Xx1:a) (x6:(X04 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X04) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X03) Xx0)
% 35.20/35.42 Found (((x35 X03) (fun (Xx1:a) (x6:(X04 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X04) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X03) Xx0)
% 35.20/35.42 Found ((((x3 x4) X03) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X03) Xx0)
% 35.20/35.42 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> ((((x3 x4) X03) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))))) as proof of ((cK X03) Xx0)
% 35.20/35.42 Found x4:(X04 Xx1)
% 35.20/35.42 Found x4 as proof of (X03 Xx1)
% 35.20/35.42 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X03 Xx1)
% 35.20/35.42 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X03 Xx1))
% 35.20/35.42 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X03 Xx1)))
% 36.13/36.32 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X03 Xx1)
% 36.13/36.32 Found ((and_rect0 (X03 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X03 Xx1)
% 36.13/36.32 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X03 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X03 Xx1)
% 36.13/36.32 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X03 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X03 Xx1)
% 36.13/36.32 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 36.13/36.32 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X04) Xx0))
% 36.13/36.32 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X04) Xx0))
% 36.13/36.32 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X04) Xx0))
% 36.13/36.32 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X04) Xx0)))
% 36.13/36.32 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X04) Xx0)
% 36.13/36.32 Found ((and_rect0 ((cK X04) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X04) Xx0)
% 36.13/36.32 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X04) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X04) Xx0)
% 36.13/36.32 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X04) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X04) Xx0)
% 36.13/36.32 Found x4:(X04 Xx1)
% 36.13/36.32 Instantiate: X04:=(cK x5):(a->Prop)
% 36.13/36.32 Found x4 as proof of (X03 Xx1)
% 36.13/36.32 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X03 Xx1)
% 36.13/36.32 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X03 Xx1))
% 36.13/36.32 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X03 Xx1)))
% 36.13/36.32 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X03 Xx1)
% 36.13/36.32 Found ((and_rect0 (X03 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X03 Xx1)
% 36.13/36.32 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X03 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X03 Xx1)
% 36.13/36.32 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X03 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X03 Xx1)
% 36.13/36.32 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 36.13/36.32 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X04) Xx0))
% 36.13/36.32 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X04) Xx0))
% 36.13/36.32 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X04) Xx0))
% 36.13/36.32 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X04) Xx0)))
% 36.13/36.32 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X04) Xx0)
% 36.42/36.65 Found ((and_rect0 ((cK X04) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X04) Xx0)
% 36.42/36.65 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X04) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X04) Xx0)
% 36.42/36.65 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X04) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X04) Xx0)
% 36.42/36.65 Found x6:(X04 Xx1)
% 36.42/36.65 Instantiate: X03:=X04:(a->Prop)
% 36.42/36.65 Found (fun (x6:(X04 Xx1))=> x6) as proof of (X03 Xx1)
% 36.42/36.65 Found (fun (Xx1:a) (x6:(X04 Xx1))=> x6) as proof of ((X04 Xx1)->(X03 Xx1))
% 36.42/36.65 Found (fun (Xx1:a) (x6:(X04 Xx1))=> x6) as proof of (forall (Xx:a), ((X04 Xx)->(X03 Xx)))
% 36.42/36.65 Found ((x350 (fun (Xx1:a) (x6:(X04 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X04) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X03) Xx0)
% 36.42/36.65 Found (((x35 X03) (fun (Xx1:a) (x6:(X04 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X04) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X03) Xx0)
% 36.42/36.65 Found ((((x3 x4) X03) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X03) Xx0)
% 36.42/36.65 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> ((((x3 x4) X03) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))))) as proof of ((cK X03) Xx0)
% 36.42/36.65 Found x4:(X04 Xx1)
% 36.42/36.65 Found x4 as proof of (X03 Xx1)
% 36.42/36.65 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X03 Xx1)
% 36.42/36.65 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X03 Xx1))
% 36.42/36.65 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X03 Xx1)))
% 36.42/36.65 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X03 Xx1)
% 36.42/36.65 Found ((and_rect0 (X03 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X03 Xx1)
% 36.42/36.65 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X03 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X03 Xx1)
% 36.42/36.65 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X03 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X03 Xx1)
% 36.42/36.65 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 36.42/36.65 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X04) Xx0))
% 36.42/36.65 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X04) Xx0))
% 36.42/36.65 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X04) Xx0))
% 36.42/36.65 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X04) Xx0)))
% 37.03/37.23 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X04) Xx0)
% 37.03/37.23 Found ((and_rect0 ((cK X04) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X04) Xx0)
% 37.03/37.23 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X04) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X04) Xx0)
% 37.03/37.23 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X04) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X04) Xx0)
% 37.03/37.23 Found x4:(X04 Xx1)
% 37.03/37.23 Instantiate: X04:=(cK x5):(a->Prop)
% 37.03/37.23 Found x4 as proof of (X03 Xx1)
% 37.03/37.23 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X03 Xx1)
% 37.03/37.23 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X03 Xx1))
% 37.03/37.23 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X03 Xx1)))
% 37.03/37.23 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X03 Xx1)
% 37.03/37.23 Found ((and_rect0 (X03 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X03 Xx1)
% 37.03/37.23 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X03 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X03 Xx1)
% 37.03/37.23 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X03 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X03 Xx1)
% 37.03/37.23 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 37.03/37.23 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X04) Xx0))
% 37.03/37.23 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X04) Xx0))
% 37.03/37.23 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X04) Xx0))
% 37.03/37.23 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X04) Xx0)))
% 37.03/37.23 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X04) Xx0)
% 37.03/37.23 Found ((and_rect0 ((cK X04) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X04) Xx0)
% 37.03/37.23 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X04) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X04) Xx0)
% 37.03/37.23 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X04) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X04) Xx0)
% 37.03/37.23 Found x6:(X04 Xx1)
% 37.03/37.23 Instantiate: X03:=X04:(a->Prop)
% 37.03/37.23 Found (fun (x6:(X04 Xx1))=> x6) as proof of (X03 Xx1)
% 37.03/37.23 Found (fun (Xx1:a) (x6:(X04 Xx1))=> x6) as proof of ((X04 Xx1)->(X03 Xx1))
% 37.03/37.23 Found (fun (Xx1:a) (x6:(X04 Xx1))=> x6) as proof of (forall (Xx:a), ((X04 Xx)->(X03 Xx)))
% 37.03/37.23 Found ((x350 (fun (Xx1:a) (x6:(X04 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X04) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X03) Xx0)
% 37.03/37.23 Found (((x35 X03) (fun (Xx1:a) (x6:(X04 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X04) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X03) Xx0)
% 39.21/39.44 Found ((((x3 x4) X03) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X03) Xx0)
% 39.21/39.44 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> ((((x3 x4) X03) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))))) as proof of ((cK X03) Xx0)
% 39.21/39.44 Found x4:(X04 Xx1)
% 39.21/39.44 Found x4 as proof of (X03 Xx1)
% 39.21/39.44 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X03 Xx1)
% 39.21/39.44 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X03 Xx1))
% 39.21/39.44 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X03 Xx1)))
% 39.21/39.44 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X03 Xx1)
% 39.21/39.44 Found ((and_rect0 (X03 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X03 Xx1)
% 39.21/39.44 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X03 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X03 Xx1)
% 39.21/39.44 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X03 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X03 Xx1)
% 39.21/39.44 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 39.21/39.44 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X04) Xx0))
% 39.21/39.44 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X04) Xx0))
% 39.21/39.44 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X04) Xx0))
% 39.21/39.44 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X04) Xx0)))
% 39.21/39.44 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X04) Xx0)
% 39.21/39.44 Found ((and_rect0 ((cK X04) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X04) Xx0)
% 39.21/39.44 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X04) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X04) Xx0)
% 39.21/39.44 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X04) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X04) Xx0)
% 39.21/39.44 Found x4:(X05 Xx1)
% 39.21/39.44 Found x4 as proof of (X04 Xx1)
% 39.21/39.44 Found (fun (x4:(X05 Xx1))=> x4) as proof of (X04 Xx1)
% 39.21/39.44 Found (fun (Xx1:a) (x4:(X05 Xx1))=> x4) as proof of ((X05 Xx1)->(X04 Xx1))
% 39.21/39.44 Found (fun (Xx1:a) (x4:(X05 Xx1))=> x4) as proof of (forall (Xx:a), ((X05 Xx)->(X04 Xx)))
% 39.21/39.44 Found x6:(X05 Xx1)
% 39.21/39.44 Found x6 as proof of (X04 Xx1)
% 39.21/39.44 Found (fun (x6:(X05 Xx1))=> x6) as proof of (X04 Xx1)
% 39.21/39.44 Found (fun (Xx1:a) (x6:(X05 Xx1))=> x6) as proof of ((X05 Xx1)->(X04 Xx1))
% 39.21/39.44 Found (fun (Xx1:a) (x6:(X05 Xx1))=> x6) as proof of (forall (Xx:a), ((X05 Xx)->(X04 Xx)))
% 44.46/44.67 Found x6:(X05 Xx1)
% 44.46/44.67 Found x6 as proof of (X04 Xx1)
% 44.46/44.67 Found (fun (x6:(X05 Xx1))=> x6) as proof of (X04 Xx1)
% 44.46/44.67 Found (fun (Xx1:a) (x6:(X05 Xx1))=> x6) as proof of ((X05 Xx1)->(X04 Xx1))
% 44.46/44.67 Found (fun (Xx1:a) (x6:(X05 Xx1))=> x6) as proof of (forall (Xx:a), ((X05 Xx)->(X04 Xx)))
% 44.46/44.67 Found x6:(X05 Xx1)
% 44.46/44.67 Found x6 as proof of (X04 Xx1)
% 44.46/44.67 Found (fun (x6:(X05 Xx1))=> x6) as proof of (X04 Xx1)
% 44.46/44.67 Found (fun (Xx1:a) (x6:(X05 Xx1))=> x6) as proof of ((X05 Xx1)->(X04 Xx1))
% 44.46/44.67 Found (fun (Xx1:a) (x6:(X05 Xx1))=> x6) as proof of (forall (Xx:a), ((X05 Xx)->(X04 Xx)))
% 44.46/44.67 Found x6:(X05 Xx1)
% 44.46/44.67 Found x6 as proof of (X04 Xx1)
% 44.46/44.67 Found (fun (x6:(X05 Xx1))=> x6) as proof of (X04 Xx1)
% 44.46/44.67 Found (fun (Xx1:a) (x6:(X05 Xx1))=> x6) as proof of ((X05 Xx1)->(X04 Xx1))
% 44.46/44.67 Found (fun (Xx1:a) (x6:(X05 Xx1))=> x6) as proof of (forall (Xx:a), ((X05 Xx)->(X04 Xx)))
% 44.46/44.67 Found x6:(X05 Xx1)
% 44.46/44.67 Found x6 as proof of (X04 Xx1)
% 44.46/44.67 Found (fun (x6:(X05 Xx1))=> x6) as proof of (X04 Xx1)
% 44.46/44.67 Found (fun (Xx1:a) (x6:(X05 Xx1))=> x6) as proof of ((X05 Xx1)->(X04 Xx1))
% 44.46/44.67 Found (fun (Xx1:a) (x6:(X05 Xx1))=> x6) as proof of (forall (Xx:a), ((X05 Xx)->(X04 Xx)))
% 44.46/44.67 Found x4:(X04 Xx1)
% 44.46/44.67 Instantiate: X04:=(cK x5):(a->Prop)
% 44.46/44.67 Found x4 as proof of (X03 Xx1)
% 44.46/44.67 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X03 Xx1)
% 44.46/44.67 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X03 Xx1))
% 44.46/44.67 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X03 Xx1)))
% 44.46/44.67 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X03 Xx1)
% 44.46/44.67 Found ((and_rect0 (X03 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X03 Xx1)
% 44.46/44.67 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X03 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X03 Xx1)
% 44.46/44.67 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X03 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X03 Xx1)
% 44.46/44.67 Found x6:(X05 Xx1)
% 44.46/44.67 Found x6 as proof of (X04 Xx1)
% 44.46/44.67 Found (fun (x6:(X05 Xx1))=> x6) as proof of (X04 Xx1)
% 44.46/44.67 Found (fun (Xx1:a) (x6:(X05 Xx1))=> x6) as proof of ((X05 Xx1)->(X04 Xx1))
% 44.46/44.67 Found (fun (Xx1:a) (x6:(X05 Xx1))=> x6) as proof of (forall (Xx:a), ((X05 Xx)->(X04 Xx)))
% 44.46/44.67 Found x6:(X05 Xx1)
% 44.46/44.67 Found x6 as proof of (X04 Xx1)
% 44.46/44.67 Found (fun (x6:(X05 Xx1))=> x6) as proof of (X04 Xx1)
% 44.46/44.67 Found (fun (Xx1:a) (x6:(X05 Xx1))=> x6) as proof of ((X05 Xx1)->(X04 Xx1))
% 44.46/44.67 Found (fun (Xx1:a) (x6:(X05 Xx1))=> x6) as proof of (forall (Xx:a), ((X05 Xx)->(X04 Xx)))
% 44.46/44.67 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 44.46/44.67 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X05) Xx0))
% 44.46/44.68 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X05) Xx0))
% 44.46/44.68 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X05) Xx0))
% 44.46/44.68 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X05) Xx0)))
% 44.46/44.68 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X05) Xx0)
% 44.46/44.68 Found ((and_rect0 ((cK X05) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X05) Xx0)
% 44.46/44.68 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X05) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X05) Xx0)
% 44.46/44.68 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X05) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X05) Xx0)
% 44.89/45.09 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 44.89/45.09 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X05) Xx0))
% 44.89/45.09 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X05) Xx0))
% 44.89/45.09 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X05) Xx0))
% 44.89/45.09 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X05) Xx0)))
% 44.89/45.09 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X05) Xx0)
% 44.89/45.09 Found ((and_rect0 ((cK X05) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X05) Xx0)
% 44.89/45.09 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X05) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X05) Xx0)
% 44.89/45.09 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X05) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X05) Xx0)
% 44.89/45.09 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 44.89/45.09 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X05) Xx0))
% 44.89/45.09 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X05) Xx0))
% 44.89/45.09 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X05) Xx0))
% 44.89/45.09 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X05) Xx0)))
% 44.89/45.09 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X05) Xx0)
% 44.89/45.09 Found ((and_rect0 ((cK X05) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X05) Xx0)
% 44.89/45.09 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X05) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X05) Xx0)
% 44.89/45.09 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X05) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X05) Xx0)
% 44.89/45.09 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 44.89/45.09 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X05) Xx0))
% 44.89/45.09 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X05) Xx0))
% 44.89/45.09 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X05) Xx0))
% 44.89/45.09 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X05) Xx0)))
% 44.89/45.09 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X05) Xx0)
% 44.89/45.09 Found ((and_rect0 ((cK X05) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X05) Xx0)
% 44.89/45.09 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X05) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X05) Xx0)
% 44.89/45.09 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X05) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X05) Xx0)
% 44.89/45.09 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 44.89/45.09 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X05) Xx0))
% 44.89/45.09 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X05) Xx0))
% 44.89/45.09 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X05) Xx0))
% 44.89/45.09 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X05) Xx0)))
% 46.51/46.70 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X05) Xx0)
% 46.51/46.70 Found ((and_rect0 ((cK X05) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X05) Xx0)
% 46.51/46.70 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X05) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X05) Xx0)
% 46.51/46.70 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X05) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X05) Xx0)
% 46.51/46.70 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 46.51/46.70 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X05) Xx0))
% 46.51/46.70 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X05) Xx0))
% 46.51/46.70 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X05) Xx0))
% 46.51/46.70 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X05) Xx0)))
% 46.51/46.70 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X05) Xx0)
% 46.51/46.70 Found ((and_rect0 ((cK X05) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X05) Xx0)
% 46.51/46.70 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X05) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X05) Xx0)
% 46.51/46.70 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X05) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X05) Xx0)
% 46.51/46.70 Found x8:(X05 Xx1)
% 46.51/46.70 Found x8 as proof of (X04 Xx1)
% 46.51/46.70 Found (fun (x8:(X05 Xx1))=> x8) as proof of (X04 Xx1)
% 46.51/46.70 Found (fun (Xx1:a) (x8:(X05 Xx1))=> x8) as proof of ((X05 Xx1)->(X04 Xx1))
% 46.51/46.70 Found (fun (Xx1:a) (x8:(X05 Xx1))=> x8) as proof of (forall (Xx:a), ((X05 Xx)->(X04 Xx)))
% 46.51/46.70 Found x600:=(x60 x7):((cK x4) Xx0)
% 46.51/46.70 Found (x60 x7) as proof of ((cK X05) Xx0)
% 46.51/46.70 Found ((x6 Xx0) x7) as proof of ((cK X05) Xx0)
% 46.51/46.70 Found ((x6 Xx0) x7) as proof of ((cK X05) Xx0)
% 46.51/46.70 Found ((x6 Xx0) x7) as proof of ((cK X05) Xx0)
% 46.51/46.70 Found x8:(X05 Xx1)
% 46.51/46.70 Found x8 as proof of (X04 Xx1)
% 46.51/46.70 Found (fun (x8:(X05 Xx1))=> x8) as proof of (X04 Xx1)
% 46.51/46.70 Found (fun (Xx1:a) (x8:(X05 Xx1))=> x8) as proof of ((X05 Xx1)->(X04 Xx1))
% 46.51/46.70 Found (fun (Xx1:a) (x8:(X05 Xx1))=> x8) as proof of (forall (Xx:a), ((X05 Xx)->(X04 Xx)))
% 46.51/46.70 Found x600:=(x60 x7):((cK x4) Xx0)
% 46.51/46.70 Found (x60 x7) as proof of ((cK X05) Xx0)
% 46.51/46.70 Found ((x6 Xx0) x7) as proof of ((cK X05) Xx0)
% 46.51/46.70 Found ((x6 Xx0) x7) as proof of ((cK X05) Xx0)
% 46.51/46.70 Found ((x6 Xx0) x7) as proof of ((cK X05) Xx0)
% 46.51/46.70 Found x8:(X05 Xx1)
% 46.51/46.70 Found x8 as proof of (X04 Xx1)
% 46.51/46.70 Found (fun (x8:(X05 Xx1))=> x8) as proof of (X04 Xx1)
% 46.51/46.70 Found (fun (Xx1:a) (x8:(X05 Xx1))=> x8) as proof of ((X05 Xx1)->(X04 Xx1))
% 46.51/46.70 Found (fun (Xx1:a) (x8:(X05 Xx1))=> x8) as proof of (forall (Xx:a), ((X05 Xx)->(X04 Xx)))
% 46.51/46.70 Found x600:=(x60 x7):((cK x4) Xx0)
% 46.51/46.70 Found (x60 x7) as proof of ((cK X05) Xx0)
% 46.51/46.70 Found ((x6 Xx0) x7) as proof of ((cK X05) Xx0)
% 46.51/46.70 Found ((x6 Xx0) x7) as proof of ((cK X05) Xx0)
% 46.51/46.70 Found ((x6 Xx0) x7) as proof of ((cK X05) Xx0)
% 46.51/46.70 Found x8:(X05 Xx1)
% 46.51/46.70 Found x8 as proof of (X04 Xx1)
% 46.51/46.70 Found (fun (x8:(X05 Xx1))=> x8) as proof of (X04 Xx1)
% 46.51/46.70 Found (fun (Xx1:a) (x8:(X05 Xx1))=> x8) as proof of ((X05 Xx1)->(X04 Xx1))
% 46.51/46.70 Found (fun (Xx1:a) (x8:(X05 Xx1))=> x8) as proof of (forall (Xx:a), ((X05 Xx)->(X04 Xx)))
% 46.51/46.70 Found x600:=(x60 x7):((cK x3) Xx0)
% 46.51/46.70 Found (x60 x7) as proof of ((cK X05) Xx0)
% 46.51/46.70 Found ((x6 Xx0) x7) as proof of ((cK X05) Xx0)
% 46.51/46.70 Found ((x6 Xx0) x7) as proof of ((cK X05) Xx0)
% 46.51/46.70 Found ((x6 Xx0) x7) as proof of ((cK X05) Xx0)
% 46.51/46.70 Found x8:(X05 Xx1)
% 47.20/47.41 Found x8 as proof of (X04 Xx1)
% 47.20/47.41 Found (fun (x8:(X05 Xx1))=> x8) as proof of (X04 Xx1)
% 47.20/47.41 Found (fun (Xx1:a) (x8:(X05 Xx1))=> x8) as proof of ((X05 Xx1)->(X04 Xx1))
% 47.20/47.41 Found (fun (Xx1:a) (x8:(X05 Xx1))=> x8) as proof of (forall (Xx:a), ((X05 Xx)->(X04 Xx)))
% 47.20/47.41 Found x600:=(x60 x7):((cK x4) Xx0)
% 47.20/47.41 Found (x60 x7) as proof of ((cK X05) Xx0)
% 47.20/47.41 Found ((x6 Xx0) x7) as proof of ((cK X05) Xx0)
% 47.20/47.41 Found ((x6 Xx0) x7) as proof of ((cK X05) Xx0)
% 47.20/47.41 Found ((x6 Xx0) x7) as proof of ((cK X05) Xx0)
% 47.20/47.41 Found x4:(X04 Xx1)
% 47.20/47.41 Found x4 as proof of (X03 Xx1)
% 47.20/47.41 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X03 Xx1)
% 47.20/47.41 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X03 Xx1))
% 47.20/47.41 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X03 Xx1)))
% 47.20/47.41 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X03 Xx1)
% 47.20/47.41 Found ((and_rect0 (X03 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X03 Xx1)
% 47.20/47.41 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X03 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X03 Xx1)
% 47.20/47.41 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X03 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X03 Xx1)
% 47.20/47.41 Found x8:(X05 Xx1)
% 47.20/47.41 Found x8 as proof of (X04 Xx1)
% 47.20/47.41 Found (fun (x8:(X05 Xx1))=> x8) as proof of (X04 Xx1)
% 47.20/47.41 Found (fun (Xx1:a) (x8:(X05 Xx1))=> x8) as proof of ((X05 Xx1)->(X04 Xx1))
% 47.20/47.41 Found (fun (Xx1:a) (x8:(X05 Xx1))=> x8) as proof of (forall (Xx:a), ((X05 Xx)->(X04 Xx)))
% 47.20/47.41 Found x600:=(x60 x7):((cK x4) Xx0)
% 47.20/47.41 Found (x60 x7) as proof of ((cK X05) Xx0)
% 47.20/47.41 Found ((x6 Xx0) x7) as proof of ((cK X05) Xx0)
% 47.20/47.41 Found ((x6 Xx0) x7) as proof of ((cK X05) Xx0)
% 47.20/47.41 Found ((x6 Xx0) x7) as proof of ((cK X05) Xx0)
% 47.20/47.41 Found x8:(X05 Xx1)
% 47.20/47.41 Found x8 as proof of (X04 Xx1)
% 47.20/47.41 Found (fun (x8:(X05 Xx1))=> x8) as proof of (X04 Xx1)
% 47.20/47.41 Found (fun (Xx1:a) (x8:(X05 Xx1))=> x8) as proof of ((X05 Xx1)->(X04 Xx1))
% 47.20/47.41 Found (fun (Xx1:a) (x8:(X05 Xx1))=> x8) as proof of (forall (Xx:a), ((X05 Xx)->(X04 Xx)))
% 47.20/47.41 Found x600:=(x60 x7):((cK x4) Xx0)
% 47.20/47.41 Found (x60 x7) as proof of ((cK X05) Xx0)
% 47.20/47.41 Found ((x6 Xx0) x7) as proof of ((cK X05) Xx0)
% 47.20/47.41 Found ((x6 Xx0) x7) as proof of ((cK X05) Xx0)
% 47.20/47.41 Found ((x6 Xx0) x7) as proof of ((cK X05) Xx0)
% 47.20/47.41 Found x8:(X05 Xx1)
% 47.20/47.41 Found x8 as proof of (X04 Xx1)
% 47.20/47.41 Found (fun (x8:(X05 Xx1))=> x8) as proof of (X04 Xx1)
% 47.20/47.41 Found (fun (Xx1:a) (x8:(X05 Xx1))=> x8) as proof of ((X05 Xx1)->(X04 Xx1))
% 47.20/47.41 Found (fun (Xx1:a) (x8:(X05 Xx1))=> x8) as proof of (forall (Xx:a), ((X05 Xx)->(X04 Xx)))
% 47.20/47.41 Found x600:=(x60 x7):((cK x4) Xx0)
% 47.20/47.41 Found (x60 x7) as proof of ((cK X05) Xx0)
% 47.20/47.41 Found ((x6 Xx0) x7) as proof of ((cK X05) Xx0)
% 47.20/47.41 Found ((x6 Xx0) x7) as proof of ((cK X05) Xx0)
% 47.20/47.41 Found ((x6 Xx0) x7) as proof of ((cK X05) Xx0)
% 47.20/47.41 Found x60:=(x6 Xx0):((x3 Xx0)->((cK x3) Xx0))
% 47.20/47.41 Found (x6 Xx0) as proof of ((x3 Xx0)->((cK X05) Xx0))
% 47.20/47.41 Found (x6 Xx0) as proof of ((x3 Xx0)->((cK X05) Xx0))
% 47.20/47.41 Found (fun (x6:(forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1))))=> (x6 Xx0)) as proof of ((x3 Xx0)->((cK X05) Xx0))
% 47.20/47.41 Found (fun (x6:(forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1)))->((x3 Xx0)->((cK X05) Xx0)))
% 47.20/47.41 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1))))=> (x6 Xx0))) as proof of ((cK X05) Xx0)
% 47.20/47.41 Found ((and_rect0 ((cK X05) Xx0)) (fun (x6:(forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1))))=> (x6 Xx0))) as proof of ((cK X05) Xx0)
% 47.20/47.41 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1)))->((x3 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1)))) (x3 Xx0)) P) x6) x4)) ((cK X05) Xx0)) (fun (x6:(forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1))))=> (x6 Xx0))) as proof of ((cK X05) Xx0)
% 48.14/48.36 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1)))->((x3 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1)))) (x3 Xx0)) P) x6) x4)) ((cK X05) Xx0)) (fun (x6:(forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1))))=> (x6 Xx0))) as proof of ((cK X05) Xx0)
% 48.14/48.36 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 48.14/48.36 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X05) Xx0))
% 48.14/48.36 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X05) Xx0))
% 48.14/48.36 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X05) Xx0))
% 48.14/48.36 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X05) Xx0)))
% 48.14/48.36 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X05) Xx0)
% 48.14/48.36 Found ((and_rect0 ((cK X05) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X05) Xx0)
% 48.14/48.36 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X05) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X05) Xx0)
% 48.14/48.36 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X05) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X05) Xx0)
% 48.14/48.36 Found x8:(X05 Xx1)
% 48.14/48.36 Found x8 as proof of (X04 Xx1)
% 48.14/48.36 Found (fun (x8:(X05 Xx1))=> x8) as proof of (X04 Xx1)
% 48.14/48.36 Found (fun (Xx1:a) (x8:(X05 Xx1))=> x8) as proof of ((X05 Xx1)->(X04 Xx1))
% 48.14/48.36 Found (fun (Xx1:a) (x8:(X05 Xx1))=> x8) as proof of (forall (Xx:a), ((X05 Xx)->(X04 Xx)))
% 48.14/48.36 Found x600:=(x60 x7):((cK x3) Xx0)
% 48.14/48.36 Found (x60 x7) as proof of ((cK X05) Xx0)
% 48.14/48.36 Found ((x6 Xx0) x7) as proof of ((cK X05) Xx0)
% 48.14/48.36 Found ((x6 Xx0) x7) as proof of ((cK X05) Xx0)
% 48.14/48.36 Found ((x6 Xx0) x7) as proof of ((cK X05) Xx0)
% 48.14/48.36 Found x8:(X05 Xx1)
% 48.14/48.36 Found x8 as proof of (X04 Xx1)
% 48.14/48.36 Found (fun (x8:(X05 Xx1))=> x8) as proof of (X04 Xx1)
% 48.14/48.36 Found (fun (Xx1:a) (x8:(X05 Xx1))=> x8) as proof of ((X05 Xx1)->(X04 Xx1))
% 48.14/48.36 Found (fun (Xx1:a) (x8:(X05 Xx1))=> x8) as proof of (forall (Xx:a), ((X05 Xx)->(X04 Xx)))
% 48.14/48.36 Found x600:=(x60 x7):((cK x4) Xx0)
% 48.14/48.36 Found (x60 x7) as proof of ((cK X05) Xx0)
% 48.14/48.36 Found ((x6 Xx0) x7) as proof of ((cK X05) Xx0)
% 48.14/48.36 Found ((x6 Xx0) x7) as proof of ((cK X05) Xx0)
% 48.14/48.36 Found ((x6 Xx0) x7) as proof of ((cK X05) Xx0)
% 48.14/48.36 Found x8:(X05 Xx1)
% 48.14/48.36 Found x8 as proof of (X04 Xx1)
% 48.14/48.36 Found (fun (x8:(X05 Xx1))=> x8) as proof of (X04 Xx1)
% 48.14/48.36 Found (fun (Xx1:a) (x8:(X05 Xx1))=> x8) as proof of ((X05 Xx1)->(X04 Xx1))
% 48.14/48.36 Found (fun (Xx1:a) (x8:(X05 Xx1))=> x8) as proof of (forall (Xx:a), ((X05 Xx)->(X04 Xx)))
% 48.14/48.36 Found x500:=(x50 x6):((cK x3) Xx0)
% 48.14/48.36 Found (x50 x6) as proof of ((cK X05) Xx0)
% 48.14/48.36 Found ((x5 Xx0) x6) as proof of ((cK X05) Xx0)
% 48.14/48.36 Found ((x5 Xx0) x6) as proof of ((cK X05) Xx0)
% 48.14/48.36 Found ((x5 Xx0) x6) as proof of ((cK X05) Xx0)
% 48.14/48.36 Found x8:(X05 Xx1)
% 48.14/48.36 Found x8 as proof of (X04 Xx1)
% 48.14/48.36 Found (fun (x8:(X05 Xx1))=> x8) as proof of (X04 Xx1)
% 48.14/48.36 Found (fun (Xx1:a) (x8:(X05 Xx1))=> x8) as proof of ((X05 Xx1)->(X04 Xx1))
% 48.14/48.36 Found (fun (Xx1:a) (x8:(X05 Xx1))=> x8) as proof of (forall (Xx:a), ((X05 Xx)->(X04 Xx)))
% 48.14/48.36 Found x600:=(x60 x7):((cK x4) Xx0)
% 48.14/48.36 Found (x60 x7) as proof of ((cK X05) Xx0)
% 48.14/48.36 Found ((x6 Xx0) x7) as proof of ((cK X05) Xx0)
% 48.14/48.36 Found ((x6 Xx0) x7) as proof of ((cK X05) Xx0)
% 48.14/48.36 Found ((x6 Xx0) x7) as proof of ((cK X05) Xx0)
% 48.14/48.36 Found x8:(X05 Xx1)
% 48.14/48.36 Found x8 as proof of (X04 Xx1)
% 48.14/48.36 Found (fun (x8:(X05 Xx1))=> x8) as proof of (X04 Xx1)
% 48.14/48.36 Found (fun (Xx1:a) (x8:(X05 Xx1))=> x8) as proof of ((X05 Xx1)->(X04 Xx1))
% 48.14/48.36 Found (fun (Xx1:a) (x8:(X05 Xx1))=> x8) as proof of (forall (Xx:a), ((X05 Xx)->(X04 Xx)))
% 48.14/48.36 Found x600:=(x60 x7):((cK x4) Xx0)
% 48.14/48.36 Found (x60 x7) as proof of ((cK X05) Xx0)
% 48.14/48.36 Found ((x6 Xx0) x7) as proof of ((cK X05) Xx0)
% 48.14/48.36 Found ((x6 Xx0) x7) as proof of ((cK X05) Xx0)
% 48.14/48.36 Found ((x6 Xx0) x7) as proof of ((cK X05) Xx0)
% 48.14/48.36 Found x8:(X05 Xx1)
% 48.72/48.95 Found x8 as proof of (X04 Xx1)
% 48.72/48.95 Found (fun (x8:(X05 Xx1))=> x8) as proof of (X04 Xx1)
% 48.72/48.95 Found (fun (Xx1:a) (x8:(X05 Xx1))=> x8) as proof of ((X05 Xx1)->(X04 Xx1))
% 48.72/48.95 Found (fun (Xx1:a) (x8:(X05 Xx1))=> x8) as proof of (forall (Xx:a), ((X05 Xx)->(X04 Xx)))
% 48.72/48.95 Found x600:=(x60 x7):((cK x4) Xx0)
% 48.72/48.95 Found (x60 x7) as proof of ((cK X05) Xx0)
% 48.72/48.95 Found ((x6 Xx0) x7) as proof of ((cK X05) Xx0)
% 48.72/48.95 Found ((x6 Xx0) x7) as proof of ((cK X05) Xx0)
% 48.72/48.95 Found ((x6 Xx0) x7) as proof of ((cK X05) Xx0)
% 48.72/48.95 Found x8:(X05 Xx1)
% 48.72/48.95 Found x8 as proof of (X04 Xx1)
% 48.72/48.95 Found (fun (x8:(X05 Xx1))=> x8) as proof of (X04 Xx1)
% 48.72/48.95 Found (fun (Xx1:a) (x8:(X05 Xx1))=> x8) as proof of ((X05 Xx1)->(X04 Xx1))
% 48.72/48.95 Found (fun (Xx1:a) (x8:(X05 Xx1))=> x8) as proof of (forall (Xx:a), ((X05 Xx)->(X04 Xx)))
% 48.72/48.95 Found x600:=(x60 x7):((cK x4) Xx0)
% 48.72/48.95 Found (x60 x7) as proof of ((cK X05) Xx0)
% 48.72/48.95 Found ((x6 Xx0) x7) as proof of ((cK X05) Xx0)
% 48.72/48.95 Found ((x6 Xx0) x7) as proof of ((cK X05) Xx0)
% 48.72/48.95 Found ((x6 Xx0) x7) as proof of ((cK X05) Xx0)
% 48.72/48.95 Found x8:(X05 Xx1)
% 48.72/48.95 Found x8 as proof of (X04 Xx1)
% 48.72/48.95 Found (fun (x8:(X05 Xx1))=> x8) as proof of (X04 Xx1)
% 48.72/48.95 Found (fun (Xx1:a) (x8:(X05 Xx1))=> x8) as proof of ((X05 Xx1)->(X04 Xx1))
% 48.72/48.95 Found (fun (Xx1:a) (x8:(X05 Xx1))=> x8) as proof of (forall (Xx:a), ((X05 Xx)->(X04 Xx)))
% 48.72/48.95 Found x600:=(x60 x7):((cK x3) Xx0)
% 48.72/48.95 Found (x60 x7) as proof of ((cK X05) Xx0)
% 48.72/48.95 Found ((x6 Xx0) x7) as proof of ((cK X05) Xx0)
% 48.72/48.95 Found ((x6 Xx0) x7) as proof of ((cK X05) Xx0)
% 48.72/48.95 Found ((x6 Xx0) x7) as proof of ((cK X05) Xx0)
% 48.72/48.95 Found x8:(X05 Xx1)
% 48.72/48.95 Found x8 as proof of (X04 Xx1)
% 48.72/48.95 Found (fun (x8:(X05 Xx1))=> x8) as proof of (X04 Xx1)
% 48.72/48.95 Found (fun (Xx1:a) (x8:(X05 Xx1))=> x8) as proof of ((X05 Xx1)->(X04 Xx1))
% 48.72/48.95 Found (fun (Xx1:a) (x8:(X05 Xx1))=> x8) as proof of (forall (Xx:a), ((X05 Xx)->(X04 Xx)))
% 48.72/48.95 Found x600:=(x60 x7):((cK x4) Xx0)
% 48.72/48.95 Found (x60 x7) as proof of ((cK X05) Xx0)
% 48.72/48.95 Found ((x6 Xx0) x7) as proof of ((cK X05) Xx0)
% 48.72/48.95 Found ((x6 Xx0) x7) as proof of ((cK X05) Xx0)
% 48.72/48.95 Found ((x6 Xx0) x7) as proof of ((cK X05) Xx0)
% 48.72/48.95 Found x8:(X05 Xx1)
% 48.72/48.95 Found x8 as proof of (X04 Xx1)
% 48.72/48.95 Found (fun (x8:(X05 Xx1))=> x8) as proof of (X04 Xx1)
% 48.72/48.95 Found (fun (Xx1:a) (x8:(X05 Xx1))=> x8) as proof of ((X05 Xx1)->(X04 Xx1))
% 48.72/48.95 Found (fun (Xx1:a) (x8:(X05 Xx1))=> x8) as proof of (forall (Xx:a), ((X05 Xx)->(X04 Xx)))
% 48.72/48.95 Found x600:=(x60 x7):((cK x4) Xx0)
% 48.72/48.95 Found (x60 x7) as proof of ((cK X05) Xx0)
% 48.72/48.95 Found ((x6 Xx0) x7) as proof of ((cK X05) Xx0)
% 48.72/48.95 Found ((x6 Xx0) x7) as proof of ((cK X05) Xx0)
% 48.72/48.95 Found ((x6 Xx0) x7) as proof of ((cK X05) Xx0)
% 48.72/48.95 Found x8:(X05 Xx1)
% 48.72/48.95 Found x8 as proof of (X04 Xx1)
% 48.72/48.95 Found (fun (x8:(X05 Xx1))=> x8) as proof of (X04 Xx1)
% 48.72/48.95 Found (fun (Xx1:a) (x8:(X05 Xx1))=> x8) as proof of ((X05 Xx1)->(X04 Xx1))
% 48.72/48.95 Found (fun (Xx1:a) (x8:(X05 Xx1))=> x8) as proof of (forall (Xx:a), ((X05 Xx)->(X04 Xx)))
% 48.72/48.95 Found x600:=(x60 x7):((cK x4) Xx0)
% 48.72/48.95 Found (x60 x7) as proof of ((cK X05) Xx0)
% 48.72/48.95 Found ((x6 Xx0) x7) as proof of ((cK X05) Xx0)
% 48.72/48.95 Found ((x6 Xx0) x7) as proof of ((cK X05) Xx0)
% 48.72/48.95 Found ((x6 Xx0) x7) as proof of ((cK X05) Xx0)
% 48.72/48.95 Found x8:(X05 Xx1)
% 48.72/48.95 Found x8 as proof of (X04 Xx1)
% 48.72/48.95 Found (fun (x8:(X05 Xx1))=> x8) as proof of (X04 Xx1)
% 48.72/48.95 Found (fun (Xx1:a) (x8:(X05 Xx1))=> x8) as proof of ((X05 Xx1)->(X04 Xx1))
% 48.72/48.95 Found (fun (Xx1:a) (x8:(X05 Xx1))=> x8) as proof of (forall (Xx:a), ((X05 Xx)->(X04 Xx)))
% 48.72/48.95 Found x600:=(x60 x7):((cK x4) Xx0)
% 48.72/48.95 Found (x60 x7) as proof of ((cK X05) Xx0)
% 48.72/48.95 Found ((x6 Xx0) x7) as proof of ((cK X05) Xx0)
% 48.72/48.95 Found ((x6 Xx0) x7) as proof of ((cK X05) Xx0)
% 48.72/48.95 Found ((x6 Xx0) x7) as proof of ((cK X05) Xx0)
% 48.72/48.95 Found x8:(X05 Xx1)
% 48.72/48.95 Found x8 as proof of (X04 Xx1)
% 48.72/48.95 Found (fun (x8:(X05 Xx1))=> x8) as proof of (X04 Xx1)
% 48.72/48.95 Found (fun (Xx1:a) (x8:(X05 Xx1))=> x8) as proof of ((X05 Xx1)->(X04 Xx1))
% 48.72/48.95 Found (fun (Xx1:a) (x8:(X05 Xx1))=> x8) as proof of (forall (Xx:a), ((X05 Xx)->(X04 Xx)))
% 48.72/48.95 Found x600:=(x60 x7):((cK x4) Xx0)
% 48.72/48.95 Found (x60 x7) as proof of ((cK X05) Xx0)
% 48.72/48.95 Found ((x6 Xx0) x7) as proof of ((cK X05) Xx0)
% 48.72/48.95 Found ((x6 Xx0) x7) as proof of ((cK X05) Xx0)
% 48.72/48.95 Found ((x6 Xx0) x7) as proof of ((cK X05) Xx0)
% 48.72/48.95 Found x8:(X05 Xx1)
% 48.72/48.95 Found x8 as proof of (X04 Xx1)
% 48.72/48.95 Found (fun (x8:(X05 Xx1))=> x8) as proof of (X04 Xx1)
% 48.72/48.95 Found (fun (Xx1:a) (x8:(X05 Xx1))=> x8) as proof of ((X05 Xx1)->(X04 Xx1))
% 48.72/48.95 Found (fun (Xx1:a) (x8:(X05 Xx1))=> x8) as proof of (forall (Xx:a), ((X05 Xx)->(X04 Xx)))
% 49.09/49.35 Found x600:=(x60 x7):((cK x4) Xx0)
% 49.09/49.35 Found (x60 x7) as proof of ((cK X05) Xx0)
% 49.09/49.35 Found ((x6 Xx0) x7) as proof of ((cK X05) Xx0)
% 49.09/49.35 Found ((x6 Xx0) x7) as proof of ((cK X05) Xx0)
% 49.09/49.35 Found ((x6 Xx0) x7) as proof of ((cK X05) Xx0)
% 49.09/49.35 Found x8:(X05 Xx1)
% 49.09/49.35 Found x8 as proof of (X04 Xx1)
% 49.09/49.35 Found (fun (x8:(X05 Xx1))=> x8) as proof of (X04 Xx1)
% 49.09/49.35 Found (fun (Xx1:a) (x8:(X05 Xx1))=> x8) as proof of ((X05 Xx1)->(X04 Xx1))
% 49.09/49.35 Found (fun (Xx1:a) (x8:(X05 Xx1))=> x8) as proof of (forall (Xx:a), ((X05 Xx)->(X04 Xx)))
% 49.09/49.35 Found x600:=(x60 x7):((cK x3) Xx0)
% 49.09/49.35 Found (x60 x7) as proof of ((cK X05) Xx0)
% 49.09/49.35 Found ((x6 Xx0) x7) as proof of ((cK X05) Xx0)
% 49.09/49.35 Found ((x6 Xx0) x7) as proof of ((cK X05) Xx0)
% 49.09/49.35 Found ((x6 Xx0) x7) as proof of ((cK X05) Xx0)
% 49.09/49.35 Found x8:(X05 Xx1)
% 49.09/49.35 Found x8 as proof of (X04 Xx1)
% 49.09/49.35 Found (fun (x8:(X05 Xx1))=> x8) as proof of (X04 Xx1)
% 49.09/49.35 Found (fun (Xx1:a) (x8:(X05 Xx1))=> x8) as proof of ((X05 Xx1)->(X04 Xx1))
% 49.09/49.35 Found (fun (Xx1:a) (x8:(X05 Xx1))=> x8) as proof of (forall (Xx:a), ((X05 Xx)->(X04 Xx)))
% 49.09/49.35 Found x600:=(x60 x7):((cK x4) Xx0)
% 49.09/49.35 Found (x60 x7) as proof of ((cK X05) Xx0)
% 49.09/49.35 Found ((x6 Xx0) x7) as proof of ((cK X05) Xx0)
% 49.09/49.35 Found ((x6 Xx0) x7) as proof of ((cK X05) Xx0)
% 49.09/49.35 Found ((x6 Xx0) x7) as proof of ((cK X05) Xx0)
% 49.09/49.35 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 49.09/49.35 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X05) Xx0))
% 49.09/49.35 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X05) Xx0))
% 49.09/49.35 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X05) Xx0))
% 49.09/49.35 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X05) Xx0)))
% 49.09/49.35 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X05) Xx0)
% 49.09/49.35 Found ((and_rect0 ((cK X05) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X05) Xx0)
% 49.09/49.35 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X05) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X05) Xx0)
% 49.09/49.35 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X05) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X05) Xx0)
% 49.09/49.35 Found x6:(X05 Xx1)
% 49.09/49.35 Instantiate: X04:=X05:(a->Prop)
% 49.09/49.35 Found (fun (x6:(X05 Xx1))=> x6) as proof of (X04 Xx1)
% 49.09/49.35 Found (fun (Xx1:a) (x6:(X05 Xx1))=> x6) as proof of ((X05 Xx1)->(X04 Xx1))
% 49.09/49.35 Found (fun (Xx1:a) (x6:(X05 Xx1))=> x6) as proof of (forall (Xx:a), ((X05 Xx)->(X04 Xx)))
% 49.09/49.35 Found ((x360 (fun (Xx1:a) (x6:(X05 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X05) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X04) Xx0)
% 49.09/49.35 Found (((x36 X04) (fun (Xx1:a) (x6:(X05 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X05) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X04) Xx0)
% 49.09/49.35 Found ((((x3 x4) X04) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X04) Xx0)
% 49.09/49.35 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> ((((x3 x4) X04) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))))) as proof of ((cK X04) Xx0)
% 50.61/50.85 Found x8:(X05 Xx1)
% 50.61/50.85 Found x8 as proof of (X04 Xx1)
% 50.61/50.85 Found (fun (x8:(X05 Xx1))=> x8) as proof of (X04 Xx1)
% 50.61/50.85 Found (fun (Xx1:a) (x8:(X05 Xx1))=> x8) as proof of ((X05 Xx1)->(X04 Xx1))
% 50.61/50.85 Found (fun (Xx1:a) (x8:(X05 Xx1))=> x8) as proof of (forall (Xx:a), ((X05 Xx)->(X04 Xx)))
% 50.61/50.85 Found x600:=(x60 x7):((cK x3) Xx0)
% 50.61/50.85 Found (x60 x7) as proof of ((cK X05) Xx0)
% 50.61/50.85 Found ((x6 Xx0) x7) as proof of ((cK X05) Xx0)
% 50.61/50.85 Found ((x6 Xx0) x7) as proof of ((cK X05) Xx0)
% 50.61/50.85 Found ((x6 Xx0) x7) as proof of ((cK X05) Xx0)
% 50.61/50.85 Found x8:(X05 Xx1)
% 50.61/50.85 Found x8 as proof of (X04 Xx1)
% 50.61/50.85 Found (fun (x8:(X05 Xx1))=> x8) as proof of (X04 Xx1)
% 50.61/50.85 Found (fun (Xx1:a) (x8:(X05 Xx1))=> x8) as proof of ((X05 Xx1)->(X04 Xx1))
% 50.61/50.85 Found (fun (Xx1:a) (x8:(X05 Xx1))=> x8) as proof of (forall (Xx:a), ((X05 Xx)->(X04 Xx)))
% 50.61/50.85 Found x600:=(x60 x7):((cK x4) Xx0)
% 50.61/50.85 Found (x60 x7) as proof of ((cK X05) Xx0)
% 50.61/50.85 Found ((x6 Xx0) x7) as proof of ((cK X05) Xx0)
% 50.61/50.85 Found ((x6 Xx0) x7) as proof of ((cK X05) Xx0)
% 50.61/50.85 Found ((x6 Xx0) x7) as proof of ((cK X05) Xx0)
% 50.61/50.85 Found x8:(X05 Xx1)
% 50.61/50.85 Found x8 as proof of (X04 Xx1)
% 50.61/50.85 Found (fun (x8:(X05 Xx1))=> x8) as proof of (X04 Xx1)
% 50.61/50.85 Found (fun (Xx1:a) (x8:(X05 Xx1))=> x8) as proof of ((X05 Xx1)->(X04 Xx1))
% 50.61/50.85 Found (fun (Xx1:a) (x8:(X05 Xx1))=> x8) as proof of (forall (Xx:a), ((X05 Xx)->(X04 Xx)))
% 50.61/50.85 Found x600:=(x60 x7):((cK x3) Xx0)
% 50.61/50.85 Found (x60 x7) as proof of ((cK X05) Xx0)
% 50.61/50.85 Found ((x6 Xx0) x7) as proof of ((cK X05) Xx0)
% 50.61/50.85 Found ((x6 Xx0) x7) as proof of ((cK X05) Xx0)
% 50.61/50.85 Found ((x6 Xx0) x7) as proof of ((cK X05) Xx0)
% 50.61/50.85 Found x8:(X05 Xx1)
% 50.61/50.85 Found x8 as proof of (X04 Xx1)
% 50.61/50.85 Found (fun (x8:(X05 Xx1))=> x8) as proof of (X04 Xx1)
% 50.61/50.85 Found (fun (Xx1:a) (x8:(X05 Xx1))=> x8) as proof of ((X05 Xx1)->(X04 Xx1))
% 50.61/50.85 Found (fun (Xx1:a) (x8:(X05 Xx1))=> x8) as proof of (forall (Xx:a), ((X05 Xx)->(X04 Xx)))
% 50.61/50.85 Found x600:=(x60 x7):((cK x4) Xx0)
% 50.61/50.85 Found (x60 x7) as proof of ((cK X05) Xx0)
% 50.61/50.85 Found ((x6 Xx0) x7) as proof of ((cK X05) Xx0)
% 50.61/50.85 Found ((x6 Xx0) x7) as proof of ((cK X05) Xx0)
% 50.61/50.85 Found ((x6 Xx0) x7) as proof of ((cK X05) Xx0)
% 50.61/50.85 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 50.61/50.85 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X05) Xx0))
% 50.61/50.85 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X05) Xx0))
% 50.61/50.85 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X05) Xx0))
% 50.61/50.85 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X05) Xx0)))
% 50.61/50.85 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X05) Xx0)
% 50.61/50.85 Found ((and_rect0 ((cK X05) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X05) Xx0)
% 50.61/50.85 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X05) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X05) Xx0)
% 50.61/50.85 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X05) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X05) Xx0)
% 50.61/50.85 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 50.61/50.85 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X05) Xx0))
% 50.61/50.85 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X05) Xx0))
% 50.61/50.85 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X05) Xx0))
% 50.61/50.85 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X05) Xx0)))
% 50.61/50.85 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X05) Xx0)
% 50.61/50.85 Found ((and_rect0 ((cK X05) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X05) Xx0)
% 50.61/50.85 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X05) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X05) Xx0)
% 50.87/51.13 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X05) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X05) Xx0)
% 50.87/51.13 Found x6:(X05 Xx1)
% 50.87/51.13 Instantiate: X04:=X05:(a->Prop)
% 50.87/51.13 Found (fun (x6:(X05 Xx1))=> x6) as proof of (X04 Xx1)
% 50.87/51.13 Found (fun (Xx1:a) (x6:(X05 Xx1))=> x6) as proof of ((X05 Xx1)->(X04 Xx1))
% 50.87/51.13 Found (fun (Xx1:a) (x6:(X05 Xx1))=> x6) as proof of (forall (Xx:a), ((X05 Xx)->(X04 Xx)))
% 50.87/51.13 Found ((x360 (fun (Xx1:a) (x6:(X05 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X05) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X04) Xx0)
% 50.87/51.13 Found (((x36 X04) (fun (Xx1:a) (x6:(X05 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X05) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X04) Xx0)
% 50.87/51.13 Found ((((x3 x4) X04) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X04) Xx0)
% 50.87/51.13 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> ((((x3 x4) X04) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))))) as proof of ((cK X04) Xx0)
% 50.87/51.13 Found x4:(X05 Xx1)
% 50.87/51.13 Instantiate: X05:=(cK x5):(a->Prop)
% 50.87/51.13 Found x4 as proof of (X04 Xx1)
% 50.87/51.13 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X04 Xx1)
% 50.87/51.13 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X04 Xx1))
% 50.87/51.13 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X04 Xx1)))
% 50.87/51.13 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X04 Xx1)
% 50.87/51.13 Found ((and_rect0 (X04 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X04 Xx1)
% 50.87/51.13 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X04 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X04 Xx1)
% 50.87/51.13 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X04 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X04 Xx1)
% 50.87/51.13 Found x4:(X05 Xx1)
% 50.87/51.13 Found x4 as proof of (X04 Xx1)
% 50.87/51.13 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X04 Xx1)
% 50.87/51.13 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X04 Xx1))
% 50.87/51.13 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X04 Xx1)))
% 50.87/51.13 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X04 Xx1)
% 50.87/51.13 Found ((and_rect0 (X04 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X04 Xx1)
% 50.87/51.13 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X04 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X04 Xx1)
% 52.05/52.30 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X04 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X04 Xx1)
% 52.05/52.30 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 52.05/52.30 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X05) Xx0))
% 52.05/52.30 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X05) Xx0))
% 52.05/52.30 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X05) Xx0))
% 52.05/52.30 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X05) Xx0)))
% 52.05/52.30 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X05) Xx0)
% 52.05/52.30 Found ((and_rect0 ((cK X05) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X05) Xx0)
% 52.05/52.30 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X05) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X05) Xx0)
% 52.05/52.30 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X05) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X05) Xx0)
% 52.05/52.30 Found x4:(X05 Xx1)
% 52.05/52.30 Instantiate: X05:=(cK x5):(a->Prop)
% 52.05/52.30 Found x4 as proof of (X04 Xx1)
% 52.05/52.30 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X04 Xx1)
% 52.05/52.30 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X04 Xx1))
% 52.05/52.30 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X04 Xx1)))
% 52.05/52.30 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X04 Xx1)
% 52.05/52.30 Found ((and_rect0 (X04 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X04 Xx1)
% 52.05/52.30 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X04 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X04 Xx1)
% 52.05/52.30 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X04 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X04 Xx1)
% 52.05/52.30 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 52.05/52.30 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X05) Xx0))
% 52.05/52.30 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X05) Xx0))
% 52.05/52.30 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X05) Xx0))
% 52.05/52.30 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X05) Xx0)))
% 52.05/52.30 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X05) Xx0)
% 52.05/52.30 Found ((and_rect0 ((cK X05) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X05) Xx0)
% 52.05/52.30 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X05) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X05) Xx0)
% 52.49/52.74 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X05) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X05) Xx0)
% 52.49/52.74 Found x6:(X05 Xx1)
% 52.49/52.74 Instantiate: X04:=X05:(a->Prop)
% 52.49/52.74 Found (fun (x6:(X05 Xx1))=> x6) as proof of (X04 Xx1)
% 52.49/52.74 Found (fun (Xx1:a) (x6:(X05 Xx1))=> x6) as proof of ((X05 Xx1)->(X04 Xx1))
% 52.49/52.74 Found (fun (Xx1:a) (x6:(X05 Xx1))=> x6) as proof of (forall (Xx:a), ((X05 Xx)->(X04 Xx)))
% 52.49/52.74 Found ((x360 (fun (Xx1:a) (x6:(X05 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X05) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X04) Xx0)
% 52.49/52.74 Found (((x36 X04) (fun (Xx1:a) (x6:(X05 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X05) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X04) Xx0)
% 52.49/52.74 Found ((((x3 x4) X04) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X04) Xx0)
% 52.49/52.74 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> ((((x3 x4) X04) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))))) as proof of ((cK X04) Xx0)
% 52.49/52.74 Found x4:(X05 Xx1)
% 52.49/52.74 Found x4 as proof of (X04 Xx1)
% 52.49/52.74 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X04 Xx1)
% 52.49/52.74 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X04 Xx1))
% 52.49/52.74 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X04 Xx1)))
% 52.49/52.74 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X04 Xx1)
% 52.49/52.74 Found ((and_rect0 (X04 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X04 Xx1)
% 52.49/52.74 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X04 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X04 Xx1)
% 52.49/52.74 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X04 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X04 Xx1)
% 52.49/52.74 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 52.49/52.74 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X05) Xx0))
% 52.49/52.74 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X05) Xx0))
% 52.49/52.74 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X05) Xx0))
% 52.49/52.74 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X05) Xx0)))
% 52.49/52.74 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X05) Xx0)
% 52.49/52.74 Found ((and_rect0 ((cK X05) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X05) Xx0)
% 52.49/52.74 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X05) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X05) Xx0)
% 53.28/53.49 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X05) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X05) Xx0)
% 53.28/53.49 Found x4:(X05 Xx1)
% 53.28/53.49 Instantiate: X05:=(cK x5):(a->Prop)
% 53.28/53.49 Found x4 as proof of (X04 Xx1)
% 53.28/53.49 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X04 Xx1)
% 53.28/53.49 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X04 Xx1))
% 53.28/53.49 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X04 Xx1)))
% 53.28/53.49 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X04 Xx1)
% 53.28/53.49 Found ((and_rect0 (X04 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X04 Xx1)
% 53.28/53.49 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X04 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X04 Xx1)
% 53.28/53.49 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X04 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X04 Xx1)
% 53.28/53.49 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 53.28/53.49 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X05) Xx0))
% 53.28/53.49 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X05) Xx0))
% 53.28/53.49 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X05) Xx0))
% 53.28/53.49 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X05) Xx0)))
% 53.28/53.49 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X05) Xx0)
% 53.28/53.49 Found ((and_rect0 ((cK X05) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X05) Xx0)
% 53.28/53.49 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X05) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X05) Xx0)
% 53.28/53.49 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X05) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X05) Xx0)
% 53.28/53.49 Found x6:(X05 Xx1)
% 53.28/53.49 Instantiate: X04:=X05:(a->Prop)
% 53.28/53.49 Found (fun (x6:(X05 Xx1))=> x6) as proof of (X04 Xx1)
% 53.28/53.49 Found (fun (Xx1:a) (x6:(X05 Xx1))=> x6) as proof of ((X05 Xx1)->(X04 Xx1))
% 53.28/53.49 Found (fun (Xx1:a) (x6:(X05 Xx1))=> x6) as proof of (forall (Xx:a), ((X05 Xx)->(X04 Xx)))
% 53.28/53.49 Found ((x360 (fun (Xx1:a) (x6:(X05 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X05) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X04) Xx0)
% 53.28/53.49 Found (((x36 X04) (fun (Xx1:a) (x6:(X05 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X05) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X04) Xx0)
% 53.28/53.49 Found ((((x3 x4) X04) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X04) Xx0)
% 54.15/54.42 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> ((((x3 x4) X04) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))))) as proof of ((cK X04) Xx0)
% 54.15/54.42 Found x4:(X05 Xx1)
% 54.15/54.42 Found x4 as proof of (X04 Xx1)
% 54.15/54.42 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X04 Xx1)
% 54.15/54.42 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X04 Xx1))
% 54.15/54.42 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X04 Xx1)))
% 54.15/54.42 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X04 Xx1)
% 54.15/54.42 Found ((and_rect0 (X04 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X04 Xx1)
% 54.15/54.42 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X04 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X04 Xx1)
% 54.15/54.42 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X04 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X04 Xx1)
% 54.15/54.42 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 54.15/54.42 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X05) Xx0))
% 54.15/54.42 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X05) Xx0))
% 54.15/54.42 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X05) Xx0))
% 54.15/54.42 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X05) Xx0)))
% 54.15/54.42 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X05) Xx0)
% 54.15/54.42 Found ((and_rect0 ((cK X05) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X05) Xx0)
% 54.15/54.42 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X05) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X05) Xx0)
% 54.15/54.42 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X05) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X05) Xx0)
% 54.15/54.42 Found x4:(X05 Xx1)
% 54.15/54.42 Instantiate: X05:=(cK x5):(a->Prop)
% 54.15/54.42 Found x4 as proof of (X04 Xx1)
% 54.15/54.42 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X04 Xx1)
% 54.15/54.42 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X04 Xx1))
% 54.15/54.42 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X04 Xx1)))
% 54.15/54.42 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X04 Xx1)
% 54.15/54.42 Found ((and_rect0 (X04 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X04 Xx1)
% 54.15/54.42 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X04 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X04 Xx1)
% 54.52/54.73 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X04 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X04 Xx1)
% 54.52/54.73 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 54.52/54.73 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X05) Xx0))
% 54.52/54.73 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X05) Xx0))
% 54.52/54.73 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X05) Xx0))
% 54.52/54.73 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X05) Xx0)))
% 54.52/54.73 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X05) Xx0)
% 54.52/54.73 Found ((and_rect0 ((cK X05) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X05) Xx0)
% 54.52/54.73 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X05) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X05) Xx0)
% 54.52/54.73 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X05) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X05) Xx0)
% 54.52/54.73 Found x6:(X05 Xx1)
% 54.52/54.73 Instantiate: X04:=X05:(a->Prop)
% 54.52/54.73 Found (fun (x6:(X05 Xx1))=> x6) as proof of (X04 Xx1)
% 54.52/54.73 Found (fun (Xx1:a) (x6:(X05 Xx1))=> x6) as proof of ((X05 Xx1)->(X04 Xx1))
% 54.52/54.73 Found (fun (Xx1:a) (x6:(X05 Xx1))=> x6) as proof of (forall (Xx:a), ((X05 Xx)->(X04 Xx)))
% 54.52/54.73 Found ((x360 (fun (Xx1:a) (x6:(X05 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X05) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X04) Xx0)
% 54.52/54.73 Found (((x36 X04) (fun (Xx1:a) (x6:(X05 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X05) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X04) Xx0)
% 54.52/54.73 Found ((((x3 x4) X04) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X04) Xx0)
% 54.52/54.73 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> ((((x3 x4) X04) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))))) as proof of ((cK X04) Xx0)
% 54.52/54.73 Found x4:(X05 Xx1)
% 54.52/54.73 Found x4 as proof of (X04 Xx1)
% 54.52/54.73 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X04 Xx1)
% 54.52/54.73 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X04 Xx1))
% 54.52/54.73 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X04 Xx1)))
% 54.52/54.73 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X04 Xx1)
% 54.52/54.73 Found ((and_rect0 (X04 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X04 Xx1)
% 54.52/54.73 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X04 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X04 Xx1)
% 56.42/56.67 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X04 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X04 Xx1)
% 56.42/56.67 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 56.42/56.67 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X05) Xx0))
% 56.42/56.67 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X05) Xx0))
% 56.42/56.67 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X05) Xx0))
% 56.42/56.67 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X05) Xx0)))
% 56.42/56.67 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X05) Xx0)
% 56.42/56.67 Found ((and_rect0 ((cK X05) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X05) Xx0)
% 56.42/56.67 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X05) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X05) Xx0)
% 56.42/56.67 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X05) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X05) Xx0)
% 56.42/56.67 Found x4:(X05 Xx1)
% 56.42/56.67 Instantiate: X05:=(cK x5):(a->Prop)
% 56.42/56.67 Found x4 as proof of (X04 Xx1)
% 56.42/56.67 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X04 Xx1)
% 56.42/56.67 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X04 Xx1))
% 56.42/56.67 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X04 Xx1)))
% 56.42/56.67 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X04 Xx1)
% 56.42/56.67 Found ((and_rect0 (X04 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X04 Xx1)
% 56.42/56.67 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X04 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X04 Xx1)
% 56.42/56.67 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X04 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X04 Xx1)
% 56.42/56.67 Found x4:(X06 Xx1)
% 56.42/56.67 Found x4 as proof of (X05 Xx1)
% 56.42/56.67 Found (fun (x4:(X06 Xx1))=> x4) as proof of (X05 Xx1)
% 56.42/56.67 Found (fun (Xx1:a) (x4:(X06 Xx1))=> x4) as proof of ((X06 Xx1)->(X05 Xx1))
% 56.42/56.67 Found (fun (Xx1:a) (x4:(X06 Xx1))=> x4) as proof of (forall (Xx:a), ((X06 Xx)->(X05 Xx)))
% 56.42/56.67 Found x4:(X05 Xx1)
% 56.42/56.67 Found x4 as proof of (X04 Xx1)
% 56.42/56.67 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X04 Xx1)
% 56.42/56.67 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X04 Xx1))
% 56.42/56.67 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X04 Xx1)))
% 56.42/56.67 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X04 Xx1)
% 56.42/56.67 Found ((and_rect0 (X04 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X04 Xx1)
% 56.42/56.67 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X04 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X04 Xx1)
% 57.75/57.98 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X04 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X04 Xx1)
% 57.75/57.98 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 57.75/57.98 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X05) Xx0))
% 57.75/57.98 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X05) Xx0))
% 57.75/57.98 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X05) Xx0))
% 57.75/57.98 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X05) Xx0)))
% 57.75/57.98 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X05) Xx0)
% 57.75/57.98 Found ((and_rect0 ((cK X05) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X05) Xx0)
% 57.75/57.98 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X05) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X05) Xx0)
% 57.75/57.98 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X05) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X05) Xx0)
% 57.75/57.98 Found x6:(X05 Xx1)
% 57.75/57.98 Instantiate: X04:=X05:(a->Prop)
% 57.75/57.98 Found (fun (x6:(X05 Xx1))=> x6) as proof of (X04 Xx1)
% 57.75/57.98 Found (fun (Xx1:a) (x6:(X05 Xx1))=> x6) as proof of ((X05 Xx1)->(X04 Xx1))
% 57.75/57.98 Found (fun (Xx1:a) (x6:(X05 Xx1))=> x6) as proof of (forall (Xx:a), ((X05 Xx)->(X04 Xx)))
% 57.75/57.98 Found ((x360 (fun (Xx1:a) (x6:(X05 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X05) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X04) Xx0)
% 57.75/57.98 Found (((x36 X04) (fun (Xx1:a) (x6:(X05 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X05) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X04) Xx0)
% 57.75/57.98 Found ((((x3 x4) X04) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X04) Xx0)
% 57.75/57.98 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> ((((x3 x4) X04) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))))) as proof of ((cK X04) Xx0)
% 57.75/57.98 Found x6:(X06 Xx1)
% 57.75/57.98 Found x6 as proof of (X05 Xx1)
% 57.75/57.98 Found (fun (x6:(X06 Xx1))=> x6) as proof of (X05 Xx1)
% 57.75/57.98 Found (fun (Xx1:a) (x6:(X06 Xx1))=> x6) as proof of ((X06 Xx1)->(X05 Xx1))
% 57.75/57.98 Found (fun (Xx1:a) (x6:(X06 Xx1))=> x6) as proof of (forall (Xx:a), ((X06 Xx)->(X05 Xx)))
% 57.75/57.98 Found x6:(X06 Xx1)
% 57.75/57.98 Found x6 as proof of (X05 Xx1)
% 57.75/57.98 Found (fun (x6:(X06 Xx1))=> x6) as proof of (X05 Xx1)
% 57.75/57.98 Found (fun (Xx1:a) (x6:(X06 Xx1))=> x6) as proof of ((X06 Xx1)->(X05 Xx1))
% 57.75/57.98 Found (fun (Xx1:a) (x6:(X06 Xx1))=> x6) as proof of (forall (Xx:a), ((X06 Xx)->(X05 Xx)))
% 57.75/57.98 Found x6:(X06 Xx1)
% 57.75/57.98 Found x6 as proof of (X05 Xx1)
% 57.75/57.98 Found (fun (x6:(X06 Xx1))=> x6) as proof of (X05 Xx1)
% 65.65/65.90 Found (fun (Xx1:a) (x6:(X06 Xx1))=> x6) as proof of ((X06 Xx1)->(X05 Xx1))
% 65.65/65.90 Found (fun (Xx1:a) (x6:(X06 Xx1))=> x6) as proof of (forall (Xx:a), ((X06 Xx)->(X05 Xx)))
% 65.65/65.90 Found x6:(X06 Xx1)
% 65.65/65.90 Found x6 as proof of (X05 Xx1)
% 65.65/65.90 Found (fun (x6:(X06 Xx1))=> x6) as proof of (X05 Xx1)
% 65.65/65.90 Found (fun (Xx1:a) (x6:(X06 Xx1))=> x6) as proof of ((X06 Xx1)->(X05 Xx1))
% 65.65/65.90 Found (fun (Xx1:a) (x6:(X06 Xx1))=> x6) as proof of (forall (Xx:a), ((X06 Xx)->(X05 Xx)))
% 65.65/65.90 Found x6:(X06 Xx1)
% 65.65/65.90 Found x6 as proof of (X05 Xx1)
% 65.65/65.90 Found (fun (x6:(X06 Xx1))=> x6) as proof of (X05 Xx1)
% 65.65/65.90 Found (fun (Xx1:a) (x6:(X06 Xx1))=> x6) as proof of ((X06 Xx1)->(X05 Xx1))
% 65.65/65.90 Found (fun (Xx1:a) (x6:(X06 Xx1))=> x6) as proof of (forall (Xx:a), ((X06 Xx)->(X05 Xx)))
% 65.65/65.90 Found x6:(X06 Xx1)
% 65.65/65.90 Found x6 as proof of (X05 Xx1)
% 65.65/65.90 Found (fun (x6:(X06 Xx1))=> x6) as proof of (X05 Xx1)
% 65.65/65.90 Found (fun (Xx1:a) (x6:(X06 Xx1))=> x6) as proof of ((X06 Xx1)->(X05 Xx1))
% 65.65/65.90 Found (fun (Xx1:a) (x6:(X06 Xx1))=> x6) as proof of (forall (Xx:a), ((X06 Xx)->(X05 Xx)))
% 65.65/65.90 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 65.65/65.90 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X05) Xx0))
% 65.65/65.90 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X05) Xx0))
% 65.65/65.90 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X05) Xx0))
% 65.65/65.90 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X05) Xx0)))
% 65.65/65.90 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X05) Xx0)
% 65.65/65.90 Found ((and_rect0 ((cK X05) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X05) Xx0)
% 65.65/65.90 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X05) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X05) Xx0)
% 65.65/65.90 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X05) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X05) Xx0)
% 65.65/65.90 Found x6:(X06 Xx1)
% 65.65/65.90 Found x6 as proof of (X05 Xx1)
% 65.65/65.90 Found (fun (x6:(X06 Xx1))=> x6) as proof of (X05 Xx1)
% 65.65/65.90 Found (fun (Xx1:a) (x6:(X06 Xx1))=> x6) as proof of ((X06 Xx1)->(X05 Xx1))
% 65.65/65.90 Found (fun (Xx1:a) (x6:(X06 Xx1))=> x6) as proof of (forall (Xx:a), ((X06 Xx)->(X05 Xx)))
% 65.65/65.90 Found x6:(X06 Xx1)
% 65.65/65.90 Found x6 as proof of (X05 Xx1)
% 65.65/65.90 Found (fun (x6:(X06 Xx1))=> x6) as proof of (X05 Xx1)
% 65.65/65.90 Found (fun (Xx1:a) (x6:(X06 Xx1))=> x6) as proof of ((X06 Xx1)->(X05 Xx1))
% 65.65/65.90 Found (fun (Xx1:a) (x6:(X06 Xx1))=> x6) as proof of (forall (Xx:a), ((X06 Xx)->(X05 Xx)))
% 65.65/65.90 Found x8:(X06 Xx1)
% 65.65/65.90 Found x8 as proof of (X05 Xx1)
% 65.65/65.90 Found (fun (x8:(X06 Xx1))=> x8) as proof of (X05 Xx1)
% 65.65/65.90 Found (fun (Xx1:a) (x8:(X06 Xx1))=> x8) as proof of ((X06 Xx1)->(X05 Xx1))
% 65.65/65.90 Found (fun (Xx1:a) (x8:(X06 Xx1))=> x8) as proof of (forall (Xx:a), ((X06 Xx)->(X05 Xx)))
% 65.65/65.90 Found x600:=(x60 x7):((cK x4) Xx0)
% 65.65/65.90 Found (x60 x7) as proof of ((cK X06) Xx0)
% 65.65/65.90 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 65.65/65.90 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 65.65/65.90 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 65.65/65.90 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 65.65/65.90 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X06) Xx0))
% 65.65/65.90 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X06) Xx0))
% 65.65/65.90 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X06) Xx0))
% 65.65/65.90 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X06) Xx0)))
% 65.65/65.90 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 65.65/65.90 Found ((and_rect0 ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 65.65/65.90 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 65.78/66.05 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 65.78/66.05 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 65.78/66.05 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X06) Xx0))
% 65.78/66.05 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X06) Xx0))
% 65.78/66.05 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X06) Xx0))
% 65.78/66.05 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X06) Xx0)))
% 65.78/66.05 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 65.78/66.05 Found ((and_rect0 ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 65.78/66.05 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 65.78/66.05 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 65.78/66.05 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 65.78/66.05 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X06) Xx0))
% 65.78/66.05 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X06) Xx0))
% 65.78/66.05 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X06) Xx0))
% 65.78/66.05 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X06) Xx0)))
% 65.78/66.05 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 65.78/66.05 Found ((and_rect0 ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 65.78/66.05 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 65.78/66.05 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 65.78/66.05 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 65.78/66.05 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X06) Xx0))
% 65.78/66.05 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X06) Xx0))
% 65.78/66.05 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X06) Xx0))
% 65.78/66.05 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X06) Xx0)))
% 65.78/66.05 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 65.78/66.05 Found ((and_rect0 ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 65.78/66.05 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 65.78/66.05 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 66.68/66.89 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 66.68/66.89 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X06) Xx0))
% 66.68/66.89 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X06) Xx0))
% 66.68/66.89 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X06) Xx0))
% 66.68/66.89 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X06) Xx0)))
% 66.68/66.89 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 66.68/66.89 Found ((and_rect0 ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 66.68/66.89 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 66.68/66.89 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 66.68/66.89 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 66.68/66.89 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X06) Xx0))
% 66.68/66.89 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X06) Xx0))
% 66.68/66.89 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X06) Xx0))
% 66.68/66.89 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X06) Xx0)))
% 66.68/66.89 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 66.68/66.89 Found ((and_rect0 ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 66.68/66.89 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 66.68/66.89 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 66.68/66.89 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 66.68/66.89 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X06) Xx0))
% 66.68/66.89 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X06) Xx0))
% 66.68/66.89 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X06) Xx0))
% 66.68/66.89 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X06) Xx0)))
% 66.68/66.89 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 66.68/66.89 Found ((and_rect0 ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 66.68/66.89 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 66.68/66.89 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 66.68/66.89 Found x8:(X06 Xx1)
% 66.68/66.89 Found x8 as proof of (X05 Xx1)
% 66.68/66.89 Found (fun (x8:(X06 Xx1))=> x8) as proof of (X05 Xx1)
% 66.68/66.89 Found (fun (Xx1:a) (x8:(X06 Xx1))=> x8) as proof of ((X06 Xx1)->(X05 Xx1))
% 66.68/66.89 Found (fun (Xx1:a) (x8:(X06 Xx1))=> x8) as proof of (forall (Xx:a), ((X06 Xx)->(X05 Xx)))
% 66.68/66.89 Found x600:=(x60 x7):((cK x4) Xx0)
% 66.68/66.89 Found (x60 x7) as proof of ((cK X06) Xx0)
% 66.68/66.89 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 66.68/66.89 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 68.67/68.90 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 68.67/68.90 Found x8:(X06 Xx1)
% 68.67/68.90 Found x8 as proof of (X05 Xx1)
% 68.67/68.90 Found (fun (x8:(X06 Xx1))=> x8) as proof of (X05 Xx1)
% 68.67/68.90 Found (fun (Xx1:a) (x8:(X06 Xx1))=> x8) as proof of ((X06 Xx1)->(X05 Xx1))
% 68.67/68.90 Found (fun (Xx1:a) (x8:(X06 Xx1))=> x8) as proof of (forall (Xx:a), ((X06 Xx)->(X05 Xx)))
% 68.67/68.90 Found x600:=(x60 x7):((cK x4) Xx0)
% 68.67/68.90 Found (x60 x7) as proof of ((cK X06) Xx0)
% 68.67/68.90 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 68.67/68.90 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 68.67/68.90 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 68.67/68.90 Found x8:(X06 Xx1)
% 68.67/68.90 Found x8 as proof of (X05 Xx1)
% 68.67/68.90 Found (fun (x8:(X06 Xx1))=> x8) as proof of (X05 Xx1)
% 68.67/68.90 Found (fun (Xx1:a) (x8:(X06 Xx1))=> x8) as proof of ((X06 Xx1)->(X05 Xx1))
% 68.67/68.90 Found (fun (Xx1:a) (x8:(X06 Xx1))=> x8) as proof of (forall (Xx:a), ((X06 Xx)->(X05 Xx)))
% 68.67/68.90 Found x600:=(x60 x7):((cK x3) Xx0)
% 68.67/68.90 Found (x60 x7) as proof of ((cK X06) Xx0)
% 68.67/68.90 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 68.67/68.90 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 68.67/68.90 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 68.67/68.90 Found x8:(X06 Xx1)
% 68.67/68.90 Found x8 as proof of (X05 Xx1)
% 68.67/68.90 Found (fun (x8:(X06 Xx1))=> x8) as proof of (X05 Xx1)
% 68.67/68.90 Found (fun (Xx1:a) (x8:(X06 Xx1))=> x8) as proof of ((X06 Xx1)->(X05 Xx1))
% 68.67/68.90 Found (fun (Xx1:a) (x8:(X06 Xx1))=> x8) as proof of (forall (Xx:a), ((X06 Xx)->(X05 Xx)))
% 68.67/68.90 Found x600:=(x60 x7):((cK x4) Xx0)
% 68.67/68.90 Found (x60 x7) as proof of ((cK X06) Xx0)
% 68.67/68.90 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 68.67/68.90 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 68.67/68.90 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 68.67/68.90 Found x8:(X06 Xx1)
% 68.67/68.90 Found x8 as proof of (X05 Xx1)
% 68.67/68.90 Found (fun (x8:(X06 Xx1))=> x8) as proof of (X05 Xx1)
% 68.67/68.90 Found (fun (Xx1:a) (x8:(X06 Xx1))=> x8) as proof of ((X06 Xx1)->(X05 Xx1))
% 68.67/68.90 Found (fun (Xx1:a) (x8:(X06 Xx1))=> x8) as proof of (forall (Xx:a), ((X06 Xx)->(X05 Xx)))
% 68.67/68.90 Found x600:=(x60 x7):((cK x4) Xx0)
% 68.67/68.90 Found (x60 x7) as proof of ((cK X06) Xx0)
% 68.67/68.90 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 68.67/68.90 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 68.67/68.90 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 68.67/68.90 Found x8:(X06 Xx1)
% 68.67/68.90 Found x8 as proof of (X05 Xx1)
% 68.67/68.90 Found (fun (x8:(X06 Xx1))=> x8) as proof of (X05 Xx1)
% 68.67/68.90 Found (fun (Xx1:a) (x8:(X06 Xx1))=> x8) as proof of ((X06 Xx1)->(X05 Xx1))
% 68.67/68.90 Found (fun (Xx1:a) (x8:(X06 Xx1))=> x8) as proof of (forall (Xx:a), ((X06 Xx)->(X05 Xx)))
% 68.67/68.90 Found x600:=(x60 x7):((cK x4) Xx0)
% 68.67/68.90 Found (x60 x7) as proof of ((cK X06) Xx0)
% 68.67/68.90 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 68.67/68.90 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 68.67/68.90 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 68.67/68.90 Found x8:(X06 Xx1)
% 68.67/68.90 Found x8 as proof of (X05 Xx1)
% 68.67/68.90 Found (fun (x8:(X06 Xx1))=> x8) as proof of (X05 Xx1)
% 68.67/68.90 Found (fun (Xx1:a) (x8:(X06 Xx1))=> x8) as proof of ((X06 Xx1)->(X05 Xx1))
% 68.67/68.90 Found (fun (Xx1:a) (x8:(X06 Xx1))=> x8) as proof of (forall (Xx:a), ((X06 Xx)->(X05 Xx)))
% 68.67/68.90 Found x600:=(x60 x7):((cK x4) Xx0)
% 68.67/68.90 Found (x60 x7) as proof of ((cK X06) Xx0)
% 68.67/68.90 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 68.67/68.90 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 68.67/68.90 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 68.67/68.90 Found x8:(X06 Xx1)
% 68.67/68.90 Found x8 as proof of (X05 Xx1)
% 68.67/68.90 Found (fun (x8:(X06 Xx1))=> x8) as proof of (X05 Xx1)
% 68.67/68.90 Found (fun (Xx1:a) (x8:(X06 Xx1))=> x8) as proof of ((X06 Xx1)->(X05 Xx1))
% 68.67/68.90 Found (fun (Xx1:a) (x8:(X06 Xx1))=> x8) as proof of (forall (Xx:a), ((X06 Xx)->(X05 Xx)))
% 68.67/68.90 Found x600:=(x60 x7):((cK x3) Xx0)
% 68.67/68.90 Found (x60 x7) as proof of ((cK X06) Xx0)
% 68.67/68.90 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 68.67/68.90 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 68.67/68.90 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 68.67/68.90 Found x8:(X06 Xx1)
% 68.67/68.90 Found x8 as proof of (X05 Xx1)
% 68.67/68.90 Found (fun (x8:(X06 Xx1))=> x8) as proof of (X05 Xx1)
% 68.67/68.90 Found (fun (Xx1:a) (x8:(X06 Xx1))=> x8) as proof of ((X06 Xx1)->(X05 Xx1))
% 68.67/68.90 Found (fun (Xx1:a) (x8:(X06 Xx1))=> x8) as proof of (forall (Xx:a), ((X06 Xx)->(X05 Xx)))
% 68.67/68.90 Found x600:=(x60 x7):((cK x4) Xx0)
% 68.67/68.90 Found (x60 x7) as proof of ((cK X06) Xx0)
% 68.67/68.90 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 68.67/68.90 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 68.67/68.90 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 68.67/68.90 Found x8:(X06 Xx1)
% 68.67/68.90 Found x8 as proof of (X05 Xx1)
% 68.67/68.90 Found (fun (x8:(X06 Xx1))=> x8) as proof of (X05 Xx1)
% 68.67/68.90 Found (fun (Xx1:a) (x8:(X06 Xx1))=> x8) as proof of ((X06 Xx1)->(X05 Xx1))
% 69.55/69.77 Found (fun (Xx1:a) (x8:(X06 Xx1))=> x8) as proof of (forall (Xx:a), ((X06 Xx)->(X05 Xx)))
% 69.55/69.77 Found x500:=(x50 x6):((cK x3) Xx0)
% 69.55/69.77 Found (x50 x6) as proof of ((cK X06) Xx0)
% 69.55/69.77 Found ((x5 Xx0) x6) as proof of ((cK X06) Xx0)
% 69.55/69.77 Found ((x5 Xx0) x6) as proof of ((cK X06) Xx0)
% 69.55/69.77 Found ((x5 Xx0) x6) as proof of ((cK X06) Xx0)
% 69.55/69.77 Found x60:=(x6 Xx0):((x3 Xx0)->((cK x3) Xx0))
% 69.55/69.77 Found (x6 Xx0) as proof of ((x3 Xx0)->((cK X06) Xx0))
% 69.55/69.77 Found (x6 Xx0) as proof of ((x3 Xx0)->((cK X06) Xx0))
% 69.55/69.77 Found (fun (x6:(forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1))))=> (x6 Xx0)) as proof of ((x3 Xx0)->((cK X06) Xx0))
% 69.55/69.77 Found (fun (x6:(forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1)))->((x3 Xx0)->((cK X06) Xx0)))
% 69.55/69.77 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 69.55/69.77 Found ((and_rect0 ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 69.55/69.77 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1)))->((x3 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1)))) (x3 Xx0)) P) x6) x4)) ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 69.55/69.77 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1)))->((x3 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1)))) (x3 Xx0)) P) x6) x4)) ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 69.55/69.77 Found x8:(X06 Xx1)
% 69.55/69.77 Found x8 as proof of (X05 Xx1)
% 69.55/69.77 Found (fun (x8:(X06 Xx1))=> x8) as proof of (X05 Xx1)
% 69.55/69.77 Found (fun (Xx1:a) (x8:(X06 Xx1))=> x8) as proof of ((X06 Xx1)->(X05 Xx1))
% 69.55/69.77 Found (fun (Xx1:a) (x8:(X06 Xx1))=> x8) as proof of (forall (Xx:a), ((X06 Xx)->(X05 Xx)))
% 69.55/69.77 Found x600:=(x60 x7):((cK x4) Xx0)
% 69.55/69.77 Found (x60 x7) as proof of ((cK X06) Xx0)
% 69.55/69.77 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 69.55/69.77 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 69.55/69.77 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 69.55/69.77 Found x8:(X06 Xx1)
% 69.55/69.77 Found x8 as proof of (X05 Xx1)
% 69.55/69.77 Found (fun (x8:(X06 Xx1))=> x8) as proof of (X05 Xx1)
% 69.55/69.77 Found (fun (Xx1:a) (x8:(X06 Xx1))=> x8) as proof of ((X06 Xx1)->(X05 Xx1))
% 69.55/69.77 Found (fun (Xx1:a) (x8:(X06 Xx1))=> x8) as proof of (forall (Xx:a), ((X06 Xx)->(X05 Xx)))
% 69.55/69.77 Found x600:=(x60 x7):((cK x4) Xx0)
% 69.55/69.77 Found (x60 x7) as proof of ((cK X06) Xx0)
% 69.55/69.77 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 69.55/69.77 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 69.55/69.77 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 69.55/69.77 Found x8:(X06 Xx1)
% 69.55/69.77 Found x8 as proof of (X05 Xx1)
% 69.55/69.77 Found (fun (x8:(X06 Xx1))=> x8) as proof of (X05 Xx1)
% 69.55/69.77 Found (fun (Xx1:a) (x8:(X06 Xx1))=> x8) as proof of ((X06 Xx1)->(X05 Xx1))
% 69.55/69.77 Found (fun (Xx1:a) (x8:(X06 Xx1))=> x8) as proof of (forall (Xx:a), ((X06 Xx)->(X05 Xx)))
% 69.55/69.77 Found x600:=(x60 x7):((cK x4) Xx0)
% 69.55/69.77 Found (x60 x7) as proof of ((cK X06) Xx0)
% 69.55/69.77 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 69.55/69.77 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 69.55/69.77 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 69.55/69.77 Found x8:(X06 Xx1)
% 69.55/69.77 Found x8 as proof of (X05 Xx1)
% 69.55/69.77 Found (fun (x8:(X06 Xx1))=> x8) as proof of (X05 Xx1)
% 69.55/69.77 Found (fun (Xx1:a) (x8:(X06 Xx1))=> x8) as proof of ((X06 Xx1)->(X05 Xx1))
% 69.55/69.77 Found (fun (Xx1:a) (x8:(X06 Xx1))=> x8) as proof of (forall (Xx:a), ((X06 Xx)->(X05 Xx)))
% 69.55/69.77 Found x600:=(x60 x7):((cK x4) Xx0)
% 69.55/69.77 Found (x60 x7) as proof of ((cK X06) Xx0)
% 69.55/69.77 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 69.55/69.77 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 69.55/69.77 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 69.55/69.77 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 69.55/69.77 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X06) Xx0))
% 69.55/69.77 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X06) Xx0))
% 69.55/69.77 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X06) Xx0))
% 69.55/69.77 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X06) Xx0)))
% 69.55/69.77 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 69.55/69.77 Found ((and_rect0 ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 70.40/70.61 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 70.40/70.61 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X06) Xx0)
% 70.40/70.61 Found x8:(X06 Xx1)
% 70.40/70.61 Found x8 as proof of (X05 Xx1)
% 70.40/70.61 Found (fun (x8:(X06 Xx1))=> x8) as proof of (X05 Xx1)
% 70.40/70.61 Found (fun (Xx1:a) (x8:(X06 Xx1))=> x8) as proof of ((X06 Xx1)->(X05 Xx1))
% 70.40/70.61 Found (fun (Xx1:a) (x8:(X06 Xx1))=> x8) as proof of (forall (Xx:a), ((X06 Xx)->(X05 Xx)))
% 70.40/70.61 Found x600:=(x60 x7):((cK x3) Xx0)
% 70.40/70.61 Found (x60 x7) as proof of ((cK X06) Xx0)
% 70.40/70.61 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 70.40/70.61 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 70.40/70.61 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 70.40/70.61 Found x8:(X06 Xx1)
% 70.40/70.61 Found x8 as proof of (X05 Xx1)
% 70.40/70.61 Found (fun (x8:(X06 Xx1))=> x8) as proof of (X05 Xx1)
% 70.40/70.61 Found (fun (Xx1:a) (x8:(X06 Xx1))=> x8) as proof of ((X06 Xx1)->(X05 Xx1))
% 70.40/70.61 Found (fun (Xx1:a) (x8:(X06 Xx1))=> x8) as proof of (forall (Xx:a), ((X06 Xx)->(X05 Xx)))
% 70.40/70.61 Found x600:=(x60 x7):((cK x4) Xx0)
% 70.40/70.61 Found (x60 x7) as proof of ((cK X06) Xx0)
% 70.40/70.61 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 70.40/70.61 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 70.40/70.61 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 70.40/70.61 Found x8:(X06 Xx1)
% 70.40/70.61 Found x8 as proof of (X05 Xx1)
% 70.40/70.61 Found (fun (x8:(X06 Xx1))=> x8) as proof of (X05 Xx1)
% 70.40/70.61 Found (fun (Xx1:a) (x8:(X06 Xx1))=> x8) as proof of ((X06 Xx1)->(X05 Xx1))
% 70.40/70.61 Found (fun (Xx1:a) (x8:(X06 Xx1))=> x8) as proof of (forall (Xx:a), ((X06 Xx)->(X05 Xx)))
% 70.40/70.61 Found x600:=(x60 x7):((cK x4) Xx0)
% 70.40/70.61 Found (x60 x7) as proof of ((cK X06) Xx0)
% 70.40/70.61 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 70.40/70.61 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 70.40/70.61 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 70.40/70.61 Found x8:(X06 Xx1)
% 70.40/70.61 Found x8 as proof of (X05 Xx1)
% 70.40/70.61 Found (fun (x8:(X06 Xx1))=> x8) as proof of (X05 Xx1)
% 70.40/70.61 Found (fun (Xx1:a) (x8:(X06 Xx1))=> x8) as proof of ((X06 Xx1)->(X05 Xx1))
% 70.40/70.61 Found (fun (Xx1:a) (x8:(X06 Xx1))=> x8) as proof of (forall (Xx:a), ((X06 Xx)->(X05 Xx)))
% 70.40/70.61 Found x600:=(x60 x7):((cK x4) Xx0)
% 70.40/70.61 Found (x60 x7) as proof of ((cK X06) Xx0)
% 70.40/70.61 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 70.40/70.61 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 70.40/70.61 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 70.40/70.61 Found x8:(X06 Xx1)
% 70.40/70.61 Found x8 as proof of (X05 Xx1)
% 70.40/70.61 Found (fun (x8:(X06 Xx1))=> x8) as proof of (X05 Xx1)
% 70.40/70.61 Found (fun (Xx1:a) (x8:(X06 Xx1))=> x8) as proof of ((X06 Xx1)->(X05 Xx1))
% 70.40/70.61 Found (fun (Xx1:a) (x8:(X06 Xx1))=> x8) as proof of (forall (Xx:a), ((X06 Xx)->(X05 Xx)))
% 70.40/70.61 Found x600:=(x60 x7):((cK x4) Xx0)
% 70.40/70.61 Found (x60 x7) as proof of ((cK X06) Xx0)
% 70.40/70.61 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 70.40/70.61 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 70.40/70.61 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 70.40/70.61 Found x8:(X06 Xx1)
% 70.40/70.61 Found x8 as proof of (X05 Xx1)
% 70.40/70.61 Found (fun (x8:(X06 Xx1))=> x8) as proof of (X05 Xx1)
% 70.40/70.61 Found (fun (Xx1:a) (x8:(X06 Xx1))=> x8) as proof of ((X06 Xx1)->(X05 Xx1))
% 70.40/70.61 Found (fun (Xx1:a) (x8:(X06 Xx1))=> x8) as proof of (forall (Xx:a), ((X06 Xx)->(X05 Xx)))
% 70.40/70.61 Found x600:=(x60 x7):((cK x4) Xx0)
% 70.40/70.61 Found (x60 x7) as proof of ((cK X06) Xx0)
% 70.40/70.61 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 70.40/70.61 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 70.40/70.61 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 70.40/70.61 Found x8:(X06 Xx1)
% 70.40/70.61 Found x8 as proof of (X05 Xx1)
% 70.40/70.61 Found (fun (x8:(X06 Xx1))=> x8) as proof of (X05 Xx1)
% 70.40/70.61 Found (fun (Xx1:a) (x8:(X06 Xx1))=> x8) as proof of ((X06 Xx1)->(X05 Xx1))
% 70.40/70.61 Found (fun (Xx1:a) (x8:(X06 Xx1))=> x8) as proof of (forall (Xx:a), ((X06 Xx)->(X05 Xx)))
% 70.40/70.61 Found x600:=(x60 x7):((cK x4) Xx0)
% 70.40/70.61 Found (x60 x7) as proof of ((cK X06) Xx0)
% 70.40/70.61 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 70.40/70.61 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 71.19/71.43 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 71.19/71.43 Found x8:(X06 Xx1)
% 71.19/71.43 Found x8 as proof of (X05 Xx1)
% 71.19/71.43 Found (fun (x8:(X06 Xx1))=> x8) as proof of (X05 Xx1)
% 71.19/71.43 Found (fun (Xx1:a) (x8:(X06 Xx1))=> x8) as proof of ((X06 Xx1)->(X05 Xx1))
% 71.19/71.43 Found (fun (Xx1:a) (x8:(X06 Xx1))=> x8) as proof of (forall (Xx:a), ((X06 Xx)->(X05 Xx)))
% 71.19/71.43 Found x600:=(x60 x7):((cK x3) Xx0)
% 71.19/71.43 Found (x60 x7) as proof of ((cK X06) Xx0)
% 71.19/71.43 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 71.19/71.43 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 71.19/71.43 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 71.19/71.43 Found x8:(X06 Xx1)
% 71.19/71.43 Found x8 as proof of (X05 Xx1)
% 71.19/71.43 Found (fun (x8:(X06 Xx1))=> x8) as proof of (X05 Xx1)
% 71.19/71.43 Found (fun (Xx1:a) (x8:(X06 Xx1))=> x8) as proof of ((X06 Xx1)->(X05 Xx1))
% 71.19/71.43 Found (fun (Xx1:a) (x8:(X06 Xx1))=> x8) as proof of (forall (Xx:a), ((X06 Xx)->(X05 Xx)))
% 71.19/71.43 Found x600:=(x60 x7):((cK x4) Xx0)
% 71.19/71.43 Found (x60 x7) as proof of ((cK X06) Xx0)
% 71.19/71.43 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 71.19/71.43 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 71.19/71.43 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 71.19/71.43 Found x8:(X06 Xx1)
% 71.19/71.43 Found x8 as proof of (X05 Xx1)
% 71.19/71.43 Found (fun (x8:(X06 Xx1))=> x8) as proof of (X05 Xx1)
% 71.19/71.43 Found (fun (Xx1:a) (x8:(X06 Xx1))=> x8) as proof of ((X06 Xx1)->(X05 Xx1))
% 71.19/71.43 Found (fun (Xx1:a) (x8:(X06 Xx1))=> x8) as proof of (forall (Xx:a), ((X06 Xx)->(X05 Xx)))
% 71.19/71.43 Found x600:=(x60 x7):((cK x4) Xx0)
% 71.19/71.43 Found (x60 x7) as proof of ((cK X06) Xx0)
% 71.19/71.43 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 71.19/71.43 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 71.19/71.43 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 71.19/71.43 Found x8:(X06 Xx1)
% 71.19/71.43 Found x8 as proof of (X05 Xx1)
% 71.19/71.43 Found (fun (x8:(X06 Xx1))=> x8) as proof of (X05 Xx1)
% 71.19/71.43 Found (fun (Xx1:a) (x8:(X06 Xx1))=> x8) as proof of ((X06 Xx1)->(X05 Xx1))
% 71.19/71.43 Found (fun (Xx1:a) (x8:(X06 Xx1))=> x8) as proof of (forall (Xx:a), ((X06 Xx)->(X05 Xx)))
% 71.19/71.43 Found x600:=(x60 x7):((cK x4) Xx0)
% 71.19/71.43 Found (x60 x7) as proof of ((cK X06) Xx0)
% 71.19/71.43 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 71.19/71.43 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 71.19/71.43 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 71.19/71.43 Found x8:(X06 Xx1)
% 71.19/71.43 Found x8 as proof of (X05 Xx1)
% 71.19/71.43 Found (fun (x8:(X06 Xx1))=> x8) as proof of (X05 Xx1)
% 71.19/71.43 Found (fun (Xx1:a) (x8:(X06 Xx1))=> x8) as proof of ((X06 Xx1)->(X05 Xx1))
% 71.19/71.43 Found (fun (Xx1:a) (x8:(X06 Xx1))=> x8) as proof of (forall (Xx:a), ((X06 Xx)->(X05 Xx)))
% 71.19/71.43 Found x600:=(x60 x7):((cK x4) Xx0)
% 71.19/71.43 Found (x60 x7) as proof of ((cK X06) Xx0)
% 71.19/71.43 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 71.19/71.43 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 71.19/71.43 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 71.19/71.43 Found x8:(X06 Xx1)
% 71.19/71.43 Found x8 as proof of (X05 Xx1)
% 71.19/71.43 Found (fun (x8:(X06 Xx1))=> x8) as proof of (X05 Xx1)
% 71.19/71.43 Found (fun (Xx1:a) (x8:(X06 Xx1))=> x8) as proof of ((X06 Xx1)->(X05 Xx1))
% 71.19/71.43 Found (fun (Xx1:a) (x8:(X06 Xx1))=> x8) as proof of (forall (Xx:a), ((X06 Xx)->(X05 Xx)))
% 71.19/71.43 Found x600:=(x60 x7):((cK x4) Xx0)
% 71.19/71.43 Found (x60 x7) as proof of ((cK X06) Xx0)
% 71.19/71.43 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 71.19/71.43 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 71.19/71.43 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 71.19/71.43 Found x8:(X06 Xx1)
% 71.19/71.43 Found x8 as proof of (X05 Xx1)
% 71.19/71.43 Found (fun (x8:(X06 Xx1))=> x8) as proof of (X05 Xx1)
% 71.19/71.43 Found (fun (Xx1:a) (x8:(X06 Xx1))=> x8) as proof of ((X06 Xx1)->(X05 Xx1))
% 71.19/71.43 Found (fun (Xx1:a) (x8:(X06 Xx1))=> x8) as proof of (forall (Xx:a), ((X06 Xx)->(X05 Xx)))
% 71.19/71.43 Found x600:=(x60 x7):((cK x4) Xx0)
% 71.19/71.43 Found (x60 x7) as proof of ((cK X06) Xx0)
% 71.19/71.43 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 71.19/71.43 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 71.19/71.43 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 71.19/71.43 Found x8:(X06 Xx1)
% 71.19/71.43 Found x8 as proof of (X05 Xx1)
% 71.19/71.43 Found (fun (x8:(X06 Xx1))=> x8) as proof of (X05 Xx1)
% 71.19/71.43 Found (fun (Xx1:a) (x8:(X06 Xx1))=> x8) as proof of ((X06 Xx1)->(X05 Xx1))
% 71.19/71.43 Found (fun (Xx1:a) (x8:(X06 Xx1))=> x8) as proof of (forall (Xx:a), ((X06 Xx)->(X05 Xx)))
% 71.19/71.43 Found x600:=(x60 x7):((cK x4) Xx0)
% 71.19/71.43 Found (x60 x7) as proof of ((cK X06) Xx0)
% 71.19/71.43 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 71.19/71.43 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 71.19/71.43 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 71.19/71.43 Found x8:(X06 Xx1)
% 71.19/71.43 Found x8 as proof of (X05 Xx1)
% 71.19/71.43 Found (fun (x8:(X06 Xx1))=> x8) as proof of (X05 Xx1)
% 71.19/71.43 Found (fun (Xx1:a) (x8:(X06 Xx1))=> x8) as proof of ((X06 Xx1)->(X05 Xx1))
% 71.68/71.90 Found (fun (Xx1:a) (x8:(X06 Xx1))=> x8) as proof of (forall (Xx:a), ((X06 Xx)->(X05 Xx)))
% 71.68/71.90 Found x600:=(x60 x7):((cK x3) Xx0)
% 71.68/71.90 Found (x60 x7) as proof of ((cK X06) Xx0)
% 71.68/71.90 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 71.68/71.90 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 71.68/71.90 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 71.68/71.90 Found x8:(X06 Xx1)
% 71.68/71.90 Found x8 as proof of (X05 Xx1)
% 71.68/71.90 Found (fun (x8:(X06 Xx1))=> x8) as proof of (X05 Xx1)
% 71.68/71.90 Found (fun (Xx1:a) (x8:(X06 Xx1))=> x8) as proof of ((X06 Xx1)->(X05 Xx1))
% 71.68/71.90 Found (fun (Xx1:a) (x8:(X06 Xx1))=> x8) as proof of (forall (Xx:a), ((X06 Xx)->(X05 Xx)))
% 71.68/71.90 Found x600:=(x60 x7):((cK x4) Xx0)
% 71.68/71.90 Found (x60 x7) as proof of ((cK X06) Xx0)
% 71.68/71.90 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 71.68/71.90 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 71.68/71.90 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 71.68/71.90 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 71.68/71.90 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X06) Xx0))
% 71.68/71.90 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X06) Xx0))
% 71.68/71.90 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X06) Xx0))
% 71.68/71.90 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X06) Xx0)))
% 71.68/71.90 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 71.68/71.90 Found ((and_rect0 ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 71.68/71.90 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 71.68/71.90 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 71.68/71.90 Found x6:(X06 Xx1)
% 71.68/71.90 Instantiate: X05:=X06:(a->Prop)
% 71.68/71.90 Found (fun (x6:(X06 Xx1))=> x6) as proof of (X05 Xx1)
% 71.68/71.90 Found (fun (Xx1:a) (x6:(X06 Xx1))=> x6) as proof of ((X06 Xx1)->(X05 Xx1))
% 71.68/71.90 Found (fun (Xx1:a) (x6:(X06 Xx1))=> x6) as proof of (forall (Xx:a), ((X06 Xx)->(X05 Xx)))
% 71.68/71.90 Found ((x370 (fun (Xx1:a) (x6:(X06 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X05) Xx0)
% 71.68/71.90 Found (((x37 X05) (fun (Xx1:a) (x6:(X06 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X05) Xx0)
% 71.68/71.90 Found ((((x3 x4) X05) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X05) Xx0)
% 71.68/71.90 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> ((((x3 x4) X05) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))))) as proof of ((cK X05) Xx0)
% 71.68/71.90 Found x8:(X06 Xx1)
% 71.68/71.90 Found x8 as proof of (X05 Xx1)
% 71.68/71.90 Found (fun (x8:(X06 Xx1))=> x8) as proof of (X05 Xx1)
% 71.68/71.90 Found (fun (Xx1:a) (x8:(X06 Xx1))=> x8) as proof of ((X06 Xx1)->(X05 Xx1))
% 71.68/71.90 Found (fun (Xx1:a) (x8:(X06 Xx1))=> x8) as proof of (forall (Xx:a), ((X06 Xx)->(X05 Xx)))
% 71.68/71.90 Found x600:=(x60 x7):((cK x3) Xx0)
% 71.68/71.90 Found (x60 x7) as proof of ((cK X06) Xx0)
% 71.68/71.90 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 72.58/72.82 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 72.58/72.82 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 72.58/72.82 Found x8:(X06 Xx1)
% 72.58/72.82 Found x8 as proof of (X05 Xx1)
% 72.58/72.82 Found (fun (x8:(X06 Xx1))=> x8) as proof of (X05 Xx1)
% 72.58/72.82 Found (fun (Xx1:a) (x8:(X06 Xx1))=> x8) as proof of ((X06 Xx1)->(X05 Xx1))
% 72.58/72.82 Found (fun (Xx1:a) (x8:(X06 Xx1))=> x8) as proof of (forall (Xx:a), ((X06 Xx)->(X05 Xx)))
% 72.58/72.82 Found x600:=(x60 x7):((cK x4) Xx0)
% 72.58/72.82 Found (x60 x7) as proof of ((cK X06) Xx0)
% 72.58/72.82 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 72.58/72.82 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 72.58/72.82 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 72.58/72.82 Found x8:(X06 Xx1)
% 72.58/72.82 Found x8 as proof of (X05 Xx1)
% 72.58/72.82 Found (fun (x8:(X06 Xx1))=> x8) as proof of (X05 Xx1)
% 72.58/72.82 Found (fun (Xx1:a) (x8:(X06 Xx1))=> x8) as proof of ((X06 Xx1)->(X05 Xx1))
% 72.58/72.82 Found (fun (Xx1:a) (x8:(X06 Xx1))=> x8) as proof of (forall (Xx:a), ((X06 Xx)->(X05 Xx)))
% 72.58/72.82 Found x600:=(x60 x7):((cK x3) Xx0)
% 72.58/72.82 Found (x60 x7) as proof of ((cK X06) Xx0)
% 72.58/72.82 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 72.58/72.82 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 72.58/72.82 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 72.58/72.82 Found x8:(X06 Xx1)
% 72.58/72.82 Found x8 as proof of (X05 Xx1)
% 72.58/72.82 Found (fun (x8:(X06 Xx1))=> x8) as proof of (X05 Xx1)
% 72.58/72.82 Found (fun (Xx1:a) (x8:(X06 Xx1))=> x8) as proof of ((X06 Xx1)->(X05 Xx1))
% 72.58/72.82 Found (fun (Xx1:a) (x8:(X06 Xx1))=> x8) as proof of (forall (Xx:a), ((X06 Xx)->(X05 Xx)))
% 72.58/72.82 Found x600:=(x60 x7):((cK x4) Xx0)
% 72.58/72.82 Found (x60 x7) as proof of ((cK X06) Xx0)
% 72.58/72.82 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 72.58/72.82 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 72.58/72.82 Found ((x6 Xx0) x7) as proof of ((cK X06) Xx0)
% 72.58/72.82 Found x4:(X05 Xx1)
% 72.58/72.82 Instantiate: X05:=(cK x5):(a->Prop)
% 72.58/72.82 Found x4 as proof of (X04 Xx1)
% 72.58/72.82 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X04 Xx1)
% 72.58/72.82 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X04 Xx1))
% 72.58/72.82 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X04 Xx1)))
% 72.58/72.82 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X04 Xx1)
% 72.58/72.82 Found ((and_rect0 (X04 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X04 Xx1)
% 72.58/72.82 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X04 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X04 Xx1)
% 72.58/72.82 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X04 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X04 Xx1)
% 72.58/72.82 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 72.58/72.82 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X06) Xx0))
% 72.58/72.82 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X06) Xx0))
% 72.58/72.82 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X06) Xx0))
% 72.58/72.82 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X06) Xx0)))
% 72.58/72.82 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 72.58/72.82 Found ((and_rect0 ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 72.58/72.82 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 72.58/72.82 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X06) Xx0)
% 73.41/73.66 Found x4:(X05 Xx1)
% 73.41/73.66 Found x4 as proof of (X04 Xx1)
% 73.41/73.66 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X04 Xx1)
% 73.41/73.66 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X04 Xx1))
% 73.41/73.66 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X04 Xx1)))
% 73.41/73.66 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X04 Xx1)
% 73.41/73.66 Found ((and_rect0 (X04 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X04 Xx1)
% 73.41/73.66 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X04 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X04 Xx1)
% 73.41/73.66 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X04 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X04 Xx1)
% 73.41/73.66 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 73.41/73.66 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X06) Xx0))
% 73.41/73.66 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X06) Xx0))
% 73.41/73.66 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X06) Xx0))
% 73.41/73.66 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X06) Xx0)))
% 73.41/73.66 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 73.41/73.66 Found ((and_rect0 ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 73.41/73.66 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 73.41/73.66 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 73.41/73.66 Found x6:(X06 Xx1)
% 73.41/73.66 Instantiate: X05:=X06:(a->Prop)
% 73.41/73.66 Found (fun (x6:(X06 Xx1))=> x6) as proof of (X05 Xx1)
% 73.41/73.66 Found (fun (Xx1:a) (x6:(X06 Xx1))=> x6) as proof of ((X06 Xx1)->(X05 Xx1))
% 73.41/73.66 Found (fun (Xx1:a) (x6:(X06 Xx1))=> x6) as proof of (forall (Xx:a), ((X06 Xx)->(X05 Xx)))
% 73.41/73.66 Found ((x370 (fun (Xx1:a) (x6:(X06 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X05) Xx0)
% 73.41/73.66 Found (((x37 X05) (fun (Xx1:a) (x6:(X06 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X05) Xx0)
% 73.41/73.66 Found ((((x3 x4) X05) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X05) Xx0)
% 73.41/73.66 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> ((((x3 x4) X05) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))))) as proof of ((cK X05) Xx0)
% 75.04/75.26 Found x4:(X06 Xx1)
% 75.04/75.26 Instantiate: X06:=(cK x5):(a->Prop)
% 75.04/75.26 Found x4 as proof of (X05 Xx1)
% 75.04/75.26 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X05 Xx1)
% 75.04/75.26 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X05 Xx1))
% 75.04/75.26 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X05 Xx1)))
% 75.04/75.26 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X05 Xx1)
% 75.04/75.26 Found ((and_rect0 (X05 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X05 Xx1)
% 75.04/75.26 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X05 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X05 Xx1)
% 75.04/75.26 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X05 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X05 Xx1)
% 75.04/75.26 Found x4:(X06 Xx1)
% 75.04/75.26 Found x4 as proof of (X05 Xx1)
% 75.04/75.26 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X05 Xx1)
% 75.04/75.26 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X05 Xx1))
% 75.04/75.26 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X05 Xx1)))
% 75.04/75.26 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X05 Xx1)
% 75.04/75.26 Found ((and_rect0 (X05 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X05 Xx1)
% 75.04/75.26 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X05 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X05 Xx1)
% 75.04/75.26 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X05 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X05 Xx1)
% 75.04/75.26 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 75.04/75.26 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X06) Xx0))
% 75.04/75.26 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X06) Xx0))
% 75.04/75.26 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X06) Xx0))
% 75.04/75.26 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X06) Xx0)))
% 75.04/75.26 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 75.04/75.26 Found ((and_rect0 ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 75.04/75.26 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 75.04/75.26 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X06) Xx0)
% 75.04/75.26 Found x4:(X06 Xx1)
% 75.04/75.26 Instantiate: X06:=(cK x5):(a->Prop)
% 75.15/75.40 Found x4 as proof of (X05 Xx1)
% 75.15/75.40 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X05 Xx1)
% 75.15/75.40 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X05 Xx1))
% 75.15/75.40 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X05 Xx1)))
% 75.15/75.40 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X05 Xx1)
% 75.15/75.40 Found ((and_rect0 (X05 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X05 Xx1)
% 75.15/75.40 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X05 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X05 Xx1)
% 75.15/75.40 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X05 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X05 Xx1)
% 75.15/75.40 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 75.15/75.40 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X06) Xx0))
% 75.15/75.40 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X06) Xx0))
% 75.15/75.40 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X06) Xx0))
% 75.15/75.40 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X06) Xx0)))
% 75.15/75.40 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 75.15/75.40 Found ((and_rect0 ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 75.15/75.40 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 75.15/75.40 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 75.15/75.40 Found x6:(X06 Xx1)
% 75.15/75.40 Instantiate: X05:=X06:(a->Prop)
% 75.15/75.40 Found (fun (x6:(X06 Xx1))=> x6) as proof of (X05 Xx1)
% 75.15/75.40 Found (fun (Xx1:a) (x6:(X06 Xx1))=> x6) as proof of ((X06 Xx1)->(X05 Xx1))
% 75.15/75.40 Found (fun (Xx1:a) (x6:(X06 Xx1))=> x6) as proof of (forall (Xx:a), ((X06 Xx)->(X05 Xx)))
% 75.15/75.40 Found ((x370 (fun (Xx1:a) (x6:(X06 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X05) Xx0)
% 75.15/75.40 Found (((x37 X05) (fun (Xx1:a) (x6:(X06 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X05) Xx0)
% 75.15/75.40 Found ((((x3 x4) X05) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X05) Xx0)
% 75.15/75.40 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> ((((x3 x4) X05) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))))) as proof of ((cK X05) Xx0)
% 76.96/77.18 Found x4:(X06 Xx1)
% 76.96/77.18 Found x4 as proof of (X05 Xx1)
% 76.96/77.18 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X05 Xx1)
% 76.96/77.18 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X05 Xx1))
% 76.96/77.18 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X05 Xx1)))
% 76.96/77.18 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X05 Xx1)
% 76.96/77.18 Found ((and_rect0 (X05 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X05 Xx1)
% 76.96/77.18 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X05 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X05 Xx1)
% 76.96/77.18 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X05 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X05 Xx1)
% 76.96/77.18 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 76.96/77.18 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X06) Xx0))
% 76.96/77.18 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X06) Xx0))
% 76.96/77.18 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X06) Xx0))
% 76.96/77.18 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X06) Xx0)))
% 76.96/77.18 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 76.96/77.18 Found ((and_rect0 ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 76.96/77.18 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 76.96/77.18 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X06) Xx0)
% 76.96/77.18 Found x4:(X06 Xx1)
% 76.96/77.18 Instantiate: X06:=(cK x5):(a->Prop)
% 76.96/77.18 Found x4 as proof of (X05 Xx1)
% 76.96/77.18 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X05 Xx1)
% 76.96/77.18 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X05 Xx1))
% 76.96/77.18 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X05 Xx1)))
% 76.96/77.18 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X05 Xx1)
% 76.96/77.18 Found ((and_rect0 (X05 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X05 Xx1)
% 76.96/77.18 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X05 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X05 Xx1)
% 76.96/77.18 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X05 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X05 Xx1)
% 76.96/77.18 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 76.96/77.18 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X06) Xx0))
% 77.49/77.72 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X06) Xx0))
% 77.49/77.72 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X06) Xx0))
% 77.49/77.72 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X06) Xx0)))
% 77.49/77.72 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 77.49/77.72 Found ((and_rect0 ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 77.49/77.72 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 77.49/77.72 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 77.49/77.72 Found x6:(X06 Xx1)
% 77.49/77.72 Instantiate: X05:=X06:(a->Prop)
% 77.49/77.72 Found (fun (x6:(X06 Xx1))=> x6) as proof of (X05 Xx1)
% 77.49/77.72 Found (fun (Xx1:a) (x6:(X06 Xx1))=> x6) as proof of ((X06 Xx1)->(X05 Xx1))
% 77.49/77.72 Found (fun (Xx1:a) (x6:(X06 Xx1))=> x6) as proof of (forall (Xx:a), ((X06 Xx)->(X05 Xx)))
% 77.49/77.72 Found ((x370 (fun (Xx1:a) (x6:(X06 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X05) Xx0)
% 77.49/77.72 Found (((x37 X05) (fun (Xx1:a) (x6:(X06 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X05) Xx0)
% 77.49/77.72 Found ((((x3 x4) X05) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X05) Xx0)
% 77.49/77.72 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> ((((x3 x4) X05) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))))) as proof of ((cK X05) Xx0)
% 77.49/77.72 Found x4:(X06 Xx1)
% 77.49/77.72 Found x4 as proof of (X05 Xx1)
% 77.49/77.72 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X05 Xx1)
% 77.49/77.72 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X05 Xx1))
% 77.49/77.72 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X05 Xx1)))
% 77.49/77.72 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X05 Xx1)
% 77.49/77.72 Found ((and_rect0 (X05 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X05 Xx1)
% 77.49/77.72 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X05 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X05 Xx1)
% 77.49/77.72 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X05 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X05 Xx1)
% 77.49/77.72 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 78.60/78.81 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X06) Xx0))
% 78.60/78.81 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X06) Xx0))
% 78.60/78.81 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X06) Xx0))
% 78.60/78.81 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X06) Xx0)))
% 78.60/78.81 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 78.60/78.81 Found ((and_rect0 ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 78.60/78.81 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 78.60/78.81 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X06) Xx0)
% 78.60/78.81 Found x4:(X06 Xx1)
% 78.60/78.81 Instantiate: X06:=(cK x5):(a->Prop)
% 78.60/78.81 Found x4 as proof of (X05 Xx1)
% 78.60/78.81 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X05 Xx1)
% 78.60/78.81 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X05 Xx1))
% 78.60/78.81 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X05 Xx1)))
% 78.60/78.81 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X05 Xx1)
% 78.60/78.81 Found ((and_rect0 (X05 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X05 Xx1)
% 78.60/78.81 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X05 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X05 Xx1)
% 78.60/78.81 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X05 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X05 Xx1)
% 78.60/78.81 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 78.60/78.81 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X06) Xx0))
% 78.60/78.81 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X06) Xx0))
% 78.60/78.81 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X06) Xx0))
% 78.60/78.81 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X06) Xx0)))
% 78.60/78.81 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 78.60/78.81 Found ((and_rect0 ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 78.60/78.81 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 78.60/78.81 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 78.60/78.81 Found x6:(X06 Xx1)
% 78.60/78.81 Instantiate: X05:=X06:(a->Prop)
% 78.60/78.81 Found (fun (x6:(X06 Xx1))=> x6) as proof of (X05 Xx1)
% 78.60/78.81 Found (fun (Xx1:a) (x6:(X06 Xx1))=> x6) as proof of ((X06 Xx1)->(X05 Xx1))
% 78.60/78.81 Found (fun (Xx1:a) (x6:(X06 Xx1))=> x6) as proof of (forall (Xx:a), ((X06 Xx)->(X05 Xx)))
% 78.60/78.81 Found ((x370 (fun (Xx1:a) (x6:(X06 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X05) Xx0)
% 79.48/79.70 Found (((x37 X05) (fun (Xx1:a) (x6:(X06 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X05) Xx0)
% 79.48/79.70 Found ((((x3 x4) X05) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X05) Xx0)
% 79.48/79.70 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> ((((x3 x4) X05) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))))) as proof of ((cK X05) Xx0)
% 79.48/79.70 Found x4:(X06 Xx1)
% 79.48/79.70 Found x4 as proof of (X05 Xx1)
% 79.48/79.70 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X05 Xx1)
% 79.48/79.70 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X05 Xx1))
% 79.48/79.70 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X05 Xx1)))
% 79.48/79.70 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X05 Xx1)
% 79.48/79.70 Found ((and_rect0 (X05 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X05 Xx1)
% 79.48/79.70 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X05 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X05 Xx1)
% 79.48/79.70 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X05 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X05 Xx1)
% 79.48/79.70 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 79.48/79.70 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X06) Xx0))
% 79.48/79.70 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X06) Xx0))
% 79.48/79.70 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X06) Xx0))
% 79.48/79.70 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X06) Xx0)))
% 79.48/79.70 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 79.48/79.70 Found ((and_rect0 ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 79.48/79.70 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 79.48/79.70 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X06) Xx0)
% 79.48/79.70 Found x4:(X06 Xx1)
% 79.48/79.70 Instantiate: X06:=(cK x5):(a->Prop)
% 79.48/79.70 Found x4 as proof of (X05 Xx1)
% 79.48/79.70 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X05 Xx1)
% 80.06/80.28 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X05 Xx1))
% 80.06/80.28 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X05 Xx1)))
% 80.06/80.28 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X05 Xx1)
% 80.06/80.28 Found ((and_rect0 (X05 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X05 Xx1)
% 80.06/80.28 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X05 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X05 Xx1)
% 80.06/80.28 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X05 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X05 Xx1)
% 80.06/80.28 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 80.06/80.28 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X06) Xx0))
% 80.06/80.28 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X06) Xx0))
% 80.06/80.28 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X06) Xx0))
% 80.06/80.28 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X06) Xx0)))
% 80.06/80.28 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 80.06/80.28 Found ((and_rect0 ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 80.06/80.28 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 80.06/80.28 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 80.06/80.28 Found x6:(X06 Xx1)
% 80.06/80.28 Instantiate: X05:=X06:(a->Prop)
% 80.06/80.28 Found (fun (x6:(X06 Xx1))=> x6) as proof of (X05 Xx1)
% 80.06/80.28 Found (fun (Xx1:a) (x6:(X06 Xx1))=> x6) as proof of ((X06 Xx1)->(X05 Xx1))
% 80.06/80.28 Found (fun (Xx1:a) (x6:(X06 Xx1))=> x6) as proof of (forall (Xx:a), ((X06 Xx)->(X05 Xx)))
% 80.06/80.28 Found ((x370 (fun (Xx1:a) (x6:(X06 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X05) Xx0)
% 80.06/80.28 Found (((x37 X05) (fun (Xx1:a) (x6:(X06 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X05) Xx0)
% 80.06/80.28 Found ((((x3 x4) X05) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X05) Xx0)
% 80.06/80.28 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> ((((x3 x4) X05) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))))) as proof of ((cK X05) Xx0)
% 80.06/80.28 Found x4:(X06 Xx1)
% 84.94/85.16 Found x4 as proof of (X05 Xx1)
% 84.94/85.16 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X05 Xx1)
% 84.94/85.16 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X05 Xx1))
% 84.94/85.16 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X05 Xx1)))
% 84.94/85.16 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X05 Xx1)
% 84.94/85.16 Found ((and_rect0 (X05 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X05 Xx1)
% 84.94/85.16 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X05 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X05 Xx1)
% 84.94/85.16 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X05 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X05 Xx1)
% 84.94/85.16 Found x4:(X07 Xx1)
% 84.94/85.16 Found x4 as proof of (X06 Xx1)
% 84.94/85.16 Found (fun (x4:(X07 Xx1))=> x4) as proof of (X06 Xx1)
% 84.94/85.16 Found (fun (Xx1:a) (x4:(X07 Xx1))=> x4) as proof of ((X07 Xx1)->(X06 Xx1))
% 84.94/85.16 Found (fun (Xx1:a) (x4:(X07 Xx1))=> x4) as proof of (forall (Xx:a), ((X07 Xx)->(X06 Xx)))
% 84.94/85.16 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 84.94/85.16 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X06) Xx0))
% 84.94/85.16 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X06) Xx0))
% 84.94/85.16 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X06) Xx0))
% 84.94/85.16 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X06) Xx0)))
% 84.94/85.16 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 84.94/85.16 Found ((and_rect0 ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 84.94/85.16 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 84.94/85.16 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X06) Xx0)
% 84.94/85.16 Found x6:(X07 Xx1)
% 84.94/85.16 Found x6 as proof of (X06 Xx1)
% 84.94/85.16 Found (fun (x6:(X07 Xx1))=> x6) as proof of (X06 Xx1)
% 84.94/85.16 Found (fun (Xx1:a) (x6:(X07 Xx1))=> x6) as proof of ((X07 Xx1)->(X06 Xx1))
% 84.94/85.16 Found (fun (Xx1:a) (x6:(X07 Xx1))=> x6) as proof of (forall (Xx:a), ((X07 Xx)->(X06 Xx)))
% 84.94/85.16 Found x6:(X07 Xx1)
% 84.94/85.16 Found x6 as proof of (X06 Xx1)
% 84.94/85.16 Found (fun (x6:(X07 Xx1))=> x6) as proof of (X06 Xx1)
% 84.94/85.16 Found (fun (Xx1:a) (x6:(X07 Xx1))=> x6) as proof of ((X07 Xx1)->(X06 Xx1))
% 84.94/85.16 Found (fun (Xx1:a) (x6:(X07 Xx1))=> x6) as proof of (forall (Xx:a), ((X07 Xx)->(X06 Xx)))
% 84.94/85.16 Found x6:(X07 Xx1)
% 84.94/85.16 Found x6 as proof of (X06 Xx1)
% 84.94/85.16 Found (fun (x6:(X07 Xx1))=> x6) as proof of (X06 Xx1)
% 84.94/85.16 Found (fun (Xx1:a) (x6:(X07 Xx1))=> x6) as proof of ((X07 Xx1)->(X06 Xx1))
% 84.94/85.16 Found (fun (Xx1:a) (x6:(X07 Xx1))=> x6) as proof of (forall (Xx:a), ((X07 Xx)->(X06 Xx)))
% 84.94/85.16 Found x6:(X07 Xx1)
% 84.94/85.16 Found x6 as proof of (X06 Xx1)
% 84.94/85.16 Found (fun (x6:(X07 Xx1))=> x6) as proof of (X06 Xx1)
% 84.94/85.16 Found (fun (Xx1:a) (x6:(X07 Xx1))=> x6) as proof of ((X07 Xx1)->(X06 Xx1))
% 84.94/85.16 Found (fun (Xx1:a) (x6:(X07 Xx1))=> x6) as proof of (forall (Xx:a), ((X07 Xx)->(X06 Xx)))
% 84.94/85.16 Found x6:(X07 Xx1)
% 84.94/85.16 Found x6 as proof of (X06 Xx1)
% 84.94/85.16 Found (fun (x6:(X07 Xx1))=> x6) as proof of (X06 Xx1)
% 84.94/85.16 Found (fun (Xx1:a) (x6:(X07 Xx1))=> x6) as proof of ((X07 Xx1)->(X06 Xx1))
% 94.96/95.22 Found (fun (Xx1:a) (x6:(X07 Xx1))=> x6) as proof of (forall (Xx:a), ((X07 Xx)->(X06 Xx)))
% 94.96/95.22 Found x6:(X07 Xx1)
% 94.96/95.22 Found x6 as proof of (X06 Xx1)
% 94.96/95.22 Found (fun (x6:(X07 Xx1))=> x6) as proof of (X06 Xx1)
% 94.96/95.22 Found (fun (Xx1:a) (x6:(X07 Xx1))=> x6) as proof of ((X07 Xx1)->(X06 Xx1))
% 94.96/95.22 Found (fun (Xx1:a) (x6:(X07 Xx1))=> x6) as proof of (forall (Xx:a), ((X07 Xx)->(X06 Xx)))
% 94.96/95.22 Found x6:(X07 Xx1)
% 94.96/95.22 Found x6 as proof of (X06 Xx1)
% 94.96/95.22 Found (fun (x6:(X07 Xx1))=> x6) as proof of (X06 Xx1)
% 94.96/95.22 Found (fun (Xx1:a) (x6:(X07 Xx1))=> x6) as proof of ((X07 Xx1)->(X06 Xx1))
% 94.96/95.22 Found (fun (Xx1:a) (x6:(X07 Xx1))=> x6) as proof of (forall (Xx:a), ((X07 Xx)->(X06 Xx)))
% 94.96/95.22 Found x6:(X07 Xx1)
% 94.96/95.22 Found x6 as proof of (X06 Xx1)
% 94.96/95.22 Found (fun (x6:(X07 Xx1))=> x6) as proof of (X06 Xx1)
% 94.96/95.22 Found (fun (Xx1:a) (x6:(X07 Xx1))=> x6) as proof of ((X07 Xx1)->(X06 Xx1))
% 94.96/95.22 Found (fun (Xx1:a) (x6:(X07 Xx1))=> x6) as proof of (forall (Xx:a), ((X07 Xx)->(X06 Xx)))
% 94.96/95.22 Found x6:(X07 Xx1)
% 94.96/95.22 Found x6 as proof of (X06 Xx1)
% 94.96/95.22 Found (fun (x6:(X07 Xx1))=> x6) as proof of (X06 Xx1)
% 94.96/95.22 Found (fun (Xx1:a) (x6:(X07 Xx1))=> x6) as proof of ((X07 Xx1)->(X06 Xx1))
% 94.96/95.22 Found (fun (Xx1:a) (x6:(X07 Xx1))=> x6) as proof of (forall (Xx:a), ((X07 Xx)->(X06 Xx)))
% 94.96/95.22 Found x8:(X07 Xx1)
% 94.96/95.22 Found x8 as proof of (X06 Xx1)
% 94.96/95.22 Found (fun (x8:(X07 Xx1))=> x8) as proof of (X06 Xx1)
% 94.96/95.22 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of ((X07 Xx1)->(X06 Xx1))
% 94.96/95.22 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of (forall (Xx:a), ((X07 Xx)->(X06 Xx)))
% 94.96/95.22 Found x600:=(x60 x7):((cK x4) Xx0)
% 94.96/95.22 Found (x60 x7) as proof of ((cK X07) Xx0)
% 94.96/95.22 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 94.96/95.22 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 94.96/95.22 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 94.96/95.22 Found x4:(X06 Xx1)
% 94.96/95.22 Instantiate: X06:=(cK x5):(a->Prop)
% 94.96/95.22 Found x4 as proof of (X05 Xx1)
% 94.96/95.22 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X05 Xx1)
% 94.96/95.22 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X05 Xx1))
% 94.96/95.22 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X05 Xx1)))
% 94.96/95.22 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X05 Xx1)
% 94.96/95.22 Found ((and_rect0 (X05 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X05 Xx1)
% 94.96/95.22 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X05 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X05 Xx1)
% 94.96/95.22 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X05 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X05 Xx1)
% 94.96/95.22 Found x8:(X07 Xx1)
% 94.96/95.22 Found x8 as proof of (X06 Xx1)
% 94.96/95.22 Found (fun (x8:(X07 Xx1))=> x8) as proof of (X06 Xx1)
% 94.96/95.22 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of ((X07 Xx1)->(X06 Xx1))
% 94.96/95.22 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of (forall (Xx:a), ((X07 Xx)->(X06 Xx)))
% 94.96/95.22 Found x600:=(x60 x7):((cK x4) Xx0)
% 94.96/95.22 Found (x60 x7) as proof of ((cK X07) Xx0)
% 94.96/95.22 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 94.96/95.22 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 94.96/95.22 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 94.96/95.22 Found x8:(X07 Xx1)
% 94.96/95.22 Found x8 as proof of (X06 Xx1)
% 94.96/95.22 Found (fun (x8:(X07 Xx1))=> x8) as proof of (X06 Xx1)
% 94.96/95.22 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of ((X07 Xx1)->(X06 Xx1))
% 94.96/95.22 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of (forall (Xx:a), ((X07 Xx)->(X06 Xx)))
% 94.96/95.22 Found x600:=(x60 x7):((cK x4) Xx0)
% 94.96/95.22 Found (x60 x7) as proof of ((cK X07) Xx0)
% 94.96/95.22 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 94.96/95.22 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 94.96/95.22 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 94.96/95.22 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 94.96/95.22 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X07) Xx0))
% 94.96/95.22 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X07) Xx0))
% 95.12/95.41 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X07) Xx0))
% 95.12/95.41 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X07) Xx0)))
% 95.12/95.41 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 95.12/95.41 Found ((and_rect0 ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 95.12/95.41 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 95.12/95.41 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 95.12/95.41 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 95.12/95.41 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X07) Xx0))
% 95.12/95.41 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X07) Xx0))
% 95.12/95.41 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X07) Xx0))
% 95.12/95.41 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X07) Xx0)))
% 95.12/95.41 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 95.12/95.41 Found ((and_rect0 ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 95.12/95.41 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 95.12/95.41 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 95.12/95.41 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 95.12/95.41 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X07) Xx0))
% 95.12/95.41 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X07) Xx0))
% 95.12/95.41 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X07) Xx0))
% 95.12/95.41 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X07) Xx0)))
% 95.12/95.41 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 95.12/95.41 Found ((and_rect0 ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 95.12/95.41 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 95.12/95.41 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 95.12/95.41 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 95.12/95.41 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X07) Xx0))
% 95.12/95.41 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X07) Xx0))
% 95.12/95.41 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X07) Xx0))
% 95.12/95.41 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X07) Xx0)))
% 95.12/95.41 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 95.12/95.41 Found ((and_rect0 ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 95.21/95.47 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 95.21/95.47 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 95.21/95.47 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 95.21/95.47 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X07) Xx0))
% 95.21/95.47 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X07) Xx0))
% 95.21/95.47 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X07) Xx0))
% 95.21/95.47 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X07) Xx0)))
% 95.21/95.47 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 95.21/95.47 Found ((and_rect0 ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 95.21/95.47 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 95.21/95.47 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 95.21/95.47 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 95.21/95.47 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X07) Xx0))
% 95.21/95.47 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X07) Xx0))
% 95.21/95.47 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X07) Xx0))
% 95.21/95.47 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X07) Xx0)))
% 95.21/95.47 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 95.21/95.47 Found ((and_rect0 ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 95.21/95.47 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 95.21/95.47 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 95.21/95.47 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 95.21/95.47 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X07) Xx0))
% 95.21/95.47 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X07) Xx0))
% 95.21/95.47 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X07) Xx0))
% 95.21/95.47 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X07) Xx0)))
% 95.21/95.47 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 95.21/95.47 Found ((and_rect0 ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 95.21/95.47 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 95.21/95.47 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 97.58/97.89 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 97.58/97.89 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X07) Xx0))
% 97.58/97.89 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X07) Xx0))
% 97.58/97.89 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X07) Xx0))
% 97.58/97.89 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X07) Xx0)))
% 97.58/97.89 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 97.58/97.89 Found ((and_rect0 ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 97.58/97.89 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 97.58/97.89 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 97.58/97.89 Found x8:(X07 Xx1)
% 97.58/97.89 Found x8 as proof of (X06 Xx1)
% 97.58/97.89 Found (fun (x8:(X07 Xx1))=> x8) as proof of (X06 Xx1)
% 97.58/97.89 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of ((X07 Xx1)->(X06 Xx1))
% 97.58/97.89 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of (forall (Xx:a), ((X07 Xx)->(X06 Xx)))
% 97.58/97.89 Found x600:=(x60 x7):((cK x3) Xx0)
% 97.58/97.89 Found (x60 x7) as proof of ((cK X07) Xx0)
% 97.58/97.89 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 97.58/97.89 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 97.58/97.89 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 97.58/97.89 Found x8:(X07 Xx1)
% 97.58/97.89 Found x8 as proof of (X06 Xx1)
% 97.58/97.89 Found (fun (x8:(X07 Xx1))=> x8) as proof of (X06 Xx1)
% 97.58/97.89 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of ((X07 Xx1)->(X06 Xx1))
% 97.58/97.89 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of (forall (Xx:a), ((X07 Xx)->(X06 Xx)))
% 97.58/97.89 Found x600:=(x60 x7):((cK x4) Xx0)
% 97.58/97.89 Found (x60 x7) as proof of ((cK X07) Xx0)
% 97.58/97.89 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 97.58/97.89 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 97.58/97.89 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 97.58/97.89 Found x8:(X07 Xx1)
% 97.58/97.89 Found x8 as proof of (X06 Xx1)
% 97.58/97.89 Found (fun (x8:(X07 Xx1))=> x8) as proof of (X06 Xx1)
% 97.58/97.89 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of ((X07 Xx1)->(X06 Xx1))
% 97.58/97.89 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of (forall (Xx:a), ((X07 Xx)->(X06 Xx)))
% 97.58/97.89 Found x600:=(x60 x7):((cK x4) Xx0)
% 97.58/97.89 Found (x60 x7) as proof of ((cK X07) Xx0)
% 97.58/97.89 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 97.58/97.89 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 97.58/97.89 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 97.58/97.89 Found x8:(X07 Xx1)
% 97.58/97.89 Found x8 as proof of (X06 Xx1)
% 97.58/97.89 Found (fun (x8:(X07 Xx1))=> x8) as proof of (X06 Xx1)
% 97.58/97.89 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of ((X07 Xx1)->(X06 Xx1))
% 97.58/97.89 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of (forall (Xx:a), ((X07 Xx)->(X06 Xx)))
% 97.58/97.89 Found x600:=(x60 x7):((cK x4) Xx0)
% 97.58/97.89 Found (x60 x7) as proof of ((cK X07) Xx0)
% 97.58/97.89 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 97.58/97.89 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 97.58/97.89 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 97.58/97.89 Found x8:(X07 Xx1)
% 97.58/97.89 Found x8 as proof of (X06 Xx1)
% 97.58/97.89 Found (fun (x8:(X07 Xx1))=> x8) as proof of (X06 Xx1)
% 97.58/97.89 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of ((X07 Xx1)->(X06 Xx1))
% 97.58/97.89 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of (forall (Xx:a), ((X07 Xx)->(X06 Xx)))
% 97.58/97.89 Found x600:=(x60 x7):((cK x4) Xx0)
% 97.58/97.89 Found (x60 x7) as proof of ((cK X07) Xx0)
% 97.58/97.89 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 97.58/97.89 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 97.58/97.89 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 97.58/97.89 Found x8:(X07 Xx1)
% 97.58/97.89 Found x8 as proof of (X06 Xx1)
% 97.58/97.89 Found (fun (x8:(X07 Xx1))=> x8) as proof of (X06 Xx1)
% 97.58/97.89 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of ((X07 Xx1)->(X06 Xx1))
% 97.58/97.89 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of (forall (Xx:a), ((X07 Xx)->(X06 Xx)))
% 99.20/99.46 Found x600:=(x60 x7):((cK x3) Xx0)
% 99.20/99.46 Found (x60 x7) as proof of ((cK X07) Xx0)
% 99.20/99.46 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 99.20/99.46 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 99.20/99.46 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 99.20/99.46 Found x8:(X07 Xx1)
% 99.20/99.46 Found x8 as proof of (X06 Xx1)
% 99.20/99.46 Found (fun (x8:(X07 Xx1))=> x8) as proof of (X06 Xx1)
% 99.20/99.46 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of ((X07 Xx1)->(X06 Xx1))
% 99.20/99.46 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of (forall (Xx:a), ((X07 Xx)->(X06 Xx)))
% 99.20/99.46 Found x600:=(x60 x7):((cK x4) Xx0)
% 99.20/99.46 Found (x60 x7) as proof of ((cK X07) Xx0)
% 99.20/99.46 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 99.20/99.46 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 99.20/99.46 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 99.20/99.46 Found x8:(X07 Xx1)
% 99.20/99.46 Found x8 as proof of (X06 Xx1)
% 99.20/99.46 Found (fun (x8:(X07 Xx1))=> x8) as proof of (X06 Xx1)
% 99.20/99.46 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of ((X07 Xx1)->(X06 Xx1))
% 99.20/99.46 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of (forall (Xx:a), ((X07 Xx)->(X06 Xx)))
% 99.20/99.46 Found x500:=(x50 x6):((cK x3) Xx0)
% 99.20/99.46 Found (x50 x6) as proof of ((cK X07) Xx0)
% 99.20/99.46 Found ((x5 Xx0) x6) as proof of ((cK X07) Xx0)
% 99.20/99.46 Found ((x5 Xx0) x6) as proof of ((cK X07) Xx0)
% 99.20/99.46 Found ((x5 Xx0) x6) as proof of ((cK X07) Xx0)
% 99.20/99.46 Found x8:(X07 Xx1)
% 99.20/99.46 Found x8 as proof of (X06 Xx1)
% 99.20/99.46 Found (fun (x8:(X07 Xx1))=> x8) as proof of (X06 Xx1)
% 99.20/99.46 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of ((X07 Xx1)->(X06 Xx1))
% 99.20/99.46 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of (forall (Xx:a), ((X07 Xx)->(X06 Xx)))
% 99.20/99.46 Found x600:=(x60 x7):((cK x4) Xx0)
% 99.20/99.46 Found (x60 x7) as proof of ((cK X07) Xx0)
% 99.20/99.46 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 99.20/99.46 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 99.20/99.46 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 99.20/99.46 Found x8:(X07 Xx1)
% 99.20/99.46 Found x8 as proof of (X06 Xx1)
% 99.20/99.46 Found (fun (x8:(X07 Xx1))=> x8) as proof of (X06 Xx1)
% 99.20/99.46 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of ((X07 Xx1)->(X06 Xx1))
% 99.20/99.46 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of (forall (Xx:a), ((X07 Xx)->(X06 Xx)))
% 99.20/99.46 Found x600:=(x60 x7):((cK x4) Xx0)
% 99.20/99.46 Found (x60 x7) as proof of ((cK X07) Xx0)
% 99.20/99.46 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 99.20/99.46 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 99.20/99.46 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 99.20/99.46 Found x8:(X07 Xx1)
% 99.20/99.46 Found x8 as proof of (X06 Xx1)
% 99.20/99.46 Found (fun (x8:(X07 Xx1))=> x8) as proof of (X06 Xx1)
% 99.20/99.46 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of ((X07 Xx1)->(X06 Xx1))
% 99.20/99.46 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of (forall (Xx:a), ((X07 Xx)->(X06 Xx)))
% 99.20/99.46 Found x600:=(x60 x7):((cK x4) Xx0)
% 99.20/99.46 Found (x60 x7) as proof of ((cK X07) Xx0)
% 99.20/99.46 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 99.20/99.46 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 99.20/99.46 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 99.20/99.46 Found x8:(X07 Xx1)
% 99.20/99.46 Found x8 as proof of (X06 Xx1)
% 99.20/99.46 Found (fun (x8:(X07 Xx1))=> x8) as proof of (X06 Xx1)
% 99.20/99.46 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of ((X07 Xx1)->(X06 Xx1))
% 99.20/99.46 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of (forall (Xx:a), ((X07 Xx)->(X06 Xx)))
% 99.20/99.46 Found x600:=(x60 x7):((cK x4) Xx0)
% 99.20/99.46 Found (x60 x7) as proof of ((cK X07) Xx0)
% 99.20/99.46 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 99.20/99.46 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 99.20/99.46 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 99.20/99.46 Found x8:(X07 Xx1)
% 99.20/99.46 Found x8 as proof of (X06 Xx1)
% 99.20/99.46 Found (fun (x8:(X07 Xx1))=> x8) as proof of (X06 Xx1)
% 99.20/99.46 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of ((X07 Xx1)->(X06 Xx1))
% 99.20/99.46 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of (forall (Xx:a), ((X07 Xx)->(X06 Xx)))
% 99.20/99.46 Found x600:=(x60 x7):((cK x3) Xx0)
% 99.20/99.46 Found (x60 x7) as proof of ((cK X07) Xx0)
% 99.20/99.46 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 99.20/99.46 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 99.20/99.46 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 99.20/99.46 Found x8:(X07 Xx1)
% 99.20/99.46 Found x8 as proof of (X06 Xx1)
% 99.20/99.46 Found (fun (x8:(X07 Xx1))=> x8) as proof of (X06 Xx1)
% 99.20/99.46 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of ((X07 Xx1)->(X06 Xx1))
% 99.20/99.46 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of (forall (Xx:a), ((X07 Xx)->(X06 Xx)))
% 99.20/99.46 Found x600:=(x60 x7):((cK x4) Xx0)
% 99.20/99.46 Found (x60 x7) as proof of ((cK X07) Xx0)
% 99.20/99.46 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 99.20/99.46 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 99.98/100.22 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 99.98/100.22 Found x60:=(x6 Xx0):((x3 Xx0)->((cK x3) Xx0))
% 99.98/100.22 Found (x6 Xx0) as proof of ((x3 Xx0)->((cK X07) Xx0))
% 99.98/100.22 Found (x6 Xx0) as proof of ((x3 Xx0)->((cK X07) Xx0))
% 99.98/100.22 Found (fun (x6:(forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1))))=> (x6 Xx0)) as proof of ((x3 Xx0)->((cK X07) Xx0))
% 99.98/100.22 Found (fun (x6:(forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1)))->((x3 Xx0)->((cK X07) Xx0)))
% 99.98/100.22 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 99.98/100.22 Found ((and_rect0 ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 99.98/100.22 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1)))->((x3 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1)))) (x3 Xx0)) P) x6) x4)) ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 99.98/100.22 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1)))->((x3 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1)))) (x3 Xx0)) P) x6) x4)) ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 99.98/100.22 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 99.98/100.22 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X07) Xx0))
% 99.98/100.22 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X07) Xx0))
% 99.98/100.22 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X07) Xx0))
% 99.98/100.22 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X07) Xx0)))
% 99.98/100.22 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 99.98/100.22 Found ((and_rect0 ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 99.98/100.22 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 99.98/100.22 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X07) Xx0)
% 99.98/100.22 Found x8:(X07 Xx1)
% 99.98/100.22 Found x8 as proof of (X06 Xx1)
% 99.98/100.22 Found (fun (x8:(X07 Xx1))=> x8) as proof of (X06 Xx1)
% 99.98/100.22 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of ((X07 Xx1)->(X06 Xx1))
% 99.98/100.22 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of (forall (Xx:a), ((X07 Xx)->(X06 Xx)))
% 99.98/100.22 Found x600:=(x60 x7):((cK x4) Xx0)
% 99.98/100.22 Found (x60 x7) as proof of ((cK X07) Xx0)
% 99.98/100.22 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 99.98/100.22 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 99.98/100.22 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 99.98/100.22 Found x8:(X07 Xx1)
% 99.98/100.22 Found x8 as proof of (X06 Xx1)
% 99.98/100.22 Found (fun (x8:(X07 Xx1))=> x8) as proof of (X06 Xx1)
% 99.98/100.22 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of ((X07 Xx1)->(X06 Xx1))
% 99.98/100.22 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of (forall (Xx:a), ((X07 Xx)->(X06 Xx)))
% 99.98/100.22 Found x600:=(x60 x7):((cK x4) Xx0)
% 99.98/100.22 Found (x60 x7) as proof of ((cK X07) Xx0)
% 99.98/100.22 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 99.98/100.22 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 99.98/100.22 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 99.98/100.22 Found x8:(X07 Xx1)
% 99.98/100.22 Found x8 as proof of (X06 Xx1)
% 99.98/100.22 Found (fun (x8:(X07 Xx1))=> x8) as proof of (X06 Xx1)
% 99.98/100.22 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of ((X07 Xx1)->(X06 Xx1))
% 99.98/100.22 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of (forall (Xx:a), ((X07 Xx)->(X06 Xx)))
% 99.98/100.22 Found x600:=(x60 x7):((cK x4) Xx0)
% 99.98/100.22 Found (x60 x7) as proof of ((cK X07) Xx0)
% 99.98/100.22 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 99.98/100.22 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 99.98/100.22 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 99.98/100.22 Found x8:(X07 Xx1)
% 99.98/100.22 Found x8 as proof of (X06 Xx1)
% 100.88/101.17 Found (fun (x8:(X07 Xx1))=> x8) as proof of (X06 Xx1)
% 100.88/101.17 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of ((X07 Xx1)->(X06 Xx1))
% 100.88/101.17 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of (forall (Xx:a), ((X07 Xx)->(X06 Xx)))
% 100.88/101.17 Found x600:=(x60 x7):((cK x4) Xx0)
% 100.88/101.17 Found (x60 x7) as proof of ((cK X07) Xx0)
% 100.88/101.17 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 100.88/101.17 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 100.88/101.17 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 100.88/101.17 Found x8:(X07 Xx1)
% 100.88/101.17 Found x8 as proof of (X06 Xx1)
% 100.88/101.17 Found (fun (x8:(X07 Xx1))=> x8) as proof of (X06 Xx1)
% 100.88/101.17 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of ((X07 Xx1)->(X06 Xx1))
% 100.88/101.17 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of (forall (Xx:a), ((X07 Xx)->(X06 Xx)))
% 100.88/101.17 Found x600:=(x60 x7):((cK x4) Xx0)
% 100.88/101.17 Found (x60 x7) as proof of ((cK X07) Xx0)
% 100.88/101.17 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 100.88/101.17 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 100.88/101.17 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 100.88/101.17 Found x8:(X07 Xx1)
% 100.88/101.17 Found x8 as proof of (X06 Xx1)
% 100.88/101.17 Found (fun (x8:(X07 Xx1))=> x8) as proof of (X06 Xx1)
% 100.88/101.17 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of ((X07 Xx1)->(X06 Xx1))
% 100.88/101.17 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of (forall (Xx:a), ((X07 Xx)->(X06 Xx)))
% 100.88/101.17 Found x600:=(x60 x7):((cK x3) Xx0)
% 100.88/101.17 Found (x60 x7) as proof of ((cK X07) Xx0)
% 100.88/101.17 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 100.88/101.17 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 100.88/101.17 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 100.88/101.17 Found x8:(X07 Xx1)
% 100.88/101.17 Found x8 as proof of (X06 Xx1)
% 100.88/101.17 Found (fun (x8:(X07 Xx1))=> x8) as proof of (X06 Xx1)
% 100.88/101.17 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of ((X07 Xx1)->(X06 Xx1))
% 100.88/101.17 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of (forall (Xx:a), ((X07 Xx)->(X06 Xx)))
% 100.88/101.17 Found x600:=(x60 x7):((cK x4) Xx0)
% 100.88/101.17 Found (x60 x7) as proof of ((cK X07) Xx0)
% 100.88/101.17 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 100.88/101.17 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 100.88/101.17 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 100.88/101.17 Found x8:(X07 Xx1)
% 100.88/101.17 Found x8 as proof of (X06 Xx1)
% 100.88/101.17 Found (fun (x8:(X07 Xx1))=> x8) as proof of (X06 Xx1)
% 100.88/101.17 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of ((X07 Xx1)->(X06 Xx1))
% 100.88/101.17 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of (forall (Xx:a), ((X07 Xx)->(X06 Xx)))
% 100.88/101.17 Found x600:=(x60 x7):((cK x4) Xx0)
% 100.88/101.17 Found (x60 x7) as proof of ((cK X07) Xx0)
% 100.88/101.17 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 100.88/101.17 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 100.88/101.17 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 100.88/101.17 Found x8:(X07 Xx1)
% 100.88/101.17 Found x8 as proof of (X06 Xx1)
% 100.88/101.17 Found (fun (x8:(X07 Xx1))=> x8) as proof of (X06 Xx1)
% 100.88/101.17 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of ((X07 Xx1)->(X06 Xx1))
% 100.88/101.17 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of (forall (Xx:a), ((X07 Xx)->(X06 Xx)))
% 100.88/101.17 Found x600:=(x60 x7):((cK x4) Xx0)
% 100.88/101.17 Found (x60 x7) as proof of ((cK X07) Xx0)
% 100.88/101.17 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 100.88/101.17 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 100.88/101.17 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 100.88/101.17 Found x8:(X07 Xx1)
% 100.88/101.17 Found x8 as proof of (X06 Xx1)
% 100.88/101.17 Found (fun (x8:(X07 Xx1))=> x8) as proof of (X06 Xx1)
% 100.88/101.17 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of ((X07 Xx1)->(X06 Xx1))
% 100.88/101.17 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of (forall (Xx:a), ((X07 Xx)->(X06 Xx)))
% 100.88/101.17 Found x600:=(x60 x7):((cK x4) Xx0)
% 100.88/101.17 Found (x60 x7) as proof of ((cK X07) Xx0)
% 100.88/101.17 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 100.88/101.17 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 100.88/101.17 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 100.88/101.17 Found x8:(X07 Xx1)
% 100.88/101.17 Found x8 as proof of (X06 Xx1)
% 100.88/101.17 Found (fun (x8:(X07 Xx1))=> x8) as proof of (X06 Xx1)
% 100.88/101.17 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of ((X07 Xx1)->(X06 Xx1))
% 100.88/101.17 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of (forall (Xx:a), ((X07 Xx)->(X06 Xx)))
% 100.88/101.17 Found x600:=(x60 x7):((cK x4) Xx0)
% 100.88/101.17 Found (x60 x7) as proof of ((cK X07) Xx0)
% 100.88/101.17 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 100.88/101.17 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 100.88/101.17 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 100.88/101.17 Found x8:(X07 Xx1)
% 100.88/101.17 Found x8 as proof of (X06 Xx1)
% 100.88/101.17 Found (fun (x8:(X07 Xx1))=> x8) as proof of (X06 Xx1)
% 100.88/101.17 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of ((X07 Xx1)->(X06 Xx1))
% 100.88/101.17 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of (forall (Xx:a), ((X07 Xx)->(X06 Xx)))
% 101.72/101.99 Found x600:=(x60 x7):((cK x4) Xx0)
% 101.72/101.99 Found (x60 x7) as proof of ((cK X07) Xx0)
% 101.72/101.99 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 101.72/101.99 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 101.72/101.99 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 101.72/101.99 Found x8:(X07 Xx1)
% 101.72/101.99 Found x8 as proof of (X06 Xx1)
% 101.72/101.99 Found (fun (x8:(X07 Xx1))=> x8) as proof of (X06 Xx1)
% 101.72/101.99 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of ((X07 Xx1)->(X06 Xx1))
% 101.72/101.99 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of (forall (Xx:a), ((X07 Xx)->(X06 Xx)))
% 101.72/101.99 Found x600:=(x60 x7):((cK x4) Xx0)
% 101.72/101.99 Found (x60 x7) as proof of ((cK X07) Xx0)
% 101.72/101.99 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 101.72/101.99 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 101.72/101.99 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 101.72/101.99 Found x8:(X07 Xx1)
% 101.72/101.99 Found x8 as proof of (X06 Xx1)
% 101.72/101.99 Found (fun (x8:(X07 Xx1))=> x8) as proof of (X06 Xx1)
% 101.72/101.99 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of ((X07 Xx1)->(X06 Xx1))
% 101.72/101.99 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of (forall (Xx:a), ((X07 Xx)->(X06 Xx)))
% 101.72/101.99 Found x600:=(x60 x7):((cK x3) Xx0)
% 101.72/101.99 Found (x60 x7) as proof of ((cK X07) Xx0)
% 101.72/101.99 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 101.72/101.99 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 101.72/101.99 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 101.72/101.99 Found x8:(X07 Xx1)
% 101.72/101.99 Found x8 as proof of (X06 Xx1)
% 101.72/101.99 Found (fun (x8:(X07 Xx1))=> x8) as proof of (X06 Xx1)
% 101.72/101.99 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of ((X07 Xx1)->(X06 Xx1))
% 101.72/101.99 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of (forall (Xx:a), ((X07 Xx)->(X06 Xx)))
% 101.72/101.99 Found x600:=(x60 x7):((cK x4) Xx0)
% 101.72/101.99 Found (x60 x7) as proof of ((cK X07) Xx0)
% 101.72/101.99 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 101.72/101.99 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 101.72/101.99 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 101.72/101.99 Found x8:(X07 Xx1)
% 101.72/101.99 Found x8 as proof of (X06 Xx1)
% 101.72/101.99 Found (fun (x8:(X07 Xx1))=> x8) as proof of (X06 Xx1)
% 101.72/101.99 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of ((X07 Xx1)->(X06 Xx1))
% 101.72/101.99 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of (forall (Xx:a), ((X07 Xx)->(X06 Xx)))
% 101.72/101.99 Found x600:=(x60 x7):((cK x4) Xx0)
% 101.72/101.99 Found (x60 x7) as proof of ((cK X07) Xx0)
% 101.72/101.99 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 101.72/101.99 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 101.72/101.99 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 101.72/101.99 Found x8:(X07 Xx1)
% 101.72/101.99 Found x8 as proof of (X06 Xx1)
% 101.72/101.99 Found (fun (x8:(X07 Xx1))=> x8) as proof of (X06 Xx1)
% 101.72/101.99 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of ((X07 Xx1)->(X06 Xx1))
% 101.72/101.99 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of (forall (Xx:a), ((X07 Xx)->(X06 Xx)))
% 101.72/101.99 Found x600:=(x60 x7):((cK x4) Xx0)
% 101.72/101.99 Found (x60 x7) as proof of ((cK X07) Xx0)
% 101.72/101.99 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 101.72/101.99 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 101.72/101.99 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 101.72/101.99 Found x8:(X07 Xx1)
% 101.72/101.99 Found x8 as proof of (X06 Xx1)
% 101.72/101.99 Found (fun (x8:(X07 Xx1))=> x8) as proof of (X06 Xx1)
% 101.72/101.99 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of ((X07 Xx1)->(X06 Xx1))
% 101.72/101.99 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of (forall (Xx:a), ((X07 Xx)->(X06 Xx)))
% 101.72/101.99 Found x600:=(x60 x7):((cK x4) Xx0)
% 101.72/101.99 Found (x60 x7) as proof of ((cK X07) Xx0)
% 101.72/101.99 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 101.72/101.99 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 101.72/101.99 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 101.72/101.99 Found x8:(X07 Xx1)
% 101.72/101.99 Found x8 as proof of (X06 Xx1)
% 101.72/101.99 Found (fun (x8:(X07 Xx1))=> x8) as proof of (X06 Xx1)
% 101.72/101.99 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of ((X07 Xx1)->(X06 Xx1))
% 101.72/101.99 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of (forall (Xx:a), ((X07 Xx)->(X06 Xx)))
% 101.72/101.99 Found x600:=(x60 x7):((cK x4) Xx0)
% 101.72/101.99 Found (x60 x7) as proof of ((cK X07) Xx0)
% 101.72/101.99 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 101.72/101.99 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 101.72/101.99 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 101.72/101.99 Found x8:(X07 Xx1)
% 101.72/101.99 Found x8 as proof of (X06 Xx1)
% 101.72/101.99 Found (fun (x8:(X07 Xx1))=> x8) as proof of (X06 Xx1)
% 101.72/101.99 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of ((X07 Xx1)->(X06 Xx1))
% 101.72/101.99 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of (forall (Xx:a), ((X07 Xx)->(X06 Xx)))
% 101.72/101.99 Found x600:=(x60 x7):((cK x4) Xx0)
% 101.72/101.99 Found (x60 x7) as proof of ((cK X07) Xx0)
% 101.72/101.99 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 101.72/101.99 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 102.14/102.43 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 102.14/102.43 Found x8:(X07 Xx1)
% 102.14/102.43 Found x8 as proof of (X06 Xx1)
% 102.14/102.43 Found (fun (x8:(X07 Xx1))=> x8) as proof of (X06 Xx1)
% 102.14/102.43 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of ((X07 Xx1)->(X06 Xx1))
% 102.14/102.43 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of (forall (Xx:a), ((X07 Xx)->(X06 Xx)))
% 102.14/102.43 Found x600:=(x60 x7):((cK x4) Xx0)
% 102.14/102.43 Found (x60 x7) as proof of ((cK X07) Xx0)
% 102.14/102.43 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 102.14/102.43 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 102.14/102.43 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 102.14/102.43 Found x8:(X07 Xx1)
% 102.14/102.43 Found x8 as proof of (X06 Xx1)
% 102.14/102.43 Found (fun (x8:(X07 Xx1))=> x8) as proof of (X06 Xx1)
% 102.14/102.43 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of ((X07 Xx1)->(X06 Xx1))
% 102.14/102.43 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of (forall (Xx:a), ((X07 Xx)->(X06 Xx)))
% 102.14/102.43 Found x600:=(x60 x7):((cK x4) Xx0)
% 102.14/102.43 Found (x60 x7) as proof of ((cK X07) Xx0)
% 102.14/102.43 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 102.14/102.43 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 102.14/102.43 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 102.14/102.43 Found x4:(X06 Xx1)
% 102.14/102.43 Found x4 as proof of (X05 Xx1)
% 102.14/102.43 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X05 Xx1)
% 102.14/102.43 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X05 Xx1))
% 102.14/102.43 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X05 Xx1)))
% 102.14/102.43 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X05 Xx1)
% 102.14/102.43 Found ((and_rect0 (X05 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X05 Xx1)
% 102.14/102.43 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X05 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X05 Xx1)
% 102.14/102.43 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X05 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X05 Xx1)
% 102.14/102.43 Found x8:(X07 Xx1)
% 102.14/102.43 Found x8 as proof of (X06 Xx1)
% 102.14/102.43 Found (fun (x8:(X07 Xx1))=> x8) as proof of (X06 Xx1)
% 102.14/102.43 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of ((X07 Xx1)->(X06 Xx1))
% 102.14/102.43 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of (forall (Xx:a), ((X07 Xx)->(X06 Xx)))
% 102.14/102.43 Found x600:=(x60 x7):((cK x3) Xx0)
% 102.14/102.43 Found (x60 x7) as proof of ((cK X07) Xx0)
% 102.14/102.43 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 102.14/102.43 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 102.14/102.43 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 102.14/102.43 Found x8:(X07 Xx1)
% 102.14/102.43 Found x8 as proof of (X06 Xx1)
% 102.14/102.43 Found (fun (x8:(X07 Xx1))=> x8) as proof of (X06 Xx1)
% 102.14/102.43 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of ((X07 Xx1)->(X06 Xx1))
% 102.14/102.43 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of (forall (Xx:a), ((X07 Xx)->(X06 Xx)))
% 102.14/102.43 Found x600:=(x60 x7):((cK x4) Xx0)
% 102.14/102.43 Found (x60 x7) as proof of ((cK X07) Xx0)
% 102.14/102.43 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 102.14/102.43 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 102.14/102.43 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 102.14/102.43 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 102.14/102.43 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X07) Xx0))
% 102.14/102.43 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X07) Xx0))
% 102.14/102.43 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X07) Xx0))
% 102.14/102.43 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X07) Xx0)))
% 102.14/102.43 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 102.14/102.43 Found ((and_rect0 ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 102.14/102.43 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 102.29/102.54 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 102.29/102.54 Found x6:(X07 Xx1)
% 102.29/102.54 Instantiate: X06:=X07:(a->Prop)
% 102.29/102.54 Found (fun (x6:(X07 Xx1))=> x6) as proof of (X06 Xx1)
% 102.29/102.54 Found (fun (Xx1:a) (x6:(X07 Xx1))=> x6) as proof of ((X07 Xx1)->(X06 Xx1))
% 102.29/102.54 Found (fun (Xx1:a) (x6:(X07 Xx1))=> x6) as proof of (forall (Xx:a), ((X07 Xx)->(X06 Xx)))
% 102.29/102.54 Found ((x380 (fun (Xx1:a) (x6:(X07 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X06) Xx0)
% 102.29/102.54 Found (((x38 X06) (fun (Xx1:a) (x6:(X07 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X06) Xx0)
% 102.29/102.54 Found ((((x3 x4) X06) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X06) Xx0)
% 102.29/102.54 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> ((((x3 x4) X06) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))))) as proof of ((cK X06) Xx0)
% 102.29/102.54 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 102.29/102.54 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X06) Xx0))
% 102.29/102.54 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X06) Xx0))
% 102.29/102.54 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X06) Xx0))
% 102.29/102.54 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X06) Xx0)))
% 102.29/102.54 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 102.29/102.54 Found ((and_rect0 ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 102.29/102.54 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 102.29/102.54 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 102.29/102.54 Found x6:(X06 Xx1)
% 102.29/102.54 Instantiate: X05:=X06:(a->Prop)
% 102.29/102.54 Found (fun (x6:(X06 Xx1))=> x6) as proof of (X05 Xx1)
% 102.29/102.54 Found (fun (Xx1:a) (x6:(X06 Xx1))=> x6) as proof of ((X06 Xx1)->(X05 Xx1))
% 102.29/102.54 Found (fun (Xx1:a) (x6:(X06 Xx1))=> x6) as proof of (forall (Xx:a), ((X06 Xx)->(X05 Xx)))
% 102.29/102.54 Found ((x370 (fun (Xx1:a) (x6:(X06 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X05) Xx0)
% 102.29/102.54 Found (((x37 X05) (fun (Xx1:a) (x6:(X06 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X05) Xx0)
% 103.48/103.77 Found ((((x3 x4) X05) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X05) Xx0)
% 103.48/103.77 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> ((((x3 x4) X05) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))))) as proof of ((cK X05) Xx0)
% 103.48/103.77 Found x8:(X07 Xx1)
% 103.48/103.77 Found x8 as proof of (X06 Xx1)
% 103.48/103.77 Found (fun (x8:(X07 Xx1))=> x8) as proof of (X06 Xx1)
% 103.48/103.77 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of ((X07 Xx1)->(X06 Xx1))
% 103.48/103.77 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of (forall (Xx:a), ((X07 Xx)->(X06 Xx)))
% 103.48/103.77 Found x600:=(x60 x7):((cK x3) Xx0)
% 103.48/103.77 Found (x60 x7) as proof of ((cK X07) Xx0)
% 103.48/103.77 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 103.48/103.77 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 103.48/103.77 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 103.48/103.77 Found x8:(X07 Xx1)
% 103.48/103.77 Found x8 as proof of (X06 Xx1)
% 103.48/103.77 Found (fun (x8:(X07 Xx1))=> x8) as proof of (X06 Xx1)
% 103.48/103.77 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of ((X07 Xx1)->(X06 Xx1))
% 103.48/103.77 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of (forall (Xx:a), ((X07 Xx)->(X06 Xx)))
% 103.48/103.77 Found x600:=(x60 x7):((cK x4) Xx0)
% 103.48/103.77 Found (x60 x7) as proof of ((cK X07) Xx0)
% 103.48/103.77 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 103.48/103.77 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 103.48/103.77 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 103.48/103.77 Found x8:(X07 Xx1)
% 103.48/103.77 Found x8 as proof of (X06 Xx1)
% 103.48/103.77 Found (fun (x8:(X07 Xx1))=> x8) as proof of (X06 Xx1)
% 103.48/103.77 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of ((X07 Xx1)->(X06 Xx1))
% 103.48/103.77 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of (forall (Xx:a), ((X07 Xx)->(X06 Xx)))
% 103.48/103.77 Found x600:=(x60 x7):((cK x3) Xx0)
% 103.48/103.77 Found (x60 x7) as proof of ((cK X07) Xx0)
% 103.48/103.77 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 103.48/103.77 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 103.48/103.77 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 103.48/103.77 Found x8:(X07 Xx1)
% 103.48/103.77 Found x8 as proof of (X06 Xx1)
% 103.48/103.77 Found (fun (x8:(X07 Xx1))=> x8) as proof of (X06 Xx1)
% 103.48/103.77 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of ((X07 Xx1)->(X06 Xx1))
% 103.48/103.77 Found (fun (Xx1:a) (x8:(X07 Xx1))=> x8) as proof of (forall (Xx:a), ((X07 Xx)->(X06 Xx)))
% 103.48/103.77 Found x600:=(x60 x7):((cK x4) Xx0)
% 103.48/103.77 Found (x60 x7) as proof of ((cK X07) Xx0)
% 103.48/103.77 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 103.48/103.77 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 103.48/103.77 Found ((x6 Xx0) x7) as proof of ((cK X07) Xx0)
% 103.48/103.77 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 103.48/103.77 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X07) Xx0))
% 103.48/103.77 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X07) Xx0))
% 103.48/103.77 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X07) Xx0))
% 103.48/103.77 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X07) Xx0)))
% 103.48/103.77 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 103.48/103.77 Found ((and_rect0 ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 103.48/103.77 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 103.48/103.77 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X07) Xx0)
% 104.40/104.73 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 104.40/104.73 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X06) Xx0))
% 104.40/104.73 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X06) Xx0))
% 104.40/104.73 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X06) Xx0))
% 104.40/104.73 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X06) Xx0)))
% 104.40/104.73 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 104.40/104.73 Found ((and_rect0 ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 104.40/104.73 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X06) Xx0)
% 104.40/104.73 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X06) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X06) Xx0)
% 104.40/104.73 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 104.40/104.73 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X07) Xx0))
% 104.40/104.73 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X07) Xx0))
% 104.40/104.73 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X07) Xx0))
% 104.40/104.73 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X07) Xx0)))
% 104.40/104.73 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 104.40/104.73 Found ((and_rect0 ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 104.40/104.73 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 104.40/104.73 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 104.40/104.73 Found x6:(X07 Xx1)
% 104.40/104.73 Instantiate: X06:=X07:(a->Prop)
% 104.40/104.73 Found (fun (x6:(X07 Xx1))=> x6) as proof of (X06 Xx1)
% 104.40/104.73 Found (fun (Xx1:a) (x6:(X07 Xx1))=> x6) as proof of ((X07 Xx1)->(X06 Xx1))
% 104.40/104.73 Found (fun (Xx1:a) (x6:(X07 Xx1))=> x6) as proof of (forall (Xx:a), ((X07 Xx)->(X06 Xx)))
% 104.40/104.73 Found ((x380 (fun (Xx1:a) (x6:(X07 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X06) Xx0)
% 104.40/104.73 Found (((x38 X06) (fun (Xx1:a) (x6:(X07 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X06) Xx0)
% 104.40/104.73 Found ((((x3 x4) X06) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X06) Xx0)
% 104.40/104.73 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> ((((x3 x4) X06) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))))) as proof of ((cK X06) Xx0)
% 105.61/105.86 Found x4:(X07 Xx1)
% 105.61/105.86 Instantiate: X07:=(cK x5):(a->Prop)
% 105.61/105.86 Found x4 as proof of (X06 Xx1)
% 105.61/105.86 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X06 Xx1)
% 105.61/105.86 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X06 Xx1))
% 105.61/105.86 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X06 Xx1)))
% 105.61/105.86 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X06 Xx1)
% 105.61/105.86 Found ((and_rect0 (X06 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X06 Xx1)
% 105.61/105.86 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X06 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X06 Xx1)
% 105.61/105.86 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X06 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X06 Xx1)
% 105.61/105.86 Found x4:(X07 Xx1)
% 105.61/105.86 Found x4 as proof of (X06 Xx1)
% 105.61/105.86 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X06 Xx1)
% 105.61/105.86 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X06 Xx1))
% 105.61/105.86 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X06 Xx1)))
% 105.61/105.86 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X06 Xx1)
% 105.61/105.86 Found ((and_rect0 (X06 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X06 Xx1)
% 105.61/105.86 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X06 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X06 Xx1)
% 105.61/105.86 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X06 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X06 Xx1)
% 105.61/105.86 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 105.61/105.86 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X07) Xx0))
% 105.61/105.86 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X07) Xx0))
% 105.61/105.86 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X07) Xx0))
% 105.61/105.86 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X07) Xx0)))
% 105.61/105.86 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 105.61/105.86 Found ((and_rect0 ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 105.61/105.86 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 105.61/105.86 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X07) Xx0)
% 105.61/105.86 Found x4:(X06 Xx1)
% 105.61/105.86 Instantiate: X06:=(cK x5):(a->Prop)
% 105.61/105.86 Found x4 as proof of (X05 Xx1)
% 106.42/106.69 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X05 Xx1)
% 106.42/106.69 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X05 Xx1))
% 106.42/106.69 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X05 Xx1)))
% 106.42/106.69 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X05 Xx1)
% 106.42/106.69 Found ((and_rect0 (X05 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X05 Xx1)
% 106.42/106.69 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X05 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X05 Xx1)
% 106.42/106.69 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X05 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X05 Xx1)
% 106.42/106.69 Found x4:(X07 Xx1)
% 106.42/106.69 Instantiate: X07:=(cK x5):(a->Prop)
% 106.42/106.69 Found x4 as proof of (X06 Xx1)
% 106.42/106.69 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X06 Xx1)
% 106.42/106.69 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X06 Xx1))
% 106.42/106.69 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X06 Xx1)))
% 106.42/106.69 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X06 Xx1)
% 106.42/106.69 Found ((and_rect0 (X06 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X06 Xx1)
% 106.42/106.69 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X06 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X06 Xx1)
% 106.42/106.69 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X06 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X06 Xx1)
% 106.42/106.69 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 106.42/106.69 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X07) Xx0))
% 106.42/106.69 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X07) Xx0))
% 106.42/106.69 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X07) Xx0))
% 106.42/106.69 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X07) Xx0)))
% 106.42/106.69 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 106.42/106.69 Found ((and_rect0 ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 106.42/106.69 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 106.42/106.69 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 106.42/106.69 Found x6:(X07 Xx1)
% 106.42/106.69 Instantiate: X06:=X07:(a->Prop)
% 106.42/106.69 Found (fun (x6:(X07 Xx1))=> x6) as proof of (X06 Xx1)
% 106.42/106.69 Found (fun (Xx1:a) (x6:(X07 Xx1))=> x6) as proof of ((X07 Xx1)->(X06 Xx1))
% 106.42/106.69 Found (fun (Xx1:a) (x6:(X07 Xx1))=> x6) as proof of (forall (Xx:a), ((X07 Xx)->(X06 Xx)))
% 106.42/106.69 Found ((x380 (fun (Xx1:a) (x6:(X07 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X06) Xx0)
% 107.05/107.31 Found (((x38 X06) (fun (Xx1:a) (x6:(X07 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X06) Xx0)
% 107.05/107.31 Found ((((x3 x4) X06) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X06) Xx0)
% 107.05/107.31 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> ((((x3 x4) X06) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))))) as proof of ((cK X06) Xx0)
% 107.05/107.31 Found x4:(X06 Xx1)
% 107.05/107.31 Found x4 as proof of (X05 Xx1)
% 107.05/107.31 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X05 Xx1)
% 107.05/107.31 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X05 Xx1))
% 107.05/107.31 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X05 Xx1)))
% 107.05/107.31 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X05 Xx1)
% 107.05/107.31 Found ((and_rect0 (X05 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X05 Xx1)
% 107.05/107.31 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X05 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X05 Xx1)
% 107.05/107.31 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X05 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X05 Xx1)
% 107.05/107.31 Found x4:(X07 Xx1)
% 107.05/107.31 Found x4 as proof of (X06 Xx1)
% 107.05/107.31 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X06 Xx1)
% 107.05/107.31 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X06 Xx1))
% 107.05/107.31 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X06 Xx1)))
% 107.05/107.31 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X06 Xx1)
% 107.05/107.31 Found ((and_rect0 (X06 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X06 Xx1)
% 107.05/107.31 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X06 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X06 Xx1)
% 107.05/107.31 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X06 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X06 Xx1)
% 107.05/107.31 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 107.05/107.31 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X07) Xx0))
% 107.05/107.31 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X07) Xx0))
% 107.05/107.31 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X07) Xx0))
% 108.00/108.27 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X07) Xx0)))
% 108.00/108.27 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 108.00/108.27 Found ((and_rect0 ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 108.00/108.27 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 108.00/108.27 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X07) Xx0)
% 108.00/108.27 Found x4:(X07 Xx1)
% 108.00/108.27 Instantiate: X07:=(cK x5):(a->Prop)
% 108.00/108.27 Found x4 as proof of (X06 Xx1)
% 108.00/108.27 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X06 Xx1)
% 108.00/108.27 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X06 Xx1))
% 108.00/108.27 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X06 Xx1)))
% 108.00/108.27 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X06 Xx1)
% 108.00/108.27 Found ((and_rect0 (X06 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X06 Xx1)
% 108.00/108.27 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X06 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X06 Xx1)
% 108.00/108.27 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X06 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X06 Xx1)
% 108.00/108.27 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 108.00/108.27 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X07) Xx0))
% 108.00/108.27 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X07) Xx0))
% 108.00/108.27 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X07) Xx0))
% 108.00/108.27 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X07) Xx0)))
% 108.00/108.27 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 108.00/108.27 Found ((and_rect0 ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 108.00/108.27 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 108.00/108.27 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 108.00/108.27 Found x6:(X07 Xx1)
% 108.00/108.27 Instantiate: X06:=X07:(a->Prop)
% 108.00/108.27 Found (fun (x6:(X07 Xx1))=> x6) as proof of (X06 Xx1)
% 108.00/108.27 Found (fun (Xx1:a) (x6:(X07 Xx1))=> x6) as proof of ((X07 Xx1)->(X06 Xx1))
% 108.00/108.27 Found (fun (Xx1:a) (x6:(X07 Xx1))=> x6) as proof of (forall (Xx:a), ((X07 Xx)->(X06 Xx)))
% 108.00/108.27 Found ((x380 (fun (Xx1:a) (x6:(X07 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X06) Xx0)
% 109.46/109.71 Found (((x38 X06) (fun (Xx1:a) (x6:(X07 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X06) Xx0)
% 109.46/109.71 Found ((((x3 x4) X06) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X06) Xx0)
% 109.46/109.71 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> ((((x3 x4) X06) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))))) as proof of ((cK X06) Xx0)
% 109.46/109.71 Found x4:(X07 Xx1)
% 109.46/109.71 Found x4 as proof of (X06 Xx1)
% 109.46/109.71 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X06 Xx1)
% 109.46/109.71 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X06 Xx1))
% 109.46/109.71 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X06 Xx1)))
% 109.46/109.71 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X06 Xx1)
% 109.46/109.71 Found ((and_rect0 (X06 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X06 Xx1)
% 109.46/109.71 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X06 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X06 Xx1)
% 109.46/109.71 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X06 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X06 Xx1)
% 109.46/109.71 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 109.46/109.71 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X07) Xx0))
% 109.46/109.71 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X07) Xx0))
% 109.46/109.71 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X07) Xx0))
% 109.46/109.71 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X07) Xx0)))
% 109.46/109.71 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 109.46/109.71 Found ((and_rect0 ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 109.46/109.71 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 109.46/109.71 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X07) Xx0)
% 109.46/109.71 Found x4:(X07 Xx1)
% 109.46/109.71 Instantiate: X07:=(cK x5):(a->Prop)
% 109.46/109.71 Found x4 as proof of (X06 Xx1)
% 109.46/109.71 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X06 Xx1)
% 109.46/109.71 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X06 Xx1))
% 109.46/109.71 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X06 Xx1)))
% 109.94/110.19 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X06 Xx1)
% 109.94/110.19 Found ((and_rect0 (X06 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X06 Xx1)
% 109.94/110.19 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X06 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X06 Xx1)
% 109.94/110.19 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X06 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X06 Xx1)
% 109.94/110.19 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 109.94/110.19 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X07) Xx0))
% 109.94/110.19 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X07) Xx0))
% 109.94/110.19 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X07) Xx0))
% 109.94/110.19 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X07) Xx0)))
% 109.94/110.19 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 109.94/110.19 Found ((and_rect0 ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 109.94/110.19 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 109.94/110.19 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 109.94/110.19 Found x6:(X07 Xx1)
% 109.94/110.19 Instantiate: X06:=X07:(a->Prop)
% 109.94/110.19 Found (fun (x6:(X07 Xx1))=> x6) as proof of (X06 Xx1)
% 109.94/110.19 Found (fun (Xx1:a) (x6:(X07 Xx1))=> x6) as proof of ((X07 Xx1)->(X06 Xx1))
% 109.94/110.19 Found (fun (Xx1:a) (x6:(X07 Xx1))=> x6) as proof of (forall (Xx:a), ((X07 Xx)->(X06 Xx)))
% 109.94/110.19 Found ((x380 (fun (Xx1:a) (x6:(X07 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X06) Xx0)
% 109.94/110.19 Found (((x38 X06) (fun (Xx1:a) (x6:(X07 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X06) Xx0)
% 109.94/110.19 Found ((((x3 x4) X06) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X06) Xx0)
% 109.94/110.19 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> ((((x3 x4) X06) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))))) as proof of ((cK X06) Xx0)
% 109.94/110.19 Found x4:(X07 Xx1)
% 109.94/110.19 Found x4 as proof of (X06 Xx1)
% 109.94/110.19 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X06 Xx1)
% 109.94/110.19 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X06 Xx1))
% 111.29/111.61 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X06 Xx1)))
% 111.29/111.61 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X06 Xx1)
% 111.29/111.61 Found ((and_rect0 (X06 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X06 Xx1)
% 111.29/111.61 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X06 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X06 Xx1)
% 111.29/111.61 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X06 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X06 Xx1)
% 111.29/111.61 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 111.29/111.61 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X07) Xx0))
% 111.29/111.61 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X07) Xx0))
% 111.29/111.61 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X07) Xx0))
% 111.29/111.61 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X07) Xx0)))
% 111.29/111.61 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 111.29/111.61 Found ((and_rect0 ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 111.29/111.61 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 111.29/111.61 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X07) Xx0)
% 111.29/111.61 Found x4:(X07 Xx1)
% 111.29/111.61 Instantiate: X07:=(cK x5):(a->Prop)
% 111.29/111.61 Found x4 as proof of (X06 Xx1)
% 111.29/111.61 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X06 Xx1)
% 111.29/111.61 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X06 Xx1))
% 111.29/111.61 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X06 Xx1)))
% 111.29/111.61 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X06 Xx1)
% 111.29/111.61 Found ((and_rect0 (X06 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X06 Xx1)
% 111.29/111.61 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X06 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X06 Xx1)
% 111.29/111.61 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X06 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X06 Xx1)
% 111.29/111.61 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 111.29/111.61 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X07) Xx0))
% 111.29/111.61 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X07) Xx0))
% 111.29/111.61 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X07) Xx0))
% 111.29/111.61 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X07) Xx0)))
% 111.73/111.99 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 111.73/111.99 Found ((and_rect0 ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 111.73/111.99 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 111.73/111.99 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 111.73/111.99 Found x6:(X07 Xx1)
% 111.73/111.99 Instantiate: X06:=X07:(a->Prop)
% 111.73/111.99 Found (fun (x6:(X07 Xx1))=> x6) as proof of (X06 Xx1)
% 111.73/111.99 Found (fun (Xx1:a) (x6:(X07 Xx1))=> x6) as proof of ((X07 Xx1)->(X06 Xx1))
% 111.73/111.99 Found (fun (Xx1:a) (x6:(X07 Xx1))=> x6) as proof of (forall (Xx:a), ((X07 Xx)->(X06 Xx)))
% 111.73/111.99 Found ((x380 (fun (Xx1:a) (x6:(X07 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X06) Xx0)
% 111.73/111.99 Found (((x38 X06) (fun (Xx1:a) (x6:(X07 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X06) Xx0)
% 111.73/111.99 Found ((((x3 x4) X06) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X06) Xx0)
% 111.73/111.99 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> ((((x3 x4) X06) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))))) as proof of ((cK X06) Xx0)
% 111.73/111.99 Found x4:(X07 Xx1)
% 111.73/111.99 Found x4 as proof of (X06 Xx1)
% 111.73/111.99 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X06 Xx1)
% 111.73/111.99 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X06 Xx1))
% 111.73/111.99 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X06 Xx1)))
% 111.73/111.99 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X06 Xx1)
% 111.73/111.99 Found ((and_rect0 (X06 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X06 Xx1)
% 111.73/111.99 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X06 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X06 Xx1)
% 111.73/111.99 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X06 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X06 Xx1)
% 111.73/111.99 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 111.73/111.99 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X07) Xx0))
% 111.73/111.99 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X07) Xx0))
% 111.73/111.99 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X07) Xx0))
% 117.68/117.93 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X07) Xx0)))
% 117.68/117.93 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 117.68/117.93 Found ((and_rect0 ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 117.68/117.93 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 117.68/117.93 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X07) Xx0)
% 117.68/117.93 Found x4:(X08 Xx1)
% 117.68/117.93 Found x4 as proof of (X07 Xx1)
% 117.68/117.93 Found (fun (x4:(X08 Xx1))=> x4) as proof of (X07 Xx1)
% 117.68/117.93 Found (fun (Xx1:a) (x4:(X08 Xx1))=> x4) as proof of ((X08 Xx1)->(X07 Xx1))
% 117.68/117.93 Found (fun (Xx1:a) (x4:(X08 Xx1))=> x4) as proof of (forall (Xx:a), ((X08 Xx)->(X07 Xx)))
% 117.68/117.93 Found x4:(X07 Xx1)
% 117.68/117.93 Instantiate: X07:=(cK x5):(a->Prop)
% 117.68/117.93 Found x4 as proof of (X06 Xx1)
% 117.68/117.93 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X06 Xx1)
% 117.68/117.93 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X06 Xx1))
% 117.68/117.93 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X06 Xx1)))
% 117.68/117.93 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X06 Xx1)
% 117.68/117.93 Found ((and_rect0 (X06 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X06 Xx1)
% 117.68/117.93 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X06 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X06 Xx1)
% 117.68/117.93 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X06 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X06 Xx1)
% 117.68/117.93 Found x6:(X08 Xx1)
% 117.68/117.93 Found x6 as proof of (X07 Xx1)
% 117.68/117.93 Found (fun (x6:(X08 Xx1))=> x6) as proof of (X07 Xx1)
% 117.68/117.93 Found (fun (Xx1:a) (x6:(X08 Xx1))=> x6) as proof of ((X08 Xx1)->(X07 Xx1))
% 117.68/117.93 Found (fun (Xx1:a) (x6:(X08 Xx1))=> x6) as proof of (forall (Xx:a), ((X08 Xx)->(X07 Xx)))
% 117.68/117.93 Found x6:(X08 Xx1)
% 117.68/117.93 Found x6 as proof of (X07 Xx1)
% 117.68/117.93 Found (fun (x6:(X08 Xx1))=> x6) as proof of (X07 Xx1)
% 117.68/117.93 Found (fun (Xx1:a) (x6:(X08 Xx1))=> x6) as proof of ((X08 Xx1)->(X07 Xx1))
% 117.68/117.93 Found (fun (Xx1:a) (x6:(X08 Xx1))=> x6) as proof of (forall (Xx:a), ((X08 Xx)->(X07 Xx)))
% 117.68/117.93 Found x6:(X08 Xx1)
% 117.68/117.93 Found x6 as proof of (X07 Xx1)
% 117.68/117.93 Found (fun (x6:(X08 Xx1))=> x6) as proof of (X07 Xx1)
% 117.68/117.93 Found (fun (Xx1:a) (x6:(X08 Xx1))=> x6) as proof of ((X08 Xx1)->(X07 Xx1))
% 117.68/117.93 Found (fun (Xx1:a) (x6:(X08 Xx1))=> x6) as proof of (forall (Xx:a), ((X08 Xx)->(X07 Xx)))
% 117.68/117.93 Found x6:(X08 Xx1)
% 117.68/117.93 Found x6 as proof of (X07 Xx1)
% 117.68/117.93 Found (fun (x6:(X08 Xx1))=> x6) as proof of (X07 Xx1)
% 117.68/117.93 Found (fun (Xx1:a) (x6:(X08 Xx1))=> x6) as proof of ((X08 Xx1)->(X07 Xx1))
% 117.68/117.93 Found (fun (Xx1:a) (x6:(X08 Xx1))=> x6) as proof of (forall (Xx:a), ((X08 Xx)->(X07 Xx)))
% 117.68/117.93 Found x6:(X08 Xx1)
% 117.68/117.93 Found x6 as proof of (X07 Xx1)
% 117.68/117.93 Found (fun (x6:(X08 Xx1))=> x6) as proof of (X07 Xx1)
% 117.68/117.93 Found (fun (Xx1:a) (x6:(X08 Xx1))=> x6) as proof of ((X08 Xx1)->(X07 Xx1))
% 117.68/117.93 Found (fun (Xx1:a) (x6:(X08 Xx1))=> x6) as proof of (forall (Xx:a), ((X08 Xx)->(X07 Xx)))
% 117.68/117.93 Found x4:(X07 Xx1)
% 117.68/117.93 Found x4 as proof of (X06 Xx1)
% 117.68/117.93 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X06 Xx1)
% 117.68/117.93 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X06 Xx1))
% 118.72/118.99 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X06 Xx1)))
% 118.72/118.99 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X06 Xx1)
% 118.72/118.99 Found ((and_rect0 (X06 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X06 Xx1)
% 118.72/118.99 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X06 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X06 Xx1)
% 118.72/118.99 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X06 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X06 Xx1)
% 118.72/118.99 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 118.72/118.99 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X07) Xx0))
% 118.72/118.99 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X07) Xx0))
% 118.72/118.99 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X07) Xx0))
% 118.72/118.99 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X07) Xx0)))
% 118.72/118.99 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 118.72/118.99 Found ((and_rect0 ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 118.72/118.99 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 118.72/118.99 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 118.72/118.99 Found x6:(X07 Xx1)
% 118.72/118.99 Instantiate: X06:=X07:(a->Prop)
% 118.72/118.99 Found (fun (x6:(X07 Xx1))=> x6) as proof of (X06 Xx1)
% 118.72/118.99 Found (fun (Xx1:a) (x6:(X07 Xx1))=> x6) as proof of ((X07 Xx1)->(X06 Xx1))
% 118.72/118.99 Found (fun (Xx1:a) (x6:(X07 Xx1))=> x6) as proof of (forall (Xx:a), ((X07 Xx)->(X06 Xx)))
% 118.72/118.99 Found ((x380 (fun (Xx1:a) (x6:(X07 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X06) Xx0)
% 118.72/118.99 Found (((x38 X06) (fun (Xx1:a) (x6:(X07 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X06) Xx0)
% 118.72/118.99 Found ((((x3 x4) X06) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X06) Xx0)
% 118.72/118.99 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> ((((x3 x4) X06) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))))) as proof of ((cK X06) Xx0)
% 118.72/118.99 Found x6:(X08 Xx1)
% 118.72/118.99 Found x6 as proof of (X07 Xx1)
% 131.65/131.95 Found (fun (x6:(X08 Xx1))=> x6) as proof of (X07 Xx1)
% 131.65/131.95 Found (fun (Xx1:a) (x6:(X08 Xx1))=> x6) as proof of ((X08 Xx1)->(X07 Xx1))
% 131.65/131.95 Found (fun (Xx1:a) (x6:(X08 Xx1))=> x6) as proof of (forall (Xx:a), ((X08 Xx)->(X07 Xx)))
% 131.65/131.95 Found x6:(X08 Xx1)
% 131.65/131.95 Found x6 as proof of (X07 Xx1)
% 131.65/131.95 Found (fun (x6:(X08 Xx1))=> x6) as proof of (X07 Xx1)
% 131.65/131.95 Found (fun (Xx1:a) (x6:(X08 Xx1))=> x6) as proof of ((X08 Xx1)->(X07 Xx1))
% 131.65/131.95 Found (fun (Xx1:a) (x6:(X08 Xx1))=> x6) as proof of (forall (Xx:a), ((X08 Xx)->(X07 Xx)))
% 131.65/131.95 Found x6:(X08 Xx1)
% 131.65/131.95 Found x6 as proof of (X07 Xx1)
% 131.65/131.95 Found (fun (x6:(X08 Xx1))=> x6) as proof of (X07 Xx1)
% 131.65/131.95 Found (fun (Xx1:a) (x6:(X08 Xx1))=> x6) as proof of ((X08 Xx1)->(X07 Xx1))
% 131.65/131.95 Found (fun (Xx1:a) (x6:(X08 Xx1))=> x6) as proof of (forall (Xx:a), ((X08 Xx)->(X07 Xx)))
% 131.65/131.95 Found x6:(X08 Xx1)
% 131.65/131.95 Found x6 as proof of (X07 Xx1)
% 131.65/131.95 Found (fun (x6:(X08 Xx1))=> x6) as proof of (X07 Xx1)
% 131.65/131.95 Found (fun (Xx1:a) (x6:(X08 Xx1))=> x6) as proof of ((X08 Xx1)->(X07 Xx1))
% 131.65/131.95 Found (fun (Xx1:a) (x6:(X08 Xx1))=> x6) as proof of (forall (Xx:a), ((X08 Xx)->(X07 Xx)))
% 131.65/131.95 Found x6:(X08 Xx1)
% 131.65/131.95 Found x6 as proof of (X07 Xx1)
% 131.65/131.95 Found (fun (x6:(X08 Xx1))=> x6) as proof of (X07 Xx1)
% 131.65/131.95 Found (fun (Xx1:a) (x6:(X08 Xx1))=> x6) as proof of ((X08 Xx1)->(X07 Xx1))
% 131.65/131.95 Found (fun (Xx1:a) (x6:(X08 Xx1))=> x6) as proof of (forall (Xx:a), ((X08 Xx)->(X07 Xx)))
% 131.65/131.95 Found x8:(X08 Xx1)
% 131.65/131.95 Found x8 as proof of (X07 Xx1)
% 131.65/131.95 Found (fun (x8:(X08 Xx1))=> x8) as proof of (X07 Xx1)
% 131.65/131.95 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of ((X08 Xx1)->(X07 Xx1))
% 131.65/131.95 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of (forall (Xx:a), ((X08 Xx)->(X07 Xx)))
% 131.65/131.95 Found x600:=(x60 x7):((cK x4) Xx0)
% 131.65/131.95 Found (x60 x7) as proof of ((cK X08) Xx0)
% 131.65/131.95 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 131.65/131.95 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 131.65/131.95 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 131.65/131.95 Found x8:(X08 Xx1)
% 131.65/131.95 Found x8 as proof of (X07 Xx1)
% 131.65/131.95 Found (fun (x8:(X08 Xx1))=> x8) as proof of (X07 Xx1)
% 131.65/131.95 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of ((X08 Xx1)->(X07 Xx1))
% 131.65/131.95 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of (forall (Xx:a), ((X08 Xx)->(X07 Xx)))
% 131.65/131.95 Found x600:=(x60 x7):((cK x4) Xx0)
% 131.65/131.95 Found (x60 x7) as proof of ((cK X08) Xx0)
% 131.65/131.95 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 131.65/131.95 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 131.65/131.95 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 131.65/131.95 Found x8:(X08 Xx1)
% 131.65/131.95 Found x8 as proof of (X07 Xx1)
% 131.65/131.95 Found (fun (x8:(X08 Xx1))=> x8) as proof of (X07 Xx1)
% 131.65/131.95 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of ((X08 Xx1)->(X07 Xx1))
% 131.65/131.95 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of (forall (Xx:a), ((X08 Xx)->(X07 Xx)))
% 131.65/131.95 Found x600:=(x60 x7):((cK x4) Xx0)
% 131.65/131.95 Found (x60 x7) as proof of ((cK X08) Xx0)
% 131.65/131.95 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 131.65/131.95 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 131.65/131.95 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 131.65/131.95 Found x8:(X08 Xx1)
% 131.65/131.95 Found x8 as proof of (X07 Xx1)
% 131.65/131.95 Found (fun (x8:(X08 Xx1))=> x8) as proof of (X07 Xx1)
% 131.65/131.95 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of ((X08 Xx1)->(X07 Xx1))
% 131.65/131.95 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of (forall (Xx:a), ((X08 Xx)->(X07 Xx)))
% 131.65/131.95 Found x600:=(x60 x7):((cK x3) Xx0)
% 131.65/131.95 Found (x60 x7) as proof of ((cK X08) Xx0)
% 131.65/131.95 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 131.65/131.95 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 131.65/131.95 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 131.65/131.95 Found x8:(X08 Xx1)
% 131.65/131.95 Found x8 as proof of (X07 Xx1)
% 131.65/131.95 Found (fun (x8:(X08 Xx1))=> x8) as proof of (X07 Xx1)
% 131.65/131.95 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of ((X08 Xx1)->(X07 Xx1))
% 131.65/131.95 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of (forall (Xx:a), ((X08 Xx)->(X07 Xx)))
% 131.65/131.95 Found x600:=(x60 x7):((cK x4) Xx0)
% 131.65/131.95 Found (x60 x7) as proof of ((cK X08) Xx0)
% 131.65/131.95 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 131.65/131.95 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 131.65/131.95 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 131.65/131.95 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 131.65/131.95 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X07) Xx0))
% 131.65/131.95 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X07) Xx0))
% 131.65/131.95 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X07) Xx0))
% 131.65/131.95 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X07) Xx0)))
% 131.89/132.17 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 131.89/132.17 Found ((and_rect0 ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 131.89/132.17 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 131.89/132.17 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X07) Xx0)
% 131.89/132.17 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 131.89/132.17 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 131.89/132.17 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 131.89/132.17 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 131.89/132.17 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X08) Xx0)))
% 131.89/132.17 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 131.89/132.17 Found ((and_rect0 ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 131.89/132.17 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 131.89/132.17 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 131.89/132.17 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 131.89/132.17 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 131.89/132.17 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 131.89/132.17 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 131.89/132.17 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X08) Xx0)))
% 131.89/132.17 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 131.89/132.17 Found ((and_rect0 ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 131.89/132.17 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 131.89/132.17 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 131.89/132.17 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 131.89/132.17 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 131.89/132.17 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 131.89/132.17 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 131.89/132.17 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X08) Xx0)))
% 131.89/132.17 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 131.89/132.17 Found ((and_rect0 ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 131.89/132.17 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 132.10/132.41 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 132.10/132.41 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 132.10/132.41 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 132.10/132.41 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 132.10/132.41 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 132.10/132.41 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X08) Xx0)))
% 132.10/132.41 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 132.10/132.41 Found ((and_rect0 ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 132.10/132.41 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 132.10/132.41 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 132.10/132.41 Found x8:(X08 Xx1)
% 132.10/132.41 Found x8 as proof of (X07 Xx1)
% 132.10/132.41 Found (fun (x8:(X08 Xx1))=> x8) as proof of (X07 Xx1)
% 132.10/132.41 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of ((X08 Xx1)->(X07 Xx1))
% 132.10/132.41 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of (forall (Xx:a), ((X08 Xx)->(X07 Xx)))
% 132.10/132.41 Found x600:=(x60 x7):((cK x4) Xx0)
% 132.10/132.41 Found (x60 x7) as proof of ((cK X08) Xx0)
% 132.10/132.41 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 132.10/132.41 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 132.10/132.41 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 132.10/132.41 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 132.10/132.41 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 132.10/132.41 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 132.10/132.41 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 132.10/132.41 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X08) Xx0)))
% 132.10/132.41 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 132.10/132.41 Found ((and_rect0 ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 132.10/132.41 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 132.10/132.41 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 132.10/132.41 Found x8:(X08 Xx1)
% 132.10/132.41 Found x8 as proof of (X07 Xx1)
% 132.10/132.41 Found (fun (x8:(X08 Xx1))=> x8) as proof of (X07 Xx1)
% 132.10/132.41 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of ((X08 Xx1)->(X07 Xx1))
% 132.10/132.41 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of (forall (Xx:a), ((X08 Xx)->(X07 Xx)))
% 132.10/132.41 Found x600:=(x60 x7):((cK x4) Xx0)
% 132.10/132.41 Found (x60 x7) as proof of ((cK X08) Xx0)
% 132.10/132.41 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 132.10/132.41 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 132.10/132.41 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 132.10/132.41 Found x8:(X08 Xx1)
% 132.10/132.41 Found x8 as proof of (X07 Xx1)
% 132.10/132.41 Found (fun (x8:(X08 Xx1))=> x8) as proof of (X07 Xx1)
% 132.10/132.41 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of ((X08 Xx1)->(X07 Xx1))
% 132.49/132.76 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of (forall (Xx:a), ((X08 Xx)->(X07 Xx)))
% 132.49/132.76 Found x600:=(x60 x7):((cK x4) Xx0)
% 132.49/132.76 Found (x60 x7) as proof of ((cK X08) Xx0)
% 132.49/132.76 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 132.49/132.76 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 132.49/132.76 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 132.49/132.76 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 132.49/132.76 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 132.49/132.76 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 132.49/132.76 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 132.49/132.76 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X08) Xx0)))
% 132.49/132.76 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 132.49/132.76 Found ((and_rect0 ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 132.49/132.76 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 132.49/132.76 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 132.49/132.76 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 132.49/132.76 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 132.49/132.76 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 132.49/132.76 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 132.49/132.76 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X08) Xx0)))
% 132.49/132.76 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 132.49/132.76 Found ((and_rect0 ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 132.49/132.76 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 132.49/132.76 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 132.49/132.76 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 132.49/132.76 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 132.49/132.76 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 132.49/132.76 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 132.49/132.76 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X08) Xx0)))
% 132.49/132.76 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 132.49/132.76 Found ((and_rect0 ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 132.49/132.76 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 132.49/132.76 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 132.49/132.76 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 132.49/132.76 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 135.29/135.61 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 135.29/135.61 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 135.29/135.61 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X08) Xx0)))
% 135.29/135.61 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 135.29/135.61 Found ((and_rect0 ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 135.29/135.61 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 135.29/135.61 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 135.29/135.61 Found x8:(X08 Xx1)
% 135.29/135.61 Found x8 as proof of (X07 Xx1)
% 135.29/135.61 Found (fun (x8:(X08 Xx1))=> x8) as proof of (X07 Xx1)
% 135.29/135.61 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of ((X08 Xx1)->(X07 Xx1))
% 135.29/135.61 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of (forall (Xx:a), ((X08 Xx)->(X07 Xx)))
% 135.29/135.61 Found x600:=(x60 x7):((cK x3) Xx0)
% 135.29/135.61 Found (x60 x7) as proof of ((cK X08) Xx0)
% 135.29/135.61 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 135.29/135.61 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 135.29/135.61 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 135.29/135.61 Found x8:(X08 Xx1)
% 135.29/135.61 Found x8 as proof of (X07 Xx1)
% 135.29/135.61 Found (fun (x8:(X08 Xx1))=> x8) as proof of (X07 Xx1)
% 135.29/135.61 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of ((X08 Xx1)->(X07 Xx1))
% 135.29/135.61 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of (forall (Xx:a), ((X08 Xx)->(X07 Xx)))
% 135.29/135.61 Found x600:=(x60 x7):((cK x4) Xx0)
% 135.29/135.61 Found (x60 x7) as proof of ((cK X08) Xx0)
% 135.29/135.61 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 135.29/135.61 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 135.29/135.61 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 135.29/135.61 Found x8:(X08 Xx1)
% 135.29/135.61 Found x8 as proof of (X07 Xx1)
% 135.29/135.61 Found (fun (x8:(X08 Xx1))=> x8) as proof of (X07 Xx1)
% 135.29/135.61 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of ((X08 Xx1)->(X07 Xx1))
% 135.29/135.61 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of (forall (Xx:a), ((X08 Xx)->(X07 Xx)))
% 135.29/135.61 Found x500:=(x50 x6):((cK x3) Xx0)
% 135.29/135.61 Found (x50 x6) as proof of ((cK X08) Xx0)
% 135.29/135.61 Found ((x5 Xx0) x6) as proof of ((cK X08) Xx0)
% 135.29/135.61 Found ((x5 Xx0) x6) as proof of ((cK X08) Xx0)
% 135.29/135.61 Found ((x5 Xx0) x6) as proof of ((cK X08) Xx0)
% 135.29/135.61 Found x8:(X08 Xx1)
% 135.29/135.61 Found x8 as proof of (X07 Xx1)
% 135.29/135.61 Found (fun (x8:(X08 Xx1))=> x8) as proof of (X07 Xx1)
% 135.29/135.61 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of ((X08 Xx1)->(X07 Xx1))
% 135.29/135.61 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of (forall (Xx:a), ((X08 Xx)->(X07 Xx)))
% 135.29/135.61 Found x600:=(x60 x7):((cK x4) Xx0)
% 135.29/135.61 Found (x60 x7) as proof of ((cK X08) Xx0)
% 135.29/135.61 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 135.29/135.61 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 135.29/135.61 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 135.29/135.61 Found x8:(X08 Xx1)
% 135.29/135.61 Found x8 as proof of (X07 Xx1)
% 135.29/135.61 Found (fun (x8:(X08 Xx1))=> x8) as proof of (X07 Xx1)
% 135.29/135.61 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of ((X08 Xx1)->(X07 Xx1))
% 135.29/135.61 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of (forall (Xx:a), ((X08 Xx)->(X07 Xx)))
% 135.29/135.61 Found x600:=(x60 x7):((cK x4) Xx0)
% 135.29/135.61 Found (x60 x7) as proof of ((cK X08) Xx0)
% 135.29/135.61 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 135.29/135.61 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 135.29/135.61 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 135.29/135.61 Found x8:(X08 Xx1)
% 135.29/135.61 Found x8 as proof of (X07 Xx1)
% 135.29/135.61 Found (fun (x8:(X08 Xx1))=> x8) as proof of (X07 Xx1)
% 135.29/135.61 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of ((X08 Xx1)->(X07 Xx1))
% 135.29/135.61 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of (forall (Xx:a), ((X08 Xx)->(X07 Xx)))
% 135.29/135.61 Found x600:=(x60 x7):((cK x4) Xx0)
% 135.29/135.61 Found (x60 x7) as proof of ((cK X08) Xx0)
% 135.29/135.61 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 135.29/135.61 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 135.29/135.61 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 135.29/135.61 Found x8:(X08 Xx1)
% 135.29/135.61 Found x8 as proof of (X07 Xx1)
% 136.93/137.25 Found (fun (x8:(X08 Xx1))=> x8) as proof of (X07 Xx1)
% 136.93/137.25 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of ((X08 Xx1)->(X07 Xx1))
% 136.93/137.25 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of (forall (Xx:a), ((X08 Xx)->(X07 Xx)))
% 136.93/137.25 Found x600:=(x60 x7):((cK x4) Xx0)
% 136.93/137.25 Found (x60 x7) as proof of ((cK X08) Xx0)
% 136.93/137.25 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 136.93/137.25 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 136.93/137.25 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 136.93/137.25 Found x8:(X08 Xx1)
% 136.93/137.25 Found x8 as proof of (X07 Xx1)
% 136.93/137.25 Found (fun (x8:(X08 Xx1))=> x8) as proof of (X07 Xx1)
% 136.93/137.25 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of ((X08 Xx1)->(X07 Xx1))
% 136.93/137.25 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of (forall (Xx:a), ((X08 Xx)->(X07 Xx)))
% 136.93/137.25 Found x600:=(x60 x7):((cK x3) Xx0)
% 136.93/137.25 Found (x60 x7) as proof of ((cK X08) Xx0)
% 136.93/137.25 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 136.93/137.25 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 136.93/137.25 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 136.93/137.25 Found x8:(X08 Xx1)
% 136.93/137.25 Found x8 as proof of (X07 Xx1)
% 136.93/137.25 Found (fun (x8:(X08 Xx1))=> x8) as proof of (X07 Xx1)
% 136.93/137.25 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of ((X08 Xx1)->(X07 Xx1))
% 136.93/137.25 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of (forall (Xx:a), ((X08 Xx)->(X07 Xx)))
% 136.93/137.25 Found x600:=(x60 x7):((cK x4) Xx0)
% 136.93/137.25 Found (x60 x7) as proof of ((cK X08) Xx0)
% 136.93/137.25 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 136.93/137.25 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 136.93/137.25 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 136.93/137.25 Found x8:(X08 Xx1)
% 136.93/137.25 Found x8 as proof of (X07 Xx1)
% 136.93/137.25 Found (fun (x8:(X08 Xx1))=> x8) as proof of (X07 Xx1)
% 136.93/137.25 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of ((X08 Xx1)->(X07 Xx1))
% 136.93/137.25 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of (forall (Xx:a), ((X08 Xx)->(X07 Xx)))
% 136.93/137.25 Found x600:=(x60 x7):((cK x4) Xx0)
% 136.93/137.25 Found (x60 x7) as proof of ((cK X08) Xx0)
% 136.93/137.25 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 136.93/137.25 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 136.93/137.25 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 136.93/137.25 Found x8:(X08 Xx1)
% 136.93/137.25 Found x8 as proof of (X07 Xx1)
% 136.93/137.25 Found (fun (x8:(X08 Xx1))=> x8) as proof of (X07 Xx1)
% 136.93/137.25 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of ((X08 Xx1)->(X07 Xx1))
% 136.93/137.25 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of (forall (Xx:a), ((X08 Xx)->(X07 Xx)))
% 136.93/137.25 Found x600:=(x60 x7):((cK x4) Xx0)
% 136.93/137.25 Found (x60 x7) as proof of ((cK X08) Xx0)
% 136.93/137.25 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 136.93/137.25 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 136.93/137.25 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 136.93/137.25 Found x8:(X08 Xx1)
% 136.93/137.25 Found x8 as proof of (X07 Xx1)
% 136.93/137.25 Found (fun (x8:(X08 Xx1))=> x8) as proof of (X07 Xx1)
% 136.93/137.25 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of ((X08 Xx1)->(X07 Xx1))
% 136.93/137.25 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of (forall (Xx:a), ((X08 Xx)->(X07 Xx)))
% 136.93/137.25 Found x600:=(x60 x7):((cK x4) Xx0)
% 136.93/137.25 Found (x60 x7) as proof of ((cK X08) Xx0)
% 136.93/137.25 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 136.93/137.25 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 136.93/137.25 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 136.93/137.25 Found x8:(X08 Xx1)
% 136.93/137.25 Found x8 as proof of (X07 Xx1)
% 136.93/137.25 Found (fun (x8:(X08 Xx1))=> x8) as proof of (X07 Xx1)
% 136.93/137.25 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of ((X08 Xx1)->(X07 Xx1))
% 136.93/137.25 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of (forall (Xx:a), ((X08 Xx)->(X07 Xx)))
% 136.93/137.25 Found x600:=(x60 x7):((cK x4) Xx0)
% 136.93/137.25 Found (x60 x7) as proof of ((cK X08) Xx0)
% 136.93/137.25 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 136.93/137.25 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 136.93/137.25 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 136.93/137.25 Found x8:(X08 Xx1)
% 136.93/137.25 Found x8 as proof of (X07 Xx1)
% 136.93/137.25 Found (fun (x8:(X08 Xx1))=> x8) as proof of (X07 Xx1)
% 136.93/137.25 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of ((X08 Xx1)->(X07 Xx1))
% 136.93/137.25 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of (forall (Xx:a), ((X08 Xx)->(X07 Xx)))
% 136.93/137.25 Found x600:=(x60 x7):((cK x4) Xx0)
% 136.93/137.25 Found (x60 x7) as proof of ((cK X08) Xx0)
% 136.93/137.25 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 136.93/137.25 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 136.93/137.25 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 136.93/137.25 Found x60:=(x6 Xx0):((x3 Xx0)->((cK x3) Xx0))
% 136.93/137.25 Found (x6 Xx0) as proof of ((x3 Xx0)->((cK X08) Xx0))
% 136.93/137.25 Found (x6 Xx0) as proof of ((x3 Xx0)->((cK X08) Xx0))
% 136.93/137.25 Found (fun (x6:(forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1))))=> (x6 Xx0)) as proof of ((x3 Xx0)->((cK X08) Xx0))
% 137.99/138.27 Found (fun (x6:(forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1)))->((x3 Xx0)->((cK X08) Xx0)))
% 137.99/138.27 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 137.99/138.27 Found ((and_rect0 ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 137.99/138.27 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1)))->((x3 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1)))) (x3 Xx0)) P) x6) x4)) ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 137.99/138.27 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1)))->((x3 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1)))) (x3 Xx0)) P) x6) x4)) ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 137.99/138.27 Found x8:(X08 Xx1)
% 137.99/138.27 Found x8 as proof of (X07 Xx1)
% 137.99/138.27 Found (fun (x8:(X08 Xx1))=> x8) as proof of (X07 Xx1)
% 137.99/138.27 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of ((X08 Xx1)->(X07 Xx1))
% 137.99/138.27 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of (forall (Xx:a), ((X08 Xx)->(X07 Xx)))
% 137.99/138.27 Found x600:=(x60 x7):((cK x3) Xx0)
% 137.99/138.27 Found (x60 x7) as proof of ((cK X08) Xx0)
% 137.99/138.27 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 137.99/138.27 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 137.99/138.27 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 137.99/138.27 Found x8:(X08 Xx1)
% 137.99/138.27 Found x8 as proof of (X07 Xx1)
% 137.99/138.27 Found (fun (x8:(X08 Xx1))=> x8) as proof of (X07 Xx1)
% 137.99/138.27 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of ((X08 Xx1)->(X07 Xx1))
% 137.99/138.27 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of (forall (Xx:a), ((X08 Xx)->(X07 Xx)))
% 137.99/138.27 Found x600:=(x60 x7):((cK x4) Xx0)
% 137.99/138.27 Found (x60 x7) as proof of ((cK X08) Xx0)
% 137.99/138.27 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 137.99/138.27 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 137.99/138.27 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 137.99/138.27 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 137.99/138.27 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 137.99/138.27 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 137.99/138.27 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 137.99/138.27 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X08) Xx0)))
% 137.99/138.27 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 137.99/138.27 Found ((and_rect0 ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 137.99/138.27 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 137.99/138.27 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X08) Xx0)
% 137.99/138.27 Found x8:(X08 Xx1)
% 137.99/138.27 Found x8 as proof of (X07 Xx1)
% 137.99/138.27 Found (fun (x8:(X08 Xx1))=> x8) as proof of (X07 Xx1)
% 137.99/138.27 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of ((X08 Xx1)->(X07 Xx1))
% 137.99/138.27 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of (forall (Xx:a), ((X08 Xx)->(X07 Xx)))
% 137.99/138.27 Found x600:=(x60 x7):((cK x4) Xx0)
% 137.99/138.27 Found (x60 x7) as proof of ((cK X08) Xx0)
% 137.99/138.27 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 137.99/138.27 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 137.99/138.27 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 137.99/138.27 Found x8:(X08 Xx1)
% 137.99/138.27 Found x8 as proof of (X07 Xx1)
% 137.99/138.27 Found (fun (x8:(X08 Xx1))=> x8) as proof of (X07 Xx1)
% 137.99/138.27 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of ((X08 Xx1)->(X07 Xx1))
% 137.99/138.27 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of (forall (Xx:a), ((X08 Xx)->(X07 Xx)))
% 137.99/138.27 Found x600:=(x60 x7):((cK x4) Xx0)
% 137.99/138.27 Found (x60 x7) as proof of ((cK X08) Xx0)
% 137.99/138.27 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 139.17/139.48 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 139.17/139.48 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 139.17/139.48 Found x8:(X08 Xx1)
% 139.17/139.48 Found x8 as proof of (X07 Xx1)
% 139.17/139.48 Found (fun (x8:(X08 Xx1))=> x8) as proof of (X07 Xx1)
% 139.17/139.48 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of ((X08 Xx1)->(X07 Xx1))
% 139.17/139.48 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of (forall (Xx:a), ((X08 Xx)->(X07 Xx)))
% 139.17/139.48 Found x600:=(x60 x7):((cK x4) Xx0)
% 139.17/139.48 Found (x60 x7) as proof of ((cK X08) Xx0)
% 139.17/139.48 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 139.17/139.48 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 139.17/139.48 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 139.17/139.48 Found x8:(X08 Xx1)
% 139.17/139.48 Found x8 as proof of (X07 Xx1)
% 139.17/139.48 Found (fun (x8:(X08 Xx1))=> x8) as proof of (X07 Xx1)
% 139.17/139.48 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of ((X08 Xx1)->(X07 Xx1))
% 139.17/139.48 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of (forall (Xx:a), ((X08 Xx)->(X07 Xx)))
% 139.17/139.48 Found x600:=(x60 x7):((cK x4) Xx0)
% 139.17/139.48 Found (x60 x7) as proof of ((cK X08) Xx0)
% 139.17/139.48 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 139.17/139.48 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 139.17/139.48 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 139.17/139.48 Found x8:(X08 Xx1)
% 139.17/139.48 Found x8 as proof of (X07 Xx1)
% 139.17/139.48 Found (fun (x8:(X08 Xx1))=> x8) as proof of (X07 Xx1)
% 139.17/139.48 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of ((X08 Xx1)->(X07 Xx1))
% 139.17/139.48 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of (forall (Xx:a), ((X08 Xx)->(X07 Xx)))
% 139.17/139.48 Found x600:=(x60 x7):((cK x4) Xx0)
% 139.17/139.48 Found (x60 x7) as proof of ((cK X08) Xx0)
% 139.17/139.48 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 139.17/139.48 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 139.17/139.48 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 139.17/139.48 Found x8:(X08 Xx1)
% 139.17/139.48 Found x8 as proof of (X07 Xx1)
% 139.17/139.48 Found (fun (x8:(X08 Xx1))=> x8) as proof of (X07 Xx1)
% 139.17/139.48 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of ((X08 Xx1)->(X07 Xx1))
% 139.17/139.48 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of (forall (Xx:a), ((X08 Xx)->(X07 Xx)))
% 139.17/139.48 Found x600:=(x60 x7):((cK x4) Xx0)
% 139.17/139.48 Found (x60 x7) as proof of ((cK X08) Xx0)
% 139.17/139.48 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 139.17/139.48 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 139.17/139.48 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 139.17/139.48 Found x8:(X08 Xx1)
% 139.17/139.48 Found x8 as proof of (X07 Xx1)
% 139.17/139.48 Found (fun (x8:(X08 Xx1))=> x8) as proof of (X07 Xx1)
% 139.17/139.48 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of ((X08 Xx1)->(X07 Xx1))
% 139.17/139.48 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of (forall (Xx:a), ((X08 Xx)->(X07 Xx)))
% 139.17/139.48 Found x600:=(x60 x7):((cK x3) Xx0)
% 139.17/139.48 Found (x60 x7) as proof of ((cK X08) Xx0)
% 139.17/139.48 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 139.17/139.48 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 139.17/139.48 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 139.17/139.48 Found x8:(X08 Xx1)
% 139.17/139.48 Found x8 as proof of (X07 Xx1)
% 139.17/139.48 Found (fun (x8:(X08 Xx1))=> x8) as proof of (X07 Xx1)
% 139.17/139.48 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of ((X08 Xx1)->(X07 Xx1))
% 139.17/139.48 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of (forall (Xx:a), ((X08 Xx)->(X07 Xx)))
% 139.17/139.48 Found x600:=(x60 x7):((cK x4) Xx0)
% 139.17/139.48 Found (x60 x7) as proof of ((cK X08) Xx0)
% 139.17/139.48 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 139.17/139.48 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 139.17/139.48 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 139.17/139.48 Found x8:(X08 Xx1)
% 139.17/139.48 Found x8 as proof of (X07 Xx1)
% 139.17/139.48 Found (fun (x8:(X08 Xx1))=> x8) as proof of (X07 Xx1)
% 139.17/139.48 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of ((X08 Xx1)->(X07 Xx1))
% 139.17/139.48 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of (forall (Xx:a), ((X08 Xx)->(X07 Xx)))
% 139.17/139.48 Found x600:=(x60 x7):((cK x4) Xx0)
% 139.17/139.48 Found (x60 x7) as proof of ((cK X08) Xx0)
% 139.17/139.48 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 139.17/139.48 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 139.17/139.48 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 139.17/139.48 Found x8:(X08 Xx1)
% 139.17/139.48 Found x8 as proof of (X07 Xx1)
% 139.17/139.48 Found (fun (x8:(X08 Xx1))=> x8) as proof of (X07 Xx1)
% 139.17/139.48 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of ((X08 Xx1)->(X07 Xx1))
% 139.17/139.48 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of (forall (Xx:a), ((X08 Xx)->(X07 Xx)))
% 139.17/139.48 Found x600:=(x60 x7):((cK x4) Xx0)
% 139.17/139.48 Found (x60 x7) as proof of ((cK X08) Xx0)
% 139.17/139.48 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 139.17/139.48 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 139.17/139.48 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 139.17/139.48 Found x8:(X08 Xx1)
% 139.17/139.48 Found x8 as proof of (X07 Xx1)
% 139.17/139.48 Found (fun (x8:(X08 Xx1))=> x8) as proof of (X07 Xx1)
% 140.05/140.32 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of ((X08 Xx1)->(X07 Xx1))
% 140.05/140.32 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of (forall (Xx:a), ((X08 Xx)->(X07 Xx)))
% 140.05/140.32 Found x600:=(x60 x7):((cK x4) Xx0)
% 140.05/140.32 Found (x60 x7) as proof of ((cK X08) Xx0)
% 140.05/140.32 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 140.05/140.32 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 140.05/140.32 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 140.05/140.32 Found x8:(X08 Xx1)
% 140.05/140.32 Found x8 as proof of (X07 Xx1)
% 140.05/140.32 Found (fun (x8:(X08 Xx1))=> x8) as proof of (X07 Xx1)
% 140.05/140.32 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of ((X08 Xx1)->(X07 Xx1))
% 140.05/140.32 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of (forall (Xx:a), ((X08 Xx)->(X07 Xx)))
% 140.05/140.32 Found x600:=(x60 x7):((cK x4) Xx0)
% 140.05/140.32 Found (x60 x7) as proof of ((cK X08) Xx0)
% 140.05/140.32 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 140.05/140.32 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 140.05/140.32 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 140.05/140.32 Found x8:(X08 Xx1)
% 140.05/140.32 Found x8 as proof of (X07 Xx1)
% 140.05/140.32 Found (fun (x8:(X08 Xx1))=> x8) as proof of (X07 Xx1)
% 140.05/140.32 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of ((X08 Xx1)->(X07 Xx1))
% 140.05/140.32 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of (forall (Xx:a), ((X08 Xx)->(X07 Xx)))
% 140.05/140.32 Found x600:=(x60 x7):((cK x4) Xx0)
% 140.05/140.32 Found (x60 x7) as proof of ((cK X08) Xx0)
% 140.05/140.32 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 140.05/140.32 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 140.05/140.32 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 140.05/140.32 Found x8:(X08 Xx1)
% 140.05/140.32 Found x8 as proof of (X07 Xx1)
% 140.05/140.32 Found (fun (x8:(X08 Xx1))=> x8) as proof of (X07 Xx1)
% 140.05/140.32 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of ((X08 Xx1)->(X07 Xx1))
% 140.05/140.32 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of (forall (Xx:a), ((X08 Xx)->(X07 Xx)))
% 140.05/140.32 Found x600:=(x60 x7):((cK x4) Xx0)
% 140.05/140.32 Found (x60 x7) as proof of ((cK X08) Xx0)
% 140.05/140.32 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 140.05/140.32 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 140.05/140.32 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 140.05/140.32 Found x8:(X08 Xx1)
% 140.05/140.32 Found x8 as proof of (X07 Xx1)
% 140.05/140.32 Found (fun (x8:(X08 Xx1))=> x8) as proof of (X07 Xx1)
% 140.05/140.32 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of ((X08 Xx1)->(X07 Xx1))
% 140.05/140.32 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of (forall (Xx:a), ((X08 Xx)->(X07 Xx)))
% 140.05/140.32 Found x600:=(x60 x7):((cK x4) Xx0)
% 140.05/140.32 Found (x60 x7) as proof of ((cK X08) Xx0)
% 140.05/140.32 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 140.05/140.32 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 140.05/140.32 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 140.05/140.32 Found x8:(X08 Xx1)
% 140.05/140.32 Found x8 as proof of (X07 Xx1)
% 140.05/140.32 Found (fun (x8:(X08 Xx1))=> x8) as proof of (X07 Xx1)
% 140.05/140.32 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of ((X08 Xx1)->(X07 Xx1))
% 140.05/140.32 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of (forall (Xx:a), ((X08 Xx)->(X07 Xx)))
% 140.05/140.32 Found x600:=(x60 x7):((cK x3) Xx0)
% 140.05/140.32 Found (x60 x7) as proof of ((cK X08) Xx0)
% 140.05/140.32 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 140.05/140.32 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 140.05/140.32 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 140.05/140.32 Found x8:(X08 Xx1)
% 140.05/140.32 Found x8 as proof of (X07 Xx1)
% 140.05/140.32 Found (fun (x8:(X08 Xx1))=> x8) as proof of (X07 Xx1)
% 140.05/140.32 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of ((X08 Xx1)->(X07 Xx1))
% 140.05/140.32 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of (forall (Xx:a), ((X08 Xx)->(X07 Xx)))
% 140.05/140.32 Found x600:=(x60 x7):((cK x4) Xx0)
% 140.05/140.32 Found (x60 x7) as proof of ((cK X08) Xx0)
% 140.05/140.32 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 140.05/140.32 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 140.05/140.32 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 140.05/140.32 Found x8:(X08 Xx1)
% 140.05/140.32 Found x8 as proof of (X07 Xx1)
% 140.05/140.32 Found (fun (x8:(X08 Xx1))=> x8) as proof of (X07 Xx1)
% 140.05/140.32 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of ((X08 Xx1)->(X07 Xx1))
% 140.05/140.32 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of (forall (Xx:a), ((X08 Xx)->(X07 Xx)))
% 140.05/140.32 Found x600:=(x60 x7):((cK x4) Xx0)
% 140.05/140.32 Found (x60 x7) as proof of ((cK X08) Xx0)
% 140.05/140.32 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 140.05/140.32 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 140.05/140.32 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 140.05/140.32 Found x8:(X08 Xx1)
% 140.05/140.32 Found x8 as proof of (X07 Xx1)
% 140.05/140.32 Found (fun (x8:(X08 Xx1))=> x8) as proof of (X07 Xx1)
% 140.05/140.32 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of ((X08 Xx1)->(X07 Xx1))
% 140.05/140.32 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of (forall (Xx:a), ((X08 Xx)->(X07 Xx)))
% 140.67/141.00 Found x600:=(x60 x7):((cK x4) Xx0)
% 140.67/141.00 Found (x60 x7) as proof of ((cK X08) Xx0)
% 140.67/141.00 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 140.67/141.00 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 140.67/141.00 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 140.67/141.00 Found x8:(X08 Xx1)
% 140.67/141.00 Found x8 as proof of (X07 Xx1)
% 140.67/141.00 Found (fun (x8:(X08 Xx1))=> x8) as proof of (X07 Xx1)
% 140.67/141.00 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of ((X08 Xx1)->(X07 Xx1))
% 140.67/141.00 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of (forall (Xx:a), ((X08 Xx)->(X07 Xx)))
% 140.67/141.00 Found x600:=(x60 x7):((cK x4) Xx0)
% 140.67/141.00 Found (x60 x7) as proof of ((cK X08) Xx0)
% 140.67/141.00 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 140.67/141.00 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 140.67/141.00 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 140.67/141.00 Found x8:(X08 Xx1)
% 140.67/141.00 Found x8 as proof of (X07 Xx1)
% 140.67/141.00 Found (fun (x8:(X08 Xx1))=> x8) as proof of (X07 Xx1)
% 140.67/141.00 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of ((X08 Xx1)->(X07 Xx1))
% 140.67/141.00 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of (forall (Xx:a), ((X08 Xx)->(X07 Xx)))
% 140.67/141.00 Found x600:=(x60 x7):((cK x4) Xx0)
% 140.67/141.00 Found (x60 x7) as proof of ((cK X08) Xx0)
% 140.67/141.00 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 140.67/141.00 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 140.67/141.00 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 140.67/141.00 Found x8:(X08 Xx1)
% 140.67/141.00 Found x8 as proof of (X07 Xx1)
% 140.67/141.00 Found (fun (x8:(X08 Xx1))=> x8) as proof of (X07 Xx1)
% 140.67/141.00 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of ((X08 Xx1)->(X07 Xx1))
% 140.67/141.00 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of (forall (Xx:a), ((X08 Xx)->(X07 Xx)))
% 140.67/141.00 Found x600:=(x60 x7):((cK x4) Xx0)
% 140.67/141.00 Found (x60 x7) as proof of ((cK X08) Xx0)
% 140.67/141.00 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 140.67/141.00 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 140.67/141.00 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 140.67/141.00 Found x8:(X08 Xx1)
% 140.67/141.00 Found x8 as proof of (X07 Xx1)
% 140.67/141.00 Found (fun (x8:(X08 Xx1))=> x8) as proof of (X07 Xx1)
% 140.67/141.00 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of ((X08 Xx1)->(X07 Xx1))
% 140.67/141.00 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of (forall (Xx:a), ((X08 Xx)->(X07 Xx)))
% 140.67/141.00 Found x600:=(x60 x7):((cK x4) Xx0)
% 140.67/141.00 Found (x60 x7) as proof of ((cK X08) Xx0)
% 140.67/141.00 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 140.67/141.00 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 140.67/141.00 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 140.67/141.00 Found x8:(X08 Xx1)
% 140.67/141.00 Found x8 as proof of (X07 Xx1)
% 140.67/141.00 Found (fun (x8:(X08 Xx1))=> x8) as proof of (X07 Xx1)
% 140.67/141.00 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of ((X08 Xx1)->(X07 Xx1))
% 140.67/141.00 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of (forall (Xx:a), ((X08 Xx)->(X07 Xx)))
% 140.67/141.00 Found x600:=(x60 x7):((cK x4) Xx0)
% 140.67/141.00 Found (x60 x7) as proof of ((cK X08) Xx0)
% 140.67/141.00 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 140.67/141.00 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 140.67/141.00 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 140.67/141.00 Found x8:(X08 Xx1)
% 140.67/141.00 Found x8 as proof of (X07 Xx1)
% 140.67/141.00 Found (fun (x8:(X08 Xx1))=> x8) as proof of (X07 Xx1)
% 140.67/141.00 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of ((X08 Xx1)->(X07 Xx1))
% 140.67/141.00 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of (forall (Xx:a), ((X08 Xx)->(X07 Xx)))
% 140.67/141.00 Found x600:=(x60 x7):((cK x4) Xx0)
% 140.67/141.00 Found (x60 x7) as proof of ((cK X08) Xx0)
% 140.67/141.00 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 140.67/141.00 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 140.67/141.00 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 140.67/141.00 Found x8:(X08 Xx1)
% 140.67/141.00 Found x8 as proof of (X07 Xx1)
% 140.67/141.00 Found (fun (x8:(X08 Xx1))=> x8) as proof of (X07 Xx1)
% 140.67/141.00 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of ((X08 Xx1)->(X07 Xx1))
% 140.67/141.00 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of (forall (Xx:a), ((X08 Xx)->(X07 Xx)))
% 140.67/141.00 Found x600:=(x60 x7):((cK x3) Xx0)
% 140.67/141.00 Found (x60 x7) as proof of ((cK X08) Xx0)
% 140.67/141.00 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 140.67/141.00 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 140.67/141.00 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 140.67/141.00 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 140.67/141.00 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 140.67/141.00 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 140.67/141.00 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 140.67/141.00 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X08) Xx0)))
% 140.67/141.00 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 141.21/141.51 Found ((and_rect0 ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 141.21/141.51 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 141.21/141.51 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 141.21/141.51 Found x6:(X08 Xx1)
% 141.21/141.51 Instantiate: X07:=X08:(a->Prop)
% 141.21/141.51 Found (fun (x6:(X08 Xx1))=> x6) as proof of (X07 Xx1)
% 141.21/141.51 Found (fun (Xx1:a) (x6:(X08 Xx1))=> x6) as proof of ((X08 Xx1)->(X07 Xx1))
% 141.21/141.51 Found (fun (Xx1:a) (x6:(X08 Xx1))=> x6) as proof of (forall (Xx:a), ((X08 Xx)->(X07 Xx)))
% 141.21/141.51 Found ((x390 (fun (Xx1:a) (x6:(X08 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X07) Xx0)
% 141.21/141.51 Found (((x39 X07) (fun (Xx1:a) (x6:(X08 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X07) Xx0)
% 141.21/141.51 Found ((((x3 x4) X07) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X07) Xx0)
% 141.21/141.51 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> ((((x3 x4) X07) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))))) as proof of ((cK X07) Xx0)
% 141.21/141.51 Found x8:(X08 Xx1)
% 141.21/141.51 Found x8 as proof of (X07 Xx1)
% 141.21/141.51 Found (fun (x8:(X08 Xx1))=> x8) as proof of (X07 Xx1)
% 141.21/141.51 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of ((X08 Xx1)->(X07 Xx1))
% 141.21/141.51 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of (forall (Xx:a), ((X08 Xx)->(X07 Xx)))
% 141.21/141.51 Found x600:=(x60 x7):((cK x4) Xx0)
% 141.21/141.51 Found (x60 x7) as proof of ((cK X08) Xx0)
% 141.21/141.51 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 141.21/141.51 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 141.21/141.51 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 141.21/141.51 Found x8:(X08 Xx1)
% 141.21/141.51 Found x8 as proof of (X07 Xx1)
% 141.21/141.51 Found (fun (x8:(X08 Xx1))=> x8) as proof of (X07 Xx1)
% 141.21/141.51 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of ((X08 Xx1)->(X07 Xx1))
% 141.21/141.51 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of (forall (Xx:a), ((X08 Xx)->(X07 Xx)))
% 141.21/141.51 Found x600:=(x60 x7):((cK x3) Xx0)
% 141.21/141.51 Found (x60 x7) as proof of ((cK X08) Xx0)
% 141.21/141.51 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 141.21/141.51 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 141.21/141.51 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 141.21/141.51 Found x8:(X08 Xx1)
% 141.21/141.51 Found x8 as proof of (X07 Xx1)
% 141.21/141.51 Found (fun (x8:(X08 Xx1))=> x8) as proof of (X07 Xx1)
% 141.21/141.51 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of ((X08 Xx1)->(X07 Xx1))
% 141.21/141.51 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of (forall (Xx:a), ((X08 Xx)->(X07 Xx)))
% 141.21/141.51 Found x600:=(x60 x7):((cK x4) Xx0)
% 141.21/141.51 Found (x60 x7) as proof of ((cK X08) Xx0)
% 141.21/141.51 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 141.21/141.51 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 141.21/141.51 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 141.21/141.51 Found x8:(X08 Xx1)
% 141.21/141.51 Found x8 as proof of (X07 Xx1)
% 141.21/141.51 Found (fun (x8:(X08 Xx1))=> x8) as proof of (X07 Xx1)
% 141.21/141.51 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of ((X08 Xx1)->(X07 Xx1))
% 141.21/141.51 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of (forall (Xx:a), ((X08 Xx)->(X07 Xx)))
% 143.37/143.64 Found x600:=(x60 x7):((cK x3) Xx0)
% 143.37/143.64 Found (x60 x7) as proof of ((cK X08) Xx0)
% 143.37/143.64 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 143.37/143.64 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 143.37/143.64 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 143.37/143.64 Found x8:(X08 Xx1)
% 143.37/143.64 Found x8 as proof of (X07 Xx1)
% 143.37/143.64 Found (fun (x8:(X08 Xx1))=> x8) as proof of (X07 Xx1)
% 143.37/143.64 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of ((X08 Xx1)->(X07 Xx1))
% 143.37/143.64 Found (fun (Xx1:a) (x8:(X08 Xx1))=> x8) as proof of (forall (Xx:a), ((X08 Xx)->(X07 Xx)))
% 143.37/143.64 Found x600:=(x60 x7):((cK x4) Xx0)
% 143.37/143.64 Found (x60 x7) as proof of ((cK X08) Xx0)
% 143.37/143.64 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 143.37/143.64 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 143.37/143.64 Found ((x6 Xx0) x7) as proof of ((cK X08) Xx0)
% 143.37/143.64 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 143.37/143.64 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 143.37/143.64 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 143.37/143.64 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 143.37/143.64 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X08) Xx0)))
% 143.37/143.64 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 143.37/143.64 Found ((and_rect0 ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 143.37/143.64 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 143.37/143.64 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X08) Xx0)
% 143.37/143.64 Found x4:(X07 Xx1)
% 143.37/143.64 Instantiate: X07:=(cK x5):(a->Prop)
% 143.37/143.64 Found x4 as proof of (X06 Xx1)
% 143.37/143.64 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X06 Xx1)
% 143.37/143.64 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X06 Xx1))
% 143.37/143.64 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X06 Xx1)))
% 143.37/143.64 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X06 Xx1)
% 143.37/143.64 Found ((and_rect0 (X06 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X06 Xx1)
% 143.37/143.64 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X06 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X06 Xx1)
% 143.37/143.64 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X06 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X06 Xx1)
% 143.37/143.64 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 143.37/143.64 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 143.37/143.64 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 143.37/143.64 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 143.37/143.64 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X08) Xx0)))
% 143.37/143.64 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 143.37/143.64 Found ((and_rect0 ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 143.37/143.64 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 143.91/144.27 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 143.91/144.27 Found x6:(X08 Xx1)
% 143.91/144.27 Instantiate: X07:=X08:(a->Prop)
% 143.91/144.27 Found (fun (x6:(X08 Xx1))=> x6) as proof of (X07 Xx1)
% 143.91/144.27 Found (fun (Xx1:a) (x6:(X08 Xx1))=> x6) as proof of ((X08 Xx1)->(X07 Xx1))
% 143.91/144.27 Found (fun (Xx1:a) (x6:(X08 Xx1))=> x6) as proof of (forall (Xx:a), ((X08 Xx)->(X07 Xx)))
% 143.91/144.27 Found ((x390 (fun (Xx1:a) (x6:(X08 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X07) Xx0)
% 143.91/144.27 Found (((x39 X07) (fun (Xx1:a) (x6:(X08 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X07) Xx0)
% 143.91/144.27 Found ((((x3 x4) X07) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X07) Xx0)
% 143.91/144.27 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> ((((x3 x4) X07) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))))) as proof of ((cK X07) Xx0)
% 143.91/144.27 Found x4:(X08 Xx1)
% 143.91/144.27 Instantiate: X08:=(cK x5):(a->Prop)
% 143.91/144.27 Found x4 as proof of (X07 Xx1)
% 143.91/144.27 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X07 Xx1)
% 143.91/144.27 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X07 Xx1))
% 143.91/144.27 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X07 Xx1)))
% 143.91/144.27 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X07 Xx1)
% 143.91/144.27 Found ((and_rect0 (X07 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X07 Xx1)
% 143.91/144.27 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X07 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X07 Xx1)
% 143.91/144.27 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X07 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X07 Xx1)
% 143.91/144.27 Found x4:(X08 Xx1)
% 143.91/144.27 Found x4 as proof of (X07 Xx1)
% 143.91/144.27 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X07 Xx1)
% 143.91/144.27 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X07 Xx1))
% 143.91/144.27 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X07 Xx1)))
% 143.91/144.27 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X07 Xx1)
% 143.91/144.27 Found ((and_rect0 (X07 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X07 Xx1)
% 144.30/144.58 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X07 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X07 Xx1)
% 144.30/144.58 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X07 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X07 Xx1)
% 144.30/144.58 Found x4:(X07 Xx1)
% 144.30/144.58 Found x4 as proof of (X06 Xx1)
% 144.30/144.58 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X06 Xx1)
% 144.30/144.58 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X06 Xx1))
% 144.30/144.58 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X06 Xx1)))
% 144.30/144.58 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X06 Xx1)
% 144.30/144.58 Found ((and_rect0 (X06 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X06 Xx1)
% 144.30/144.58 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X06 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X06 Xx1)
% 144.30/144.58 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X06 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X06 Xx1)
% 144.30/144.58 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 144.30/144.58 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X07) Xx0))
% 144.30/144.58 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X07) Xx0))
% 144.30/144.58 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X07) Xx0))
% 144.30/144.58 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X07) Xx0)))
% 144.30/144.58 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 144.30/144.58 Found ((and_rect0 ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 144.30/144.58 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 144.30/144.58 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 144.30/144.58 Found x6:(X07 Xx1)
% 144.30/144.58 Instantiate: X06:=X07:(a->Prop)
% 144.30/144.58 Found (fun (x6:(X07 Xx1))=> x6) as proof of (X06 Xx1)
% 144.30/144.58 Found (fun (Xx1:a) (x6:(X07 Xx1))=> x6) as proof of ((X07 Xx1)->(X06 Xx1))
% 144.30/144.58 Found (fun (Xx1:a) (x6:(X07 Xx1))=> x6) as proof of (forall (Xx:a), ((X07 Xx)->(X06 Xx)))
% 144.30/144.58 Found ((x380 (fun (Xx1:a) (x6:(X07 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X06) Xx0)
% 144.30/144.58 Found (((x38 X06) (fun (Xx1:a) (x6:(X07 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X06) Xx0)
% 145.67/145.95 Found ((((x3 x4) X06) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X06) Xx0)
% 145.67/145.95 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> ((((x3 x4) X06) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))))) as proof of ((cK X06) Xx0)
% 145.67/145.95 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 145.67/145.95 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 145.67/145.95 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 145.67/145.95 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 145.67/145.95 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X08) Xx0)))
% 145.67/145.95 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 145.67/145.95 Found ((and_rect0 ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 145.67/145.95 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 145.67/145.95 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X08) Xx0)
% 145.67/145.95 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 145.67/145.95 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X07) Xx0))
% 145.67/145.95 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X07) Xx0))
% 145.67/145.95 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X07) Xx0))
% 145.67/145.95 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X07) Xx0)))
% 145.67/145.95 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 145.67/145.95 Found ((and_rect0 ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 145.67/145.95 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X07) Xx0)
% 145.67/145.95 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X07) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X07) Xx0)
% 145.67/145.95 Found x4:(X08 Xx1)
% 145.67/145.95 Instantiate: X08:=(cK x5):(a->Prop)
% 145.67/145.95 Found x4 as proof of (X07 Xx1)
% 145.67/145.95 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X07 Xx1)
% 145.67/145.95 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X07 Xx1))
% 145.67/145.95 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X07 Xx1)))
% 145.67/145.95 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X07 Xx1)
% 145.67/145.95 Found ((and_rect0 (X07 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X07 Xx1)
% 145.67/145.95 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X07 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X07 Xx1)
% 146.04/146.36 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X07 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X07 Xx1)
% 146.04/146.36 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 146.04/146.36 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 146.04/146.36 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 146.04/146.36 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 146.04/146.36 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X08) Xx0)))
% 146.04/146.36 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 146.04/146.36 Found ((and_rect0 ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 146.04/146.36 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 146.04/146.36 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 146.04/146.36 Found x6:(X08 Xx1)
% 146.04/146.36 Instantiate: X07:=X08:(a->Prop)
% 146.04/146.36 Found (fun (x6:(X08 Xx1))=> x6) as proof of (X07 Xx1)
% 146.04/146.36 Found (fun (Xx1:a) (x6:(X08 Xx1))=> x6) as proof of ((X08 Xx1)->(X07 Xx1))
% 146.04/146.36 Found (fun (Xx1:a) (x6:(X08 Xx1))=> x6) as proof of (forall (Xx:a), ((X08 Xx)->(X07 Xx)))
% 146.04/146.36 Found ((x390 (fun (Xx1:a) (x6:(X08 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X07) Xx0)
% 146.04/146.36 Found (((x39 X07) (fun (Xx1:a) (x6:(X08 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X07) Xx0)
% 146.04/146.36 Found ((((x3 x4) X07) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X07) Xx0)
% 146.04/146.36 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> ((((x3 x4) X07) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))))) as proof of ((cK X07) Xx0)
% 146.04/146.36 Found x4:(X08 Xx1)
% 146.04/146.36 Found x4 as proof of (X07 Xx1)
% 146.04/146.36 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X07 Xx1)
% 146.04/146.36 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X07 Xx1))
% 146.04/146.36 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X07 Xx1)))
% 146.04/146.36 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X07 Xx1)
% 146.04/146.36 Found ((and_rect0 (X07 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X07 Xx1)
% 147.43/147.74 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X07 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X07 Xx1)
% 147.43/147.74 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X07 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X07 Xx1)
% 147.43/147.74 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 147.43/147.74 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 147.43/147.74 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 147.43/147.74 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 147.43/147.74 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X08) Xx0)))
% 147.43/147.74 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 147.43/147.74 Found ((and_rect0 ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 147.43/147.74 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 147.43/147.74 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X08) Xx0)
% 147.43/147.74 Found x4:(X07 Xx1)
% 147.43/147.74 Instantiate: X07:=(cK x5):(a->Prop)
% 147.43/147.74 Found x4 as proof of (X06 Xx1)
% 147.43/147.74 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X06 Xx1)
% 147.43/147.74 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X06 Xx1))
% 147.43/147.74 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X06 Xx1)))
% 147.43/147.74 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X06 Xx1)
% 147.43/147.74 Found ((and_rect0 (X06 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X06 Xx1)
% 147.43/147.74 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X06 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X06 Xx1)
% 147.43/147.74 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X06 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X06 Xx1)
% 147.43/147.74 Found x4:(X08 Xx1)
% 147.43/147.74 Instantiate: X08:=(cK x5):(a->Prop)
% 147.43/147.74 Found x4 as proof of (X07 Xx1)
% 147.43/147.74 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X07 Xx1)
% 147.43/147.74 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X07 Xx1))
% 147.43/147.74 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X07 Xx1)))
% 147.43/147.74 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X07 Xx1)
% 147.43/147.74 Found ((and_rect0 (X07 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X07 Xx1)
% 147.43/147.74 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X07 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X07 Xx1)
% 147.82/148.13 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X07 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X07 Xx1)
% 147.82/148.13 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 147.82/148.13 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 147.82/148.13 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 147.82/148.13 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 147.82/148.13 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X08) Xx0)))
% 147.82/148.13 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 147.82/148.13 Found ((and_rect0 ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 147.82/148.13 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 147.82/148.13 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 147.82/148.13 Found x6:(X08 Xx1)
% 147.82/148.13 Instantiate: X07:=X08:(a->Prop)
% 147.82/148.13 Found (fun (x6:(X08 Xx1))=> x6) as proof of (X07 Xx1)
% 147.82/148.13 Found (fun (Xx1:a) (x6:(X08 Xx1))=> x6) as proof of ((X08 Xx1)->(X07 Xx1))
% 147.82/148.13 Found (fun (Xx1:a) (x6:(X08 Xx1))=> x6) as proof of (forall (Xx:a), ((X08 Xx)->(X07 Xx)))
% 147.82/148.13 Found ((x390 (fun (Xx1:a) (x6:(X08 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X07) Xx0)
% 147.82/148.13 Found (((x39 X07) (fun (Xx1:a) (x6:(X08 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X07) Xx0)
% 147.82/148.13 Found ((((x3 x4) X07) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X07) Xx0)
% 147.82/148.13 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> ((((x3 x4) X07) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))))) as proof of ((cK X07) Xx0)
% 147.82/148.13 Found x4:(X07 Xx1)
% 147.82/148.13 Found x4 as proof of (X06 Xx1)
% 147.82/148.13 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X06 Xx1)
% 147.82/148.13 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X06 Xx1))
% 147.82/148.13 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X06 Xx1)))
% 147.82/148.13 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X06 Xx1)
% 147.82/148.13 Found ((and_rect0 (X06 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X06 Xx1)
% 147.82/148.13 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X06 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X06 Xx1)
% 149.31/149.58 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X06 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X06 Xx1)
% 149.31/149.58 Found x4:(X08 Xx1)
% 149.31/149.58 Found x4 as proof of (X07 Xx1)
% 149.31/149.58 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X07 Xx1)
% 149.31/149.58 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X07 Xx1))
% 149.31/149.58 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X07 Xx1)))
% 149.31/149.58 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X07 Xx1)
% 149.31/149.58 Found ((and_rect0 (X07 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X07 Xx1)
% 149.31/149.58 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X07 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X07 Xx1)
% 149.31/149.58 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X07 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X07 Xx1)
% 149.31/149.58 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 149.31/149.58 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 149.31/149.58 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 149.31/149.58 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 149.31/149.58 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X08) Xx0)))
% 149.31/149.58 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 149.31/149.58 Found ((and_rect0 ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 149.31/149.58 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 149.31/149.58 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X08) Xx0)
% 149.31/149.58 Found x4:(X08 Xx1)
% 149.31/149.58 Instantiate: X08:=(cK x5):(a->Prop)
% 149.31/149.58 Found x4 as proof of (X07 Xx1)
% 149.31/149.58 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X07 Xx1)
% 149.31/149.58 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X07 Xx1))
% 149.31/149.58 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X07 Xx1)))
% 149.31/149.58 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X07 Xx1)
% 149.31/149.58 Found ((and_rect0 (X07 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X07 Xx1)
% 149.31/149.58 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X07 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X07 Xx1)
% 149.74/150.03 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X07 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X07 Xx1)
% 149.74/150.03 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 149.74/150.03 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 149.74/150.03 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 149.74/150.03 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 149.74/150.03 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X08) Xx0)))
% 149.74/150.03 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 149.74/150.03 Found ((and_rect0 ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 149.74/150.03 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 149.74/150.03 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 149.74/150.03 Found x6:(X08 Xx1)
% 149.74/150.03 Instantiate: X07:=X08:(a->Prop)
% 149.74/150.03 Found (fun (x6:(X08 Xx1))=> x6) as proof of (X07 Xx1)
% 149.74/150.03 Found (fun (Xx1:a) (x6:(X08 Xx1))=> x6) as proof of ((X08 Xx1)->(X07 Xx1))
% 149.74/150.03 Found (fun (Xx1:a) (x6:(X08 Xx1))=> x6) as proof of (forall (Xx:a), ((X08 Xx)->(X07 Xx)))
% 149.74/150.03 Found ((x390 (fun (Xx1:a) (x6:(X08 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X07) Xx0)
% 149.74/150.03 Found (((x39 X07) (fun (Xx1:a) (x6:(X08 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X07) Xx0)
% 149.74/150.03 Found ((((x3 x4) X07) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X07) Xx0)
% 149.74/150.03 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> ((((x3 x4) X07) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))))) as proof of ((cK X07) Xx0)
% 149.74/150.03 Found x4:(X08 Xx1)
% 149.74/150.03 Found x4 as proof of (X07 Xx1)
% 149.74/150.03 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X07 Xx1)
% 149.74/150.03 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X07 Xx1))
% 149.74/150.03 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X07 Xx1)))
% 149.74/150.03 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X07 Xx1)
% 149.74/150.03 Found ((and_rect0 (X07 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X07 Xx1)
% 149.74/150.03 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X07 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X07 Xx1)
% 151.39/151.70 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X07 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X07 Xx1)
% 151.39/151.70 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 151.39/151.70 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 151.39/151.70 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 151.39/151.70 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 151.39/151.70 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X08) Xx0)))
% 151.39/151.70 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 151.39/151.70 Found ((and_rect0 ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 151.39/151.70 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 151.39/151.70 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X08) Xx0)
% 151.39/151.70 Found x4:(X08 Xx1)
% 151.39/151.70 Instantiate: X08:=(cK x5):(a->Prop)
% 151.39/151.70 Found x4 as proof of (X07 Xx1)
% 151.39/151.70 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X07 Xx1)
% 151.39/151.70 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X07 Xx1))
% 151.39/151.70 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X07 Xx1)))
% 151.39/151.70 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X07 Xx1)
% 151.39/151.70 Found ((and_rect0 (X07 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X07 Xx1)
% 151.39/151.70 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X07 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X07 Xx1)
% 151.39/151.70 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X07 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X07 Xx1)
% 151.39/151.70 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 151.39/151.70 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 151.39/151.70 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 151.39/151.70 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 151.39/151.70 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X08) Xx0)))
% 151.39/151.70 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 151.39/151.70 Found ((and_rect0 ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 151.39/151.70 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 151.39/151.70 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 151.89/152.15 Found x6:(X08 Xx1)
% 151.89/152.15 Instantiate: X07:=X08:(a->Prop)
% 151.89/152.15 Found (fun (x6:(X08 Xx1))=> x6) as proof of (X07 Xx1)
% 151.89/152.15 Found (fun (Xx1:a) (x6:(X08 Xx1))=> x6) as proof of ((X08 Xx1)->(X07 Xx1))
% 151.89/152.15 Found (fun (Xx1:a) (x6:(X08 Xx1))=> x6) as proof of (forall (Xx:a), ((X08 Xx)->(X07 Xx)))
% 151.89/152.15 Found ((x390 (fun (Xx1:a) (x6:(X08 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X07) Xx0)
% 151.89/152.15 Found (((x39 X07) (fun (Xx1:a) (x6:(X08 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X07) Xx0)
% 151.89/152.15 Found ((((x3 x4) X07) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X07) Xx0)
% 151.89/152.15 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> ((((x3 x4) X07) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))))) as proof of ((cK X07) Xx0)
% 151.89/152.15 Found x4:(X08 Xx1)
% 151.89/152.15 Found x4 as proof of (X07 Xx1)
% 151.89/152.15 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X07 Xx1)
% 151.89/152.15 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X07 Xx1))
% 151.89/152.15 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X07 Xx1)))
% 151.89/152.15 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X07 Xx1)
% 151.89/152.15 Found ((and_rect0 (X07 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X07 Xx1)
% 151.89/152.15 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X07 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X07 Xx1)
% 151.89/152.15 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X07 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X07 Xx1)
% 151.89/152.15 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 151.89/152.15 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 151.89/152.15 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 151.89/152.15 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 151.89/152.15 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X08) Xx0)))
% 151.89/152.15 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 151.89/152.15 Found ((and_rect0 ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 151.89/152.15 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 153.90/154.17 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X08) Xx0)
% 153.90/154.17 Found x4:(X08 Xx1)
% 153.90/154.17 Instantiate: X08:=(cK x5):(a->Prop)
% 153.90/154.17 Found x4 as proof of (X07 Xx1)
% 153.90/154.17 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X07 Xx1)
% 153.90/154.17 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X07 Xx1))
% 153.90/154.17 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X07 Xx1)))
% 153.90/154.17 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X07 Xx1)
% 153.90/154.17 Found ((and_rect0 (X07 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X07 Xx1)
% 153.90/154.17 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X07 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X07 Xx1)
% 153.90/154.17 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X07 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X07 Xx1)
% 153.90/154.17 Found x4:(X09 Xx1)
% 153.90/154.17 Found x4 as proof of (X08 Xx1)
% 153.90/154.17 Found (fun (x4:(X09 Xx1))=> x4) as proof of (X08 Xx1)
% 153.90/154.17 Found (fun (Xx1:a) (x4:(X09 Xx1))=> x4) as proof of ((X09 Xx1)->(X08 Xx1))
% 153.90/154.17 Found (fun (Xx1:a) (x4:(X09 Xx1))=> x4) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 153.90/154.17 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 153.90/154.17 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 153.90/154.17 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 153.90/154.17 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 153.90/154.17 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X08) Xx0)))
% 153.90/154.17 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 153.90/154.17 Found ((and_rect0 ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 153.90/154.17 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 153.90/154.17 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 153.90/154.17 Found x6:(X08 Xx1)
% 153.90/154.17 Instantiate: X07:=X08:(a->Prop)
% 153.90/154.17 Found (fun (x6:(X08 Xx1))=> x6) as proof of (X07 Xx1)
% 153.90/154.17 Found (fun (Xx1:a) (x6:(X08 Xx1))=> x6) as proof of ((X08 Xx1)->(X07 Xx1))
% 153.90/154.17 Found (fun (Xx1:a) (x6:(X08 Xx1))=> x6) as proof of (forall (Xx:a), ((X08 Xx)->(X07 Xx)))
% 153.90/154.17 Found ((x390 (fun (Xx1:a) (x6:(X08 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X07) Xx0)
% 153.90/154.17 Found (((x39 X07) (fun (Xx1:a) (x6:(X08 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X07) Xx0)
% 157.81/158.16 Found ((((x3 x4) X07) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X07) Xx0)
% 157.81/158.16 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> ((((x3 x4) X07) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))))) as proof of ((cK X07) Xx0)
% 157.81/158.16 Found x4:(X08 Xx1)
% 157.81/158.16 Found x4 as proof of (X07 Xx1)
% 157.81/158.16 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X07 Xx1)
% 157.81/158.16 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X07 Xx1))
% 157.81/158.16 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X07 Xx1)))
% 157.81/158.16 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X07 Xx1)
% 157.81/158.16 Found ((and_rect0 (X07 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X07 Xx1)
% 157.81/158.16 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X07 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X07 Xx1)
% 157.81/158.16 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X07 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X07 Xx1)
% 157.81/158.16 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 157.81/158.16 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 157.81/158.16 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 157.81/158.16 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 157.81/158.16 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X08) Xx0)))
% 157.81/158.16 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 157.81/158.16 Found ((and_rect0 ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 157.81/158.16 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 157.81/158.16 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X08) Xx0)
% 157.81/158.16 Found x6:(X09 Xx1)
% 157.81/158.16 Found x6 as proof of (X08 Xx1)
% 157.81/158.16 Found (fun (x6:(X09 Xx1))=> x6) as proof of (X08 Xx1)
% 157.81/158.16 Found (fun (Xx1:a) (x6:(X09 Xx1))=> x6) as proof of ((X09 Xx1)->(X08 Xx1))
% 157.81/158.16 Found (fun (Xx1:a) (x6:(X09 Xx1))=> x6) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 157.81/158.16 Found x6:(X09 Xx1)
% 157.81/158.16 Found x6 as proof of (X08 Xx1)
% 157.81/158.16 Found (fun (x6:(X09 Xx1))=> x6) as proof of (X08 Xx1)
% 157.81/158.16 Found (fun (Xx1:a) (x6:(X09 Xx1))=> x6) as proof of ((X09 Xx1)->(X08 Xx1))
% 157.81/158.16 Found (fun (Xx1:a) (x6:(X09 Xx1))=> x6) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 157.81/158.16 Found x6:(X09 Xx1)
% 157.81/158.16 Found x6 as proof of (X08 Xx1)
% 157.81/158.16 Found (fun (x6:(X09 Xx1))=> x6) as proof of (X08 Xx1)
% 157.81/158.16 Found (fun (Xx1:a) (x6:(X09 Xx1))=> x6) as proof of ((X09 Xx1)->(X08 Xx1))
% 157.81/158.16 Found (fun (Xx1:a) (x6:(X09 Xx1))=> x6) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 174.81/175.11 Found x6:(X09 Xx1)
% 174.81/175.11 Found x6 as proof of (X08 Xx1)
% 174.81/175.11 Found (fun (x6:(X09 Xx1))=> x6) as proof of (X08 Xx1)
% 174.81/175.11 Found (fun (Xx1:a) (x6:(X09 Xx1))=> x6) as proof of ((X09 Xx1)->(X08 Xx1))
% 174.81/175.11 Found (fun (Xx1:a) (x6:(X09 Xx1))=> x6) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 174.81/175.11 Found x6:(X09 Xx1)
% 174.81/175.11 Found x6 as proof of (X08 Xx1)
% 174.81/175.11 Found (fun (x6:(X09 Xx1))=> x6) as proof of (X08 Xx1)
% 174.81/175.11 Found (fun (Xx1:a) (x6:(X09 Xx1))=> x6) as proof of ((X09 Xx1)->(X08 Xx1))
% 174.81/175.11 Found (fun (Xx1:a) (x6:(X09 Xx1))=> x6) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 174.81/175.11 Found x6:(X09 Xx1)
% 174.81/175.11 Found x6 as proof of (X08 Xx1)
% 174.81/175.11 Found (fun (x6:(X09 Xx1))=> x6) as proof of (X08 Xx1)
% 174.81/175.11 Found (fun (Xx1:a) (x6:(X09 Xx1))=> x6) as proof of ((X09 Xx1)->(X08 Xx1))
% 174.81/175.11 Found (fun (Xx1:a) (x6:(X09 Xx1))=> x6) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 174.81/175.11 Found x6:(X09 Xx1)
% 174.81/175.11 Found x6 as proof of (X08 Xx1)
% 174.81/175.11 Found (fun (x6:(X09 Xx1))=> x6) as proof of (X08 Xx1)
% 174.81/175.11 Found (fun (Xx1:a) (x6:(X09 Xx1))=> x6) as proof of ((X09 Xx1)->(X08 Xx1))
% 174.81/175.11 Found (fun (Xx1:a) (x6:(X09 Xx1))=> x6) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 174.81/175.11 Found x6:(X09 Xx1)
% 174.81/175.11 Found x6 as proof of (X08 Xx1)
% 174.81/175.11 Found (fun (x6:(X09 Xx1))=> x6) as proof of (X08 Xx1)
% 174.81/175.11 Found (fun (Xx1:a) (x6:(X09 Xx1))=> x6) as proof of ((X09 Xx1)->(X08 Xx1))
% 174.81/175.11 Found (fun (Xx1:a) (x6:(X09 Xx1))=> x6) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 174.81/175.11 Found x6:(X09 Xx1)
% 174.81/175.11 Found x6 as proof of (X08 Xx1)
% 174.81/175.11 Found (fun (x6:(X09 Xx1))=> x6) as proof of (X08 Xx1)
% 174.81/175.11 Found (fun (Xx1:a) (x6:(X09 Xx1))=> x6) as proof of ((X09 Xx1)->(X08 Xx1))
% 174.81/175.11 Found (fun (Xx1:a) (x6:(X09 Xx1))=> x6) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 174.81/175.11 Found x6:(X09 Xx1)
% 174.81/175.11 Found x6 as proof of (X08 Xx1)
% 174.81/175.11 Found (fun (x6:(X09 Xx1))=> x6) as proof of (X08 Xx1)
% 174.81/175.11 Found (fun (Xx1:a) (x6:(X09 Xx1))=> x6) as proof of ((X09 Xx1)->(X08 Xx1))
% 174.81/175.11 Found (fun (Xx1:a) (x6:(X09 Xx1))=> x6) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 174.81/175.11 Found x8:(X09 Xx1)
% 174.81/175.11 Found x8 as proof of (X08 Xx1)
% 174.81/175.11 Found (fun (x8:(X09 Xx1))=> x8) as proof of (X08 Xx1)
% 174.81/175.11 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of ((X09 Xx1)->(X08 Xx1))
% 174.81/175.11 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 174.81/175.11 Found x600:=(x60 x7):((cK x4) Xx0)
% 174.81/175.11 Found (x60 x7) as proof of ((cK X09) Xx0)
% 174.81/175.11 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 174.81/175.11 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 174.81/175.11 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 174.81/175.11 Found x6:(X09 Xx1)
% 174.81/175.11 Found x6 as proof of (X08 Xx1)
% 174.81/175.11 Found (fun (x6:(X09 Xx1))=> x6) as proof of (X08 Xx1)
% 174.81/175.11 Found (fun (Xx1:a) (x6:(X09 Xx1))=> x6) as proof of ((X09 Xx1)->(X08 Xx1))
% 174.81/175.11 Found (fun (Xx1:a) (x6:(X09 Xx1))=> x6) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 174.81/175.11 Found x8:(X09 Xx1)
% 174.81/175.11 Found x8 as proof of (X08 Xx1)
% 174.81/175.11 Found (fun (x8:(X09 Xx1))=> x8) as proof of (X08 Xx1)
% 174.81/175.11 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of ((X09 Xx1)->(X08 Xx1))
% 174.81/175.11 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 174.81/175.11 Found x600:=(x60 x7):((cK x4) Xx0)
% 174.81/175.11 Found (x60 x7) as proof of ((cK X09) Xx0)
% 174.81/175.11 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 174.81/175.11 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 174.81/175.11 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 174.81/175.11 Found x8:(X09 Xx1)
% 174.81/175.11 Found x8 as proof of (X08 Xx1)
% 174.81/175.11 Found (fun (x8:(X09 Xx1))=> x8) as proof of (X08 Xx1)
% 174.81/175.11 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of ((X09 Xx1)->(X08 Xx1))
% 174.81/175.11 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 174.81/175.11 Found x600:=(x60 x7):((cK x4) Xx0)
% 174.81/175.11 Found (x60 x7) as proof of ((cK X09) Xx0)
% 174.81/175.11 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 174.81/175.11 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 174.81/175.11 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 174.81/175.11 Found x8:(X09 Xx1)
% 174.81/175.11 Found x8 as proof of (X08 Xx1)
% 174.81/175.11 Found (fun (x8:(X09 Xx1))=> x8) as proof of (X08 Xx1)
% 174.81/175.11 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of ((X09 Xx1)->(X08 Xx1))
% 174.81/175.11 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 174.81/175.11 Found x600:=(x60 x7):((cK x3) Xx0)
% 174.81/175.11 Found (x60 x7) as proof of ((cK X09) Xx0)
% 174.81/175.11 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 174.81/175.11 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 178.02/178.31 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 178.02/178.31 Found x8:(X09 Xx1)
% 178.02/178.31 Found x8 as proof of (X08 Xx1)
% 178.02/178.31 Found (fun (x8:(X09 Xx1))=> x8) as proof of (X08 Xx1)
% 178.02/178.31 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of ((X09 Xx1)->(X08 Xx1))
% 178.02/178.31 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 178.02/178.31 Found x600:=(x60 x7):((cK x4) Xx0)
% 178.02/178.31 Found (x60 x7) as proof of ((cK X09) Xx0)
% 178.02/178.31 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 178.02/178.31 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 178.02/178.31 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 178.02/178.31 Found x8:(X09 Xx1)
% 178.02/178.31 Found x8 as proof of (X08 Xx1)
% 178.02/178.31 Found (fun (x8:(X09 Xx1))=> x8) as proof of (X08 Xx1)
% 178.02/178.31 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of ((X09 Xx1)->(X08 Xx1))
% 178.02/178.31 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 178.02/178.31 Found x600:=(x60 x7):((cK x4) Xx0)
% 178.02/178.31 Found (x60 x7) as proof of ((cK X09) Xx0)
% 178.02/178.31 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 178.02/178.31 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 178.02/178.31 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 178.02/178.31 Found x8:(X09 Xx1)
% 178.02/178.31 Found x8 as proof of (X08 Xx1)
% 178.02/178.31 Found (fun (x8:(X09 Xx1))=> x8) as proof of (X08 Xx1)
% 178.02/178.31 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of ((X09 Xx1)->(X08 Xx1))
% 178.02/178.31 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 178.02/178.31 Found x600:=(x60 x7):((cK x4) Xx0)
% 178.02/178.31 Found (x60 x7) as proof of ((cK X09) Xx0)
% 178.02/178.31 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 178.02/178.31 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 178.02/178.31 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 178.02/178.31 Found x8:(X09 Xx1)
% 178.02/178.31 Found x8 as proof of (X08 Xx1)
% 178.02/178.31 Found (fun (x8:(X09 Xx1))=> x8) as proof of (X08 Xx1)
% 178.02/178.31 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of ((X09 Xx1)->(X08 Xx1))
% 178.02/178.31 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 178.02/178.31 Found x600:=(x60 x7):((cK x4) Xx0)
% 178.02/178.31 Found (x60 x7) as proof of ((cK X09) Xx0)
% 178.02/178.31 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 178.02/178.31 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 178.02/178.31 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 178.02/178.31 Found x8:(X09 Xx1)
% 178.02/178.31 Found x8 as proof of (X08 Xx1)
% 178.02/178.31 Found (fun (x8:(X09 Xx1))=> x8) as proof of (X08 Xx1)
% 178.02/178.31 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of ((X09 Xx1)->(X08 Xx1))
% 178.02/178.31 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 178.02/178.31 Found x600:=(x60 x7):((cK x3) Xx0)
% 178.02/178.31 Found (x60 x7) as proof of ((cK X09) Xx0)
% 178.02/178.31 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 178.02/178.31 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 178.02/178.31 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 178.02/178.31 Found x8:(X09 Xx1)
% 178.02/178.31 Found x8 as proof of (X08 Xx1)
% 178.02/178.31 Found (fun (x8:(X09 Xx1))=> x8) as proof of (X08 Xx1)
% 178.02/178.31 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of ((X09 Xx1)->(X08 Xx1))
% 178.02/178.31 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 178.02/178.31 Found x600:=(x60 x7):((cK x4) Xx0)
% 178.02/178.31 Found (x60 x7) as proof of ((cK X09) Xx0)
% 178.02/178.31 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 178.02/178.31 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 178.02/178.31 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 178.02/178.31 Found x8:(X09 Xx1)
% 178.02/178.31 Found x8 as proof of (X08 Xx1)
% 178.02/178.31 Found (fun (x8:(X09 Xx1))=> x8) as proof of (X08 Xx1)
% 178.02/178.31 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of ((X09 Xx1)->(X08 Xx1))
% 178.02/178.31 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 178.02/178.31 Found x500:=(x50 x6):((cK x3) Xx0)
% 178.02/178.31 Found (x50 x6) as proof of ((cK X09) Xx0)
% 178.02/178.31 Found ((x5 Xx0) x6) as proof of ((cK X09) Xx0)
% 178.02/178.31 Found ((x5 Xx0) x6) as proof of ((cK X09) Xx0)
% 178.02/178.31 Found ((x5 Xx0) x6) as proof of ((cK X09) Xx0)
% 178.02/178.31 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 178.02/178.31 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 178.02/178.31 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 178.02/178.31 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 178.02/178.31 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X09) Xx0)))
% 178.02/178.31 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 178.02/178.31 Found ((and_rect0 ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 178.42/178.74 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 178.42/178.74 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 178.42/178.74 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 178.42/178.74 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 178.42/178.74 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 178.42/178.74 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 178.42/178.74 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X09) Xx0)))
% 178.42/178.74 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 178.42/178.74 Found ((and_rect0 ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 178.42/178.74 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 178.42/178.74 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 178.42/178.74 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 178.42/178.74 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 178.42/178.74 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 178.42/178.74 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 178.42/178.74 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X09) Xx0)))
% 178.42/178.74 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 178.42/178.74 Found ((and_rect0 ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 178.42/178.74 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 178.42/178.74 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 178.42/178.74 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 178.42/178.74 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 178.42/178.74 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 178.42/178.74 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 178.42/178.74 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X09) Xx0)))
% 178.42/178.74 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 178.42/178.74 Found ((and_rect0 ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 178.42/178.74 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 178.42/178.74 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 178.61/178.90 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 178.61/178.90 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 178.61/178.90 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 178.61/178.90 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 178.61/178.90 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X09) Xx0)))
% 178.61/178.90 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 178.61/178.90 Found ((and_rect0 ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 178.61/178.90 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 178.61/178.90 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 178.61/178.90 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 178.61/178.90 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 178.61/178.90 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 178.61/178.90 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 178.61/178.90 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X09) Xx0)))
% 178.61/178.90 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 178.61/178.90 Found ((and_rect0 ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 178.61/178.90 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 178.61/178.90 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 178.61/178.90 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 178.61/178.90 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 178.61/178.90 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 178.61/178.90 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 178.61/178.90 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X09) Xx0)))
% 178.61/178.90 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 178.61/178.90 Found ((and_rect0 ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 178.61/178.90 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 178.61/178.90 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 178.61/178.90 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 178.61/178.90 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 178.61/178.90 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 178.61/178.90 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 179.11/179.40 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X09) Xx0)))
% 179.11/179.40 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 179.11/179.40 Found ((and_rect0 ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 179.11/179.40 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 179.11/179.40 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 179.11/179.40 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 179.11/179.40 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 179.11/179.40 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 179.11/179.40 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 179.11/179.40 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X09) Xx0)))
% 179.11/179.40 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 179.11/179.40 Found ((and_rect0 ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 179.11/179.40 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 179.11/179.40 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 179.11/179.40 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 179.11/179.40 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 179.11/179.40 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 179.11/179.40 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 179.11/179.40 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X09) Xx0)))
% 179.11/179.40 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 179.11/179.40 Found ((and_rect0 ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 179.11/179.40 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 179.11/179.40 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 179.11/179.40 Found x8:(X09 Xx1)
% 179.11/179.40 Found x8 as proof of (X08 Xx1)
% 179.11/179.40 Found (fun (x8:(X09 Xx1))=> x8) as proof of (X08 Xx1)
% 179.11/179.40 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of ((X09 Xx1)->(X08 Xx1))
% 179.11/179.40 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 179.11/179.40 Found x600:=(x60 x7):((cK x4) Xx0)
% 179.11/179.40 Found (x60 x7) as proof of ((cK X09) Xx0)
% 179.11/179.40 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 179.11/179.40 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 179.11/179.40 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 179.11/179.40 Found x8:(X09 Xx1)
% 179.11/179.40 Found x8 as proof of (X08 Xx1)
% 179.11/179.40 Found (fun (x8:(X09 Xx1))=> x8) as proof of (X08 Xx1)
% 179.11/179.40 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of ((X09 Xx1)->(X08 Xx1))
% 179.11/179.40 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 182.47/182.78 Found x600:=(x60 x7):((cK x4) Xx0)
% 182.47/182.78 Found (x60 x7) as proof of ((cK X09) Xx0)
% 182.47/182.78 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 182.47/182.78 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 182.47/182.78 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 182.47/182.78 Found x8:(X09 Xx1)
% 182.47/182.78 Found x8 as proof of (X08 Xx1)
% 182.47/182.78 Found (fun (x8:(X09 Xx1))=> x8) as proof of (X08 Xx1)
% 182.47/182.78 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of ((X09 Xx1)->(X08 Xx1))
% 182.47/182.78 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 182.47/182.78 Found x600:=(x60 x7):((cK x4) Xx0)
% 182.47/182.78 Found (x60 x7) as proof of ((cK X09) Xx0)
% 182.47/182.78 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 182.47/182.78 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 182.47/182.78 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 182.47/182.78 Found x8:(X09 Xx1)
% 182.47/182.78 Found x8 as proof of (X08 Xx1)
% 182.47/182.78 Found (fun (x8:(X09 Xx1))=> x8) as proof of (X08 Xx1)
% 182.47/182.78 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of ((X09 Xx1)->(X08 Xx1))
% 182.47/182.78 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 182.47/182.78 Found x600:=(x60 x7):((cK x4) Xx0)
% 182.47/182.78 Found (x60 x7) as proof of ((cK X09) Xx0)
% 182.47/182.78 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 182.47/182.78 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 182.47/182.78 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 182.47/182.78 Found x8:(X09 Xx1)
% 182.47/182.78 Found x8 as proof of (X08 Xx1)
% 182.47/182.78 Found (fun (x8:(X09 Xx1))=> x8) as proof of (X08 Xx1)
% 182.47/182.78 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of ((X09 Xx1)->(X08 Xx1))
% 182.47/182.78 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 182.47/182.78 Found x600:=(x60 x7):((cK x3) Xx0)
% 182.47/182.78 Found (x60 x7) as proof of ((cK X09) Xx0)
% 182.47/182.78 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 182.47/182.78 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 182.47/182.78 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 182.47/182.78 Found x8:(X09 Xx1)
% 182.47/182.78 Found x8 as proof of (X08 Xx1)
% 182.47/182.78 Found (fun (x8:(X09 Xx1))=> x8) as proof of (X08 Xx1)
% 182.47/182.78 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of ((X09 Xx1)->(X08 Xx1))
% 182.47/182.78 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 182.47/182.78 Found x600:=(x60 x7):((cK x4) Xx0)
% 182.47/182.78 Found (x60 x7) as proof of ((cK X09) Xx0)
% 182.47/182.78 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 182.47/182.78 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 182.47/182.78 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 182.47/182.78 Found x8:(X09 Xx1)
% 182.47/182.78 Found x8 as proof of (X08 Xx1)
% 182.47/182.78 Found (fun (x8:(X09 Xx1))=> x8) as proof of (X08 Xx1)
% 182.47/182.78 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of ((X09 Xx1)->(X08 Xx1))
% 182.47/182.78 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 182.47/182.78 Found x600:=(x60 x7):((cK x4) Xx0)
% 182.47/182.78 Found (x60 x7) as proof of ((cK X09) Xx0)
% 182.47/182.78 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 182.47/182.78 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 182.47/182.78 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 182.47/182.78 Found x8:(X09 Xx1)
% 182.47/182.78 Found x8 as proof of (X08 Xx1)
% 182.47/182.78 Found (fun (x8:(X09 Xx1))=> x8) as proof of (X08 Xx1)
% 182.47/182.78 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of ((X09 Xx1)->(X08 Xx1))
% 182.47/182.78 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 182.47/182.78 Found x600:=(x60 x7):((cK x4) Xx0)
% 182.47/182.78 Found (x60 x7) as proof of ((cK X09) Xx0)
% 182.47/182.78 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 182.47/182.78 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 182.47/182.78 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 182.47/182.78 Found x8:(X09 Xx1)
% 182.47/182.78 Found x8 as proof of (X08 Xx1)
% 182.47/182.78 Found (fun (x8:(X09 Xx1))=> x8) as proof of (X08 Xx1)
% 182.47/182.78 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of ((X09 Xx1)->(X08 Xx1))
% 182.47/182.78 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 182.47/182.78 Found x600:=(x60 x7):((cK x4) Xx0)
% 182.47/182.78 Found (x60 x7) as proof of ((cK X09) Xx0)
% 182.47/182.78 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 182.47/182.78 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 182.47/182.78 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 182.47/182.78 Found x8:(X09 Xx1)
% 182.47/182.78 Found x8 as proof of (X08 Xx1)
% 182.47/182.78 Found (fun (x8:(X09 Xx1))=> x8) as proof of (X08 Xx1)
% 182.47/182.78 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of ((X09 Xx1)->(X08 Xx1))
% 182.47/182.78 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 182.47/182.78 Found x600:=(x60 x7):((cK x4) Xx0)
% 182.47/182.78 Found (x60 x7) as proof of ((cK X09) Xx0)
% 182.47/182.78 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 183.78/184.15 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 183.78/184.15 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 183.78/184.15 Found x8:(X09 Xx1)
% 183.78/184.15 Found x8 as proof of (X08 Xx1)
% 183.78/184.15 Found (fun (x8:(X09 Xx1))=> x8) as proof of (X08 Xx1)
% 183.78/184.15 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of ((X09 Xx1)->(X08 Xx1))
% 183.78/184.15 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 183.78/184.15 Found x600:=(x60 x7):((cK x4) Xx0)
% 183.78/184.15 Found (x60 x7) as proof of ((cK X09) Xx0)
% 183.78/184.15 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 183.78/184.15 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 183.78/184.15 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 183.78/184.15 Found x8:(X09 Xx1)
% 183.78/184.15 Found x8 as proof of (X08 Xx1)
% 183.78/184.15 Found (fun (x8:(X09 Xx1))=> x8) as proof of (X08 Xx1)
% 183.78/184.15 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of ((X09 Xx1)->(X08 Xx1))
% 183.78/184.15 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 183.78/184.15 Found x600:=(x60 x7):((cK x3) Xx0)
% 183.78/184.15 Found (x60 x7) as proof of ((cK X09) Xx0)
% 183.78/184.15 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 183.78/184.15 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 183.78/184.15 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 183.78/184.15 Found x8:(X09 Xx1)
% 183.78/184.15 Found x8 as proof of (X08 Xx1)
% 183.78/184.15 Found (fun (x8:(X09 Xx1))=> x8) as proof of (X08 Xx1)
% 183.78/184.15 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of ((X09 Xx1)->(X08 Xx1))
% 183.78/184.15 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 183.78/184.15 Found x600:=(x60 x7):((cK x4) Xx0)
% 183.78/184.15 Found (x60 x7) as proof of ((cK X09) Xx0)
% 183.78/184.15 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 183.78/184.15 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 183.78/184.15 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 183.78/184.15 Found x8:(X09 Xx1)
% 183.78/184.15 Found x8 as proof of (X08 Xx1)
% 183.78/184.15 Found (fun (x8:(X09 Xx1))=> x8) as proof of (X08 Xx1)
% 183.78/184.15 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of ((X09 Xx1)->(X08 Xx1))
% 183.78/184.15 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 183.78/184.15 Found x600:=(x60 x7):((cK x4) Xx0)
% 183.78/184.15 Found (x60 x7) as proof of ((cK X09) Xx0)
% 183.78/184.15 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 183.78/184.15 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 183.78/184.15 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 183.78/184.15 Found x8:(X09 Xx1)
% 183.78/184.15 Found x8 as proof of (X08 Xx1)
% 183.78/184.15 Found (fun (x8:(X09 Xx1))=> x8) as proof of (X08 Xx1)
% 183.78/184.15 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of ((X09 Xx1)->(X08 Xx1))
% 183.78/184.15 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 183.78/184.15 Found x600:=(x60 x7):((cK x4) Xx0)
% 183.78/184.15 Found (x60 x7) as proof of ((cK X09) Xx0)
% 183.78/184.15 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 183.78/184.15 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 183.78/184.15 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 183.78/184.15 Found x60:=(x6 Xx0):((x3 Xx0)->((cK x3) Xx0))
% 183.78/184.15 Found (x6 Xx0) as proof of ((x3 Xx0)->((cK X09) Xx0))
% 183.78/184.15 Found (x6 Xx0) as proof of ((x3 Xx0)->((cK X09) Xx0))
% 183.78/184.15 Found (fun (x6:(forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1))))=> (x6 Xx0)) as proof of ((x3 Xx0)->((cK X09) Xx0))
% 183.78/184.15 Found (fun (x6:(forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1)))->((x3 Xx0)->((cK X09) Xx0)))
% 183.78/184.15 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 183.78/184.15 Found ((and_rect0 ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 183.78/184.15 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1)))->((x3 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1)))) (x3 Xx0)) P) x6) x4)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 183.78/184.15 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1)))->((x3 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1)))) (x3 Xx0)) P) x6) x4)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 183.78/184.15 Found x8:(X09 Xx1)
% 183.78/184.15 Found x8 as proof of (X08 Xx1)
% 183.78/184.15 Found (fun (x8:(X09 Xx1))=> x8) as proof of (X08 Xx1)
% 183.78/184.15 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of ((X09 Xx1)->(X08 Xx1))
% 183.78/184.15 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 183.78/184.15 Found x600:=(x60 x7):((cK x4) Xx0)
% 183.78/184.15 Found (x60 x7) as proof of ((cK X09) Xx0)
% 185.35/185.65 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 185.35/185.65 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 185.35/185.65 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 185.35/185.65 Found x8:(X09 Xx1)
% 185.35/185.65 Found x8 as proof of (X08 Xx1)
% 185.35/185.65 Found (fun (x8:(X09 Xx1))=> x8) as proof of (X08 Xx1)
% 185.35/185.65 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of ((X09 Xx1)->(X08 Xx1))
% 185.35/185.65 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 185.35/185.65 Found x600:=(x60 x7):((cK x4) Xx0)
% 185.35/185.65 Found (x60 x7) as proof of ((cK X09) Xx0)
% 185.35/185.65 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 185.35/185.65 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 185.35/185.65 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 185.35/185.65 Found x8:(X09 Xx1)
% 185.35/185.65 Found x8 as proof of (X08 Xx1)
% 185.35/185.65 Found (fun (x8:(X09 Xx1))=> x8) as proof of (X08 Xx1)
% 185.35/185.65 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of ((X09 Xx1)->(X08 Xx1))
% 185.35/185.65 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 185.35/185.65 Found x600:=(x60 x7):((cK x4) Xx0)
% 185.35/185.65 Found (x60 x7) as proof of ((cK X09) Xx0)
% 185.35/185.65 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 185.35/185.65 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 185.35/185.65 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 185.35/185.65 Found x8:(X09 Xx1)
% 185.35/185.65 Found x8 as proof of (X08 Xx1)
% 185.35/185.65 Found (fun (x8:(X09 Xx1))=> x8) as proof of (X08 Xx1)
% 185.35/185.65 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of ((X09 Xx1)->(X08 Xx1))
% 185.35/185.65 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 185.35/185.65 Found x600:=(x60 x7):((cK x4) Xx0)
% 185.35/185.65 Found (x60 x7) as proof of ((cK X09) Xx0)
% 185.35/185.65 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 185.35/185.65 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 185.35/185.65 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 185.35/185.65 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 185.35/185.65 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 185.35/185.65 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 185.35/185.65 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 185.35/185.65 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X09) Xx0)))
% 185.35/185.65 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 185.35/185.65 Found ((and_rect0 ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 185.35/185.65 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 185.35/185.65 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X09) Xx0)
% 185.35/185.65 Found x8:(X09 Xx1)
% 185.35/185.65 Found x8 as proof of (X08 Xx1)
% 185.35/185.65 Found (fun (x8:(X09 Xx1))=> x8) as proof of (X08 Xx1)
% 185.35/185.65 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of ((X09 Xx1)->(X08 Xx1))
% 185.35/185.65 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 185.35/185.65 Found x600:=(x60 x7):((cK x3) Xx0)
% 185.35/185.65 Found (x60 x7) as proof of ((cK X09) Xx0)
% 185.35/185.65 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 185.35/185.65 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 185.35/185.65 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 185.35/185.65 Found x8:(X09 Xx1)
% 185.35/185.65 Found x8 as proof of (X08 Xx1)
% 185.35/185.65 Found (fun (x8:(X09 Xx1))=> x8) as proof of (X08 Xx1)
% 185.35/185.65 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of ((X09 Xx1)->(X08 Xx1))
% 185.35/185.65 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 185.35/185.65 Found x600:=(x60 x7):((cK x4) Xx0)
% 185.35/185.65 Found (x60 x7) as proof of ((cK X09) Xx0)
% 185.35/185.65 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 185.35/185.65 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 185.35/185.65 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 185.35/185.65 Found x8:(X09 Xx1)
% 185.35/185.65 Found x8 as proof of (X08 Xx1)
% 185.35/185.65 Found (fun (x8:(X09 Xx1))=> x8) as proof of (X08 Xx1)
% 185.35/185.65 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of ((X09 Xx1)->(X08 Xx1))
% 185.35/185.65 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 186.18/186.50 Found x600:=(x60 x7):((cK x4) Xx0)
% 186.18/186.50 Found (x60 x7) as proof of ((cK X09) Xx0)
% 186.18/186.50 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 186.18/186.50 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 186.18/186.50 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 186.18/186.50 Found x8:(X09 Xx1)
% 186.18/186.50 Found x8 as proof of (X08 Xx1)
% 186.18/186.50 Found (fun (x8:(X09 Xx1))=> x8) as proof of (X08 Xx1)
% 186.18/186.50 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of ((X09 Xx1)->(X08 Xx1))
% 186.18/186.50 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 186.18/186.50 Found x600:=(x60 x7):((cK x4) Xx0)
% 186.18/186.50 Found (x60 x7) as proof of ((cK X09) Xx0)
% 186.18/186.50 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 186.18/186.50 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 186.18/186.50 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 186.18/186.50 Found x8:(X09 Xx1)
% 186.18/186.50 Found x8 as proof of (X08 Xx1)
% 186.18/186.50 Found (fun (x8:(X09 Xx1))=> x8) as proof of (X08 Xx1)
% 186.18/186.50 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of ((X09 Xx1)->(X08 Xx1))
% 186.18/186.50 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 186.18/186.50 Found x600:=(x60 x7):((cK x4) Xx0)
% 186.18/186.50 Found (x60 x7) as proof of ((cK X09) Xx0)
% 186.18/186.50 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 186.18/186.50 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 186.18/186.50 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 186.18/186.50 Found x8:(X09 Xx1)
% 186.18/186.50 Found x8 as proof of (X08 Xx1)
% 186.18/186.50 Found (fun (x8:(X09 Xx1))=> x8) as proof of (X08 Xx1)
% 186.18/186.50 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of ((X09 Xx1)->(X08 Xx1))
% 186.18/186.50 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 186.18/186.50 Found x600:=(x60 x7):((cK x4) Xx0)
% 186.18/186.50 Found (x60 x7) as proof of ((cK X09) Xx0)
% 186.18/186.50 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 186.18/186.50 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 186.18/186.50 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 186.18/186.50 Found x8:(X09 Xx1)
% 186.18/186.50 Found x8 as proof of (X08 Xx1)
% 186.18/186.50 Found (fun (x8:(X09 Xx1))=> x8) as proof of (X08 Xx1)
% 186.18/186.50 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of ((X09 Xx1)->(X08 Xx1))
% 186.18/186.50 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 186.18/186.50 Found x600:=(x60 x7):((cK x4) Xx0)
% 186.18/186.50 Found (x60 x7) as proof of ((cK X09) Xx0)
% 186.18/186.50 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 186.18/186.50 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 186.18/186.50 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 186.18/186.50 Found x8:(X09 Xx1)
% 186.18/186.50 Found x8 as proof of (X08 Xx1)
% 186.18/186.50 Found (fun (x8:(X09 Xx1))=> x8) as proof of (X08 Xx1)
% 186.18/186.50 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of ((X09 Xx1)->(X08 Xx1))
% 186.18/186.50 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 186.18/186.50 Found x600:=(x60 x7):((cK x4) Xx0)
% 186.18/186.50 Found (x60 x7) as proof of ((cK X09) Xx0)
% 186.18/186.50 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 186.18/186.50 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 186.18/186.50 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 186.18/186.50 Found x8:(X09 Xx1)
% 186.18/186.50 Found x8 as proof of (X08 Xx1)
% 186.18/186.50 Found (fun (x8:(X09 Xx1))=> x8) as proof of (X08 Xx1)
% 186.18/186.50 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of ((X09 Xx1)->(X08 Xx1))
% 186.18/186.50 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 186.18/186.50 Found x600:=(x60 x7):((cK x4) Xx0)
% 186.18/186.50 Found (x60 x7) as proof of ((cK X09) Xx0)
% 186.18/186.50 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 186.18/186.50 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 186.18/186.50 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 186.18/186.50 Found x8:(X09 Xx1)
% 186.18/186.50 Found x8 as proof of (X08 Xx1)
% 186.18/186.50 Found (fun (x8:(X09 Xx1))=> x8) as proof of (X08 Xx1)
% 186.18/186.50 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of ((X09 Xx1)->(X08 Xx1))
% 186.18/186.50 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 186.18/186.50 Found x600:=(x60 x7):((cK x3) Xx0)
% 186.18/186.50 Found (x60 x7) as proof of ((cK X09) Xx0)
% 186.18/186.50 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 186.18/186.50 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 186.18/186.50 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 186.18/186.50 Found x4:(X08 Xx1)
% 186.18/186.50 Instantiate: X08:=(cK x5):(a->Prop)
% 186.18/186.50 Found x4 as proof of (X07 Xx1)
% 186.18/186.50 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X07 Xx1)
% 186.18/186.50 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X07 Xx1))
% 186.18/186.50 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X07 Xx1)))
% 186.87/187.20 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X07 Xx1)
% 186.87/187.20 Found ((and_rect0 (X07 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X07 Xx1)
% 186.87/187.20 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X07 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X07 Xx1)
% 186.87/187.20 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X07 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X07 Xx1)
% 186.87/187.20 Found x8:(X09 Xx1)
% 186.87/187.20 Found x8 as proof of (X08 Xx1)
% 186.87/187.20 Found (fun (x8:(X09 Xx1))=> x8) as proof of (X08 Xx1)
% 186.87/187.20 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of ((X09 Xx1)->(X08 Xx1))
% 186.87/187.20 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 186.87/187.20 Found x600:=(x60 x7):((cK x4) Xx0)
% 186.87/187.20 Found (x60 x7) as proof of ((cK X09) Xx0)
% 186.87/187.20 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 186.87/187.20 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 186.87/187.20 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 186.87/187.20 Found x8:(X09 Xx1)
% 186.87/187.20 Found x8 as proof of (X08 Xx1)
% 186.87/187.20 Found (fun (x8:(X09 Xx1))=> x8) as proof of (X08 Xx1)
% 186.87/187.20 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of ((X09 Xx1)->(X08 Xx1))
% 186.87/187.20 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 186.87/187.20 Found x600:=(x60 x7):((cK x4) Xx0)
% 186.87/187.20 Found (x60 x7) as proof of ((cK X09) Xx0)
% 186.87/187.20 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 186.87/187.20 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 186.87/187.20 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 186.87/187.20 Found x8:(X09 Xx1)
% 186.87/187.20 Found x8 as proof of (X08 Xx1)
% 186.87/187.20 Found (fun (x8:(X09 Xx1))=> x8) as proof of (X08 Xx1)
% 186.87/187.20 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of ((X09 Xx1)->(X08 Xx1))
% 186.87/187.20 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 186.87/187.20 Found x600:=(x60 x7):((cK x4) Xx0)
% 186.87/187.20 Found (x60 x7) as proof of ((cK X09) Xx0)
% 186.87/187.20 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 186.87/187.20 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 186.87/187.20 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 186.87/187.20 Found x8:(X09 Xx1)
% 186.87/187.20 Found x8 as proof of (X08 Xx1)
% 186.87/187.20 Found (fun (x8:(X09 Xx1))=> x8) as proof of (X08 Xx1)
% 186.87/187.20 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of ((X09 Xx1)->(X08 Xx1))
% 186.87/187.20 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 186.87/187.20 Found x600:=(x60 x7):((cK x4) Xx0)
% 186.87/187.20 Found (x60 x7) as proof of ((cK X09) Xx0)
% 186.87/187.20 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 186.87/187.20 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 186.87/187.20 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 186.87/187.20 Found x8:(X09 Xx1)
% 186.87/187.20 Found x8 as proof of (X08 Xx1)
% 186.87/187.20 Found (fun (x8:(X09 Xx1))=> x8) as proof of (X08 Xx1)
% 186.87/187.20 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of ((X09 Xx1)->(X08 Xx1))
% 186.87/187.20 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 186.87/187.20 Found x600:=(x60 x7):((cK x4) Xx0)
% 186.87/187.20 Found (x60 x7) as proof of ((cK X09) Xx0)
% 186.87/187.20 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 186.87/187.20 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 186.87/187.20 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 186.87/187.20 Found x8:(X09 Xx1)
% 186.87/187.20 Found x8 as proof of (X08 Xx1)
% 186.87/187.20 Found (fun (x8:(X09 Xx1))=> x8) as proof of (X08 Xx1)
% 186.87/187.20 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of ((X09 Xx1)->(X08 Xx1))
% 186.87/187.20 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 186.87/187.20 Found x600:=(x60 x7):((cK x4) Xx0)
% 186.87/187.20 Found (x60 x7) as proof of ((cK X09) Xx0)
% 186.87/187.20 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 186.87/187.20 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 186.87/187.20 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 186.87/187.20 Found x8:(X09 Xx1)
% 186.87/187.20 Found x8 as proof of (X08 Xx1)
% 186.87/187.20 Found (fun (x8:(X09 Xx1))=> x8) as proof of (X08 Xx1)
% 186.87/187.20 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of ((X09 Xx1)->(X08 Xx1))
% 186.87/187.20 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 187.73/188.07 Found x600:=(x60 x7):((cK x4) Xx0)
% 187.73/188.07 Found (x60 x7) as proof of ((cK X09) Xx0)
% 187.73/188.07 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 187.73/188.07 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 187.73/188.07 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 187.73/188.07 Found x8:(X09 Xx1)
% 187.73/188.07 Found x8 as proof of (X08 Xx1)
% 187.73/188.07 Found (fun (x8:(X09 Xx1))=> x8) as proof of (X08 Xx1)
% 187.73/188.07 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of ((X09 Xx1)->(X08 Xx1))
% 187.73/188.07 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 187.73/188.07 Found x600:=(x60 x7):((cK x4) Xx0)
% 187.73/188.07 Found (x60 x7) as proof of ((cK X09) Xx0)
% 187.73/188.07 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 187.73/188.07 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 187.73/188.07 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 187.73/188.07 Found x8:(X09 Xx1)
% 187.73/188.07 Found x8 as proof of (X08 Xx1)
% 187.73/188.07 Found (fun (x8:(X09 Xx1))=> x8) as proof of (X08 Xx1)
% 187.73/188.07 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of ((X09 Xx1)->(X08 Xx1))
% 187.73/188.07 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 187.73/188.07 Found x600:=(x60 x7):((cK x4) Xx0)
% 187.73/188.07 Found (x60 x7) as proof of ((cK X09) Xx0)
% 187.73/188.07 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 187.73/188.07 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 187.73/188.07 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 187.73/188.07 Found x8:(X09 Xx1)
% 187.73/188.07 Found x8 as proof of (X08 Xx1)
% 187.73/188.07 Found (fun (x8:(X09 Xx1))=> x8) as proof of (X08 Xx1)
% 187.73/188.07 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of ((X09 Xx1)->(X08 Xx1))
% 187.73/188.07 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 187.73/188.07 Found x600:=(x60 x7):((cK x3) Xx0)
% 187.73/188.07 Found (x60 x7) as proof of ((cK X09) Xx0)
% 187.73/188.07 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 187.73/188.07 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 187.73/188.07 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 187.73/188.07 Found x8:(X09 Xx1)
% 187.73/188.07 Found x8 as proof of (X08 Xx1)
% 187.73/188.07 Found (fun (x8:(X09 Xx1))=> x8) as proof of (X08 Xx1)
% 187.73/188.07 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of ((X09 Xx1)->(X08 Xx1))
% 187.73/188.07 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 187.73/188.07 Found x600:=(x60 x7):((cK x4) Xx0)
% 187.73/188.07 Found (x60 x7) as proof of ((cK X09) Xx0)
% 187.73/188.07 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 187.73/188.07 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 187.73/188.07 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 187.73/188.07 Found x8:(X09 Xx1)
% 187.73/188.07 Found x8 as proof of (X08 Xx1)
% 187.73/188.07 Found (fun (x8:(X09 Xx1))=> x8) as proof of (X08 Xx1)
% 187.73/188.07 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of ((X09 Xx1)->(X08 Xx1))
% 187.73/188.07 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 187.73/188.07 Found x600:=(x60 x7):((cK x4) Xx0)
% 187.73/188.07 Found (x60 x7) as proof of ((cK X09) Xx0)
% 187.73/188.07 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 187.73/188.07 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 187.73/188.07 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 187.73/188.07 Found x8:(X09 Xx1)
% 187.73/188.07 Found x8 as proof of (X08 Xx1)
% 187.73/188.07 Found (fun (x8:(X09 Xx1))=> x8) as proof of (X08 Xx1)
% 187.73/188.07 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of ((X09 Xx1)->(X08 Xx1))
% 187.73/188.07 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 187.73/188.07 Found x600:=(x60 x7):((cK x4) Xx0)
% 187.73/188.07 Found (x60 x7) as proof of ((cK X09) Xx0)
% 187.73/188.07 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 187.73/188.07 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 187.73/188.07 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 187.73/188.07 Found x8:(X09 Xx1)
% 187.73/188.07 Found x8 as proof of (X08 Xx1)
% 187.73/188.07 Found (fun (x8:(X09 Xx1))=> x8) as proof of (X08 Xx1)
% 187.73/188.07 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of ((X09 Xx1)->(X08 Xx1))
% 187.73/188.07 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 187.73/188.07 Found x600:=(x60 x7):((cK x4) Xx0)
% 187.73/188.07 Found (x60 x7) as proof of ((cK X09) Xx0)
% 187.73/188.07 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 187.73/188.07 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 187.73/188.07 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 187.73/188.07 Found x8:(X09 Xx1)
% 187.73/188.07 Found x8 as proof of (X08 Xx1)
% 187.73/188.07 Found (fun (x8:(X09 Xx1))=> x8) as proof of (X08 Xx1)
% 187.73/188.07 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of ((X09 Xx1)->(X08 Xx1))
% 187.73/188.07 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 187.73/188.07 Found x600:=(x60 x7):((cK x4) Xx0)
% 187.73/188.07 Found (x60 x7) as proof of ((cK X09) Xx0)
% 187.73/188.07 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 187.73/188.07 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 187.73/188.07 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 188.30/188.59 Found x8:(X09 Xx1)
% 188.30/188.59 Found x8 as proof of (X08 Xx1)
% 188.30/188.59 Found (fun (x8:(X09 Xx1))=> x8) as proof of (X08 Xx1)
% 188.30/188.59 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of ((X09 Xx1)->(X08 Xx1))
% 188.30/188.59 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 188.30/188.59 Found x600:=(x60 x7):((cK x4) Xx0)
% 188.30/188.59 Found (x60 x7) as proof of ((cK X09) Xx0)
% 188.30/188.59 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 188.30/188.59 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 188.30/188.59 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 188.30/188.59 Found x8:(X09 Xx1)
% 188.30/188.59 Found x8 as proof of (X08 Xx1)
% 188.30/188.59 Found (fun (x8:(X09 Xx1))=> x8) as proof of (X08 Xx1)
% 188.30/188.59 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of ((X09 Xx1)->(X08 Xx1))
% 188.30/188.59 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 188.30/188.59 Found x600:=(x60 x7):((cK x4) Xx0)
% 188.30/188.59 Found (x60 x7) as proof of ((cK X09) Xx0)
% 188.30/188.59 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 188.30/188.59 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 188.30/188.59 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 188.30/188.59 Found x8:(X09 Xx1)
% 188.30/188.59 Found x8 as proof of (X08 Xx1)
% 188.30/188.59 Found (fun (x8:(X09 Xx1))=> x8) as proof of (X08 Xx1)
% 188.30/188.59 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of ((X09 Xx1)->(X08 Xx1))
% 188.30/188.59 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 188.30/188.59 Found x600:=(x60 x7):((cK x4) Xx0)
% 188.30/188.59 Found (x60 x7) as proof of ((cK X09) Xx0)
% 188.30/188.59 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 188.30/188.59 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 188.30/188.59 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 188.30/188.59 Found x8:(X09 Xx1)
% 188.30/188.59 Found x8 as proof of (X08 Xx1)
% 188.30/188.59 Found (fun (x8:(X09 Xx1))=> x8) as proof of (X08 Xx1)
% 188.30/188.59 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of ((X09 Xx1)->(X08 Xx1))
% 188.30/188.59 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 188.30/188.59 Found x600:=(x60 x7):((cK x4) Xx0)
% 188.30/188.59 Found (x60 x7) as proof of ((cK X09) Xx0)
% 188.30/188.59 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 188.30/188.59 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 188.30/188.59 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 188.30/188.59 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 188.30/188.59 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 188.30/188.59 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 188.30/188.59 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 188.30/188.59 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X09) Xx0)))
% 188.30/188.59 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 188.30/188.59 Found ((and_rect0 ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 188.30/188.59 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 188.30/188.59 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 188.30/188.59 Found x6:(X09 Xx1)
% 188.30/188.59 Instantiate: X08:=X09:(a->Prop)
% 188.30/188.59 Found (fun (x6:(X09 Xx1))=> x6) as proof of (X08 Xx1)
% 188.30/188.59 Found (fun (Xx1:a) (x6:(X09 Xx1))=> x6) as proof of ((X09 Xx1)->(X08 Xx1))
% 188.30/188.59 Found (fun (Xx1:a) (x6:(X09 Xx1))=> x6) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 188.30/188.59 Found ((x3110 (fun (Xx1:a) (x6:(X09 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X08) Xx0)
% 188.30/188.59 Found (((x311 X08) (fun (Xx1:a) (x6:(X09 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X08) Xx0)
% 189.48/189.84 Found ((((x3 x4) X08) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X08) Xx0)
% 189.48/189.84 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> ((((x3 x4) X08) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))))) as proof of ((cK X08) Xx0)
% 189.48/189.84 Found x8:(X09 Xx1)
% 189.48/189.84 Found x8 as proof of (X08 Xx1)
% 189.48/189.84 Found (fun (x8:(X09 Xx1))=> x8) as proof of (X08 Xx1)
% 189.48/189.84 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of ((X09 Xx1)->(X08 Xx1))
% 189.48/189.84 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 189.48/189.84 Found x600:=(x60 x7):((cK x4) Xx0)
% 189.48/189.84 Found (x60 x7) as proof of ((cK X09) Xx0)
% 189.48/189.84 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 189.48/189.84 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 189.48/189.84 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 189.48/189.84 Found x8:(X09 Xx1)
% 189.48/189.84 Found x8 as proof of (X08 Xx1)
% 189.48/189.84 Found (fun (x8:(X09 Xx1))=> x8) as proof of (X08 Xx1)
% 189.48/189.84 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of ((X09 Xx1)->(X08 Xx1))
% 189.48/189.84 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 189.48/189.84 Found x600:=(x60 x7):((cK x3) Xx0)
% 189.48/189.84 Found (x60 x7) as proof of ((cK X09) Xx0)
% 189.48/189.84 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 189.48/189.84 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 189.48/189.84 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 189.48/189.84 Found x8:(X09 Xx1)
% 189.48/189.84 Found x8 as proof of (X08 Xx1)
% 189.48/189.84 Found (fun (x8:(X09 Xx1))=> x8) as proof of (X08 Xx1)
% 189.48/189.84 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of ((X09 Xx1)->(X08 Xx1))
% 189.48/189.84 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 189.48/189.84 Found x600:=(x60 x7):((cK x4) Xx0)
% 189.48/189.84 Found (x60 x7) as proof of ((cK X09) Xx0)
% 189.48/189.84 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 189.48/189.84 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 189.48/189.84 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 189.48/189.84 Found x8:(X09 Xx1)
% 189.48/189.84 Found x8 as proof of (X08 Xx1)
% 189.48/189.84 Found (fun (x8:(X09 Xx1))=> x8) as proof of (X08 Xx1)
% 189.48/189.84 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of ((X09 Xx1)->(X08 Xx1))
% 189.48/189.84 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 189.48/189.84 Found x600:=(x60 x7):((cK x3) Xx0)
% 189.48/189.84 Found (x60 x7) as proof of ((cK X09) Xx0)
% 189.48/189.84 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 189.48/189.84 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 189.48/189.84 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 189.48/189.84 Found x8:(X09 Xx1)
% 189.48/189.84 Found x8 as proof of (X08 Xx1)
% 189.48/189.84 Found (fun (x8:(X09 Xx1))=> x8) as proof of (X08 Xx1)
% 189.48/189.84 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of ((X09 Xx1)->(X08 Xx1))
% 189.48/189.84 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 189.48/189.84 Found x600:=(x60 x7):((cK x4) Xx0)
% 189.48/189.84 Found (x60 x7) as proof of ((cK X09) Xx0)
% 189.48/189.84 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 189.48/189.84 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 189.48/189.84 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 189.48/189.84 Found x8:(X09 Xx1)
% 189.48/189.84 Found x8 as proof of (X08 Xx1)
% 189.48/189.84 Found (fun (x8:(X09 Xx1))=> x8) as proof of (X08 Xx1)
% 189.48/189.84 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of ((X09 Xx1)->(X08 Xx1))
% 189.48/189.84 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 189.48/189.84 Found x600:=(x60 x7):((cK x3) Xx0)
% 189.48/189.84 Found (x60 x7) as proof of ((cK X09) Xx0)
% 189.48/189.84 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 189.48/189.84 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 189.48/189.84 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 189.48/189.84 Found x8:(X09 Xx1)
% 189.48/189.84 Found x8 as proof of (X08 Xx1)
% 189.48/189.84 Found (fun (x8:(X09 Xx1))=> x8) as proof of (X08 Xx1)
% 189.48/189.84 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of ((X09 Xx1)->(X08 Xx1))
% 189.48/189.84 Found (fun (Xx1:a) (x8:(X09 Xx1))=> x8) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 189.48/189.84 Found x600:=(x60 x7):((cK x4) Xx0)
% 189.48/189.84 Found (x60 x7) as proof of ((cK X09) Xx0)
% 189.48/189.84 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 189.48/189.84 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 190.10/190.44 Found ((x6 Xx0) x7) as proof of ((cK X09) Xx0)
% 190.10/190.44 Found x4:(X08 Xx1)
% 190.10/190.44 Found x4 as proof of (X07 Xx1)
% 190.10/190.44 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X07 Xx1)
% 190.10/190.44 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X07 Xx1))
% 190.10/190.44 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X07 Xx1)))
% 190.10/190.44 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X07 Xx1)
% 190.10/190.44 Found ((and_rect0 (X07 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X07 Xx1)
% 190.10/190.44 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X07 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X07 Xx1)
% 190.10/190.44 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X07 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X07 Xx1)
% 190.10/190.44 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 190.10/190.44 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 190.10/190.44 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 190.10/190.44 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 190.10/190.44 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X08) Xx0)))
% 190.10/190.44 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 190.10/190.44 Found ((and_rect0 ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 190.10/190.44 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 190.10/190.44 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 190.10/190.44 Found x6:(X08 Xx1)
% 190.10/190.44 Instantiate: X07:=X08:(a->Prop)
% 190.10/190.44 Found (fun (x6:(X08 Xx1))=> x6) as proof of (X07 Xx1)
% 190.10/190.44 Found (fun (Xx1:a) (x6:(X08 Xx1))=> x6) as proof of ((X08 Xx1)->(X07 Xx1))
% 190.10/190.44 Found (fun (Xx1:a) (x6:(X08 Xx1))=> x6) as proof of (forall (Xx:a), ((X08 Xx)->(X07 Xx)))
% 190.10/190.44 Found ((x390 (fun (Xx1:a) (x6:(X08 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X07) Xx0)
% 190.10/190.44 Found (((x39 X07) (fun (Xx1:a) (x6:(X08 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X07) Xx0)
% 190.10/190.44 Found ((((x3 x4) X07) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X07) Xx0)
% 190.10/190.44 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> ((((x3 x4) X07) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))))) as proof of ((cK X07) Xx0)
% 191.60/191.93 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 191.60/191.93 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 191.60/191.93 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 191.60/191.93 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 191.60/191.93 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X09) Xx0)))
% 191.60/191.93 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 191.60/191.93 Found ((and_rect0 ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 191.60/191.93 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 191.60/191.93 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X09) Xx0)
% 191.60/191.93 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 191.60/191.93 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 191.60/191.93 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 191.60/191.93 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 191.60/191.93 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X08) Xx0)))
% 191.60/191.93 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 191.60/191.93 Found ((and_rect0 ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 191.60/191.93 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 191.60/191.93 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X08) Xx0)
% 191.60/191.93 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 191.60/191.93 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 191.60/191.93 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 191.60/191.93 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 191.60/191.93 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X09) Xx0)))
% 191.60/191.93 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 191.60/191.93 Found ((and_rect0 ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 191.60/191.93 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 191.60/191.93 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 191.60/191.93 Found x6:(X09 Xx1)
% 191.60/191.93 Instantiate: X08:=X09:(a->Prop)
% 191.60/191.93 Found (fun (x6:(X09 Xx1))=> x6) as proof of (X08 Xx1)
% 191.60/191.93 Found (fun (Xx1:a) (x6:(X09 Xx1))=> x6) as proof of ((X09 Xx1)->(X08 Xx1))
% 192.30/192.63 Found (fun (Xx1:a) (x6:(X09 Xx1))=> x6) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 192.30/192.63 Found ((x3110 (fun (Xx1:a) (x6:(X09 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X08) Xx0)
% 192.30/192.63 Found (((x311 X08) (fun (Xx1:a) (x6:(X09 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X08) Xx0)
% 192.30/192.63 Found ((((x3 x4) X08) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X08) Xx0)
% 192.30/192.63 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> ((((x3 x4) X08) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))))) as proof of ((cK X08) Xx0)
% 192.30/192.63 Found x4:(X09 Xx1)
% 192.30/192.63 Instantiate: X09:=(cK x5):(a->Prop)
% 192.30/192.63 Found x4 as proof of (X08 Xx1)
% 192.30/192.63 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X08 Xx1)
% 192.30/192.63 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X08 Xx1))
% 192.30/192.63 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X08 Xx1)))
% 192.30/192.63 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X08 Xx1)
% 192.30/192.63 Found ((and_rect0 (X08 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X08 Xx1)
% 192.30/192.63 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X08 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X08 Xx1)
% 192.30/192.63 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X08 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X08 Xx1)
% 192.30/192.63 Found x4:(X09 Xx1)
% 192.30/192.63 Found x4 as proof of (X08 Xx1)
% 192.30/192.63 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X08 Xx1)
% 192.30/192.63 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X08 Xx1))
% 192.30/192.63 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X08 Xx1)))
% 192.30/192.63 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X08 Xx1)
% 192.30/192.63 Found ((and_rect0 (X08 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X08 Xx1)
% 192.30/192.63 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X08 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X08 Xx1)
% 192.30/192.63 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X08 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X08 Xx1)
% 194.03/194.37 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 194.03/194.37 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 194.03/194.37 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 194.03/194.37 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 194.03/194.37 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X09) Xx0)))
% 194.03/194.37 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 194.03/194.37 Found ((and_rect0 ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 194.03/194.37 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 194.03/194.37 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X09) Xx0)
% 194.03/194.37 Found x4:(X09 Xx1)
% 194.03/194.37 Instantiate: X09:=(cK x5):(a->Prop)
% 194.03/194.37 Found x4 as proof of (X08 Xx1)
% 194.03/194.37 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X08 Xx1)
% 194.03/194.37 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X08 Xx1))
% 194.03/194.37 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X08 Xx1)))
% 194.03/194.37 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X08 Xx1)
% 194.03/194.37 Found ((and_rect0 (X08 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X08 Xx1)
% 194.03/194.37 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X08 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X08 Xx1)
% 194.03/194.37 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X08 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X08 Xx1)
% 194.03/194.37 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 194.03/194.37 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 194.03/194.37 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 194.03/194.37 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 194.03/194.37 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X09) Xx0)))
% 194.03/194.37 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 194.03/194.37 Found ((and_rect0 ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 194.03/194.37 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 194.03/194.37 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 194.03/194.37 Found x6:(X09 Xx1)
% 194.03/194.37 Instantiate: X08:=X09:(a->Prop)
% 194.03/194.37 Found (fun (x6:(X09 Xx1))=> x6) as proof of (X08 Xx1)
% 194.03/194.37 Found (fun (Xx1:a) (x6:(X09 Xx1))=> x6) as proof of ((X09 Xx1)->(X08 Xx1))
% 194.03/194.37 Found (fun (Xx1:a) (x6:(X09 Xx1))=> x6) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 196.02/196.32 Found ((x3110 (fun (Xx1:a) (x6:(X09 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X08) Xx0)
% 196.02/196.32 Found (((x311 X08) (fun (Xx1:a) (x6:(X09 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X08) Xx0)
% 196.02/196.32 Found ((((x3 x4) X08) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X08) Xx0)
% 196.02/196.32 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> ((((x3 x4) X08) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))))) as proof of ((cK X08) Xx0)
% 196.02/196.32 Found x4:(X08 Xx1)
% 196.02/196.32 Instantiate: X08:=(cK x5):(a->Prop)
% 196.02/196.32 Found x4 as proof of (X07 Xx1)
% 196.02/196.32 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X07 Xx1)
% 196.02/196.32 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X07 Xx1))
% 196.02/196.32 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X07 Xx1)))
% 196.02/196.32 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X07 Xx1)
% 196.02/196.32 Found ((and_rect0 (X07 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X07 Xx1)
% 196.02/196.32 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X07 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X07 Xx1)
% 196.02/196.32 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X07 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X07 Xx1)
% 196.02/196.32 Found x4:(X09 Xx1)
% 196.02/196.32 Found x4 as proof of (X08 Xx1)
% 196.02/196.32 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X08 Xx1)
% 196.02/196.32 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X08 Xx1))
% 196.02/196.32 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X08 Xx1)))
% 196.02/196.32 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X08 Xx1)
% 196.02/196.32 Found ((and_rect0 (X08 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X08 Xx1)
% 196.02/196.32 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X08 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X08 Xx1)
% 196.02/196.32 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X08 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X08 Xx1)
% 196.02/196.32 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 196.25/196.58 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 196.25/196.58 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 196.25/196.58 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 196.25/196.58 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X09) Xx0)))
% 196.25/196.58 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 196.25/196.58 Found ((and_rect0 ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 196.25/196.58 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 196.25/196.58 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X09) Xx0)
% 196.25/196.58 Found x4:(X08 Xx1)
% 196.25/196.58 Found x4 as proof of (X07 Xx1)
% 196.25/196.58 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X07 Xx1)
% 196.25/196.58 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X07 Xx1))
% 196.25/196.58 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X07 Xx1)))
% 196.25/196.58 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X07 Xx1)
% 196.25/196.58 Found ((and_rect0 (X07 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X07 Xx1)
% 196.25/196.58 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X07 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X07 Xx1)
% 196.25/196.58 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X07 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X07 Xx1)
% 196.25/196.58 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 196.25/196.58 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 196.25/196.58 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 196.25/196.58 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 196.25/196.58 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X08) Xx0)))
% 196.25/196.58 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 196.25/196.58 Found ((and_rect0 ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 196.25/196.58 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 196.25/196.58 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 196.25/196.58 Found x6:(X08 Xx1)
% 196.25/196.58 Instantiate: X07:=X08:(a->Prop)
% 196.25/196.58 Found (fun (x6:(X08 Xx1))=> x6) as proof of (X07 Xx1)
% 196.25/196.58 Found (fun (Xx1:a) (x6:(X08 Xx1))=> x6) as proof of ((X08 Xx1)->(X07 Xx1))
% 196.25/196.58 Found (fun (Xx1:a) (x6:(X08 Xx1))=> x6) as proof of (forall (Xx:a), ((X08 Xx)->(X07 Xx)))
% 196.25/196.58 Found ((x390 (fun (Xx1:a) (x6:(X08 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X07) Xx0)
% 197.39/197.71 Found (((x39 X07) (fun (Xx1:a) (x6:(X08 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X07) Xx0)
% 197.39/197.71 Found ((((x3 x4) X07) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X07) Xx0)
% 197.39/197.71 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> ((((x3 x4) X07) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))))) as proof of ((cK X07) Xx0)
% 197.39/197.71 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 197.39/197.71 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 197.39/197.71 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 197.39/197.71 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X08) Xx0))
% 197.39/197.71 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X08) Xx0)))
% 197.39/197.71 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 197.39/197.71 Found ((and_rect0 ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 197.39/197.71 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X08) Xx0)
% 197.39/197.71 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X08) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X08) Xx0)
% 197.39/197.71 Found x4:(X09 Xx1)
% 197.39/197.71 Instantiate: X09:=(cK x5):(a->Prop)
% 197.39/197.71 Found x4 as proof of (X08 Xx1)
% 197.39/197.71 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X08 Xx1)
% 197.39/197.71 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X08 Xx1))
% 197.39/197.71 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X08 Xx1)))
% 197.39/197.71 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X08 Xx1)
% 197.39/197.71 Found ((and_rect0 (X08 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X08 Xx1)
% 197.39/197.71 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X08 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X08 Xx1)
% 197.39/197.71 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X08 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X08 Xx1)
% 197.39/197.71 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 197.39/197.71 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 197.39/197.71 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 198.04/198.41 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 198.04/198.41 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X09) Xx0)))
% 198.04/198.41 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 198.04/198.41 Found ((and_rect0 ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 198.04/198.41 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 198.04/198.41 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 198.04/198.41 Found x6:(X09 Xx1)
% 198.04/198.41 Instantiate: X08:=X09:(a->Prop)
% 198.04/198.41 Found (fun (x6:(X09 Xx1))=> x6) as proof of (X08 Xx1)
% 198.04/198.41 Found (fun (Xx1:a) (x6:(X09 Xx1))=> x6) as proof of ((X09 Xx1)->(X08 Xx1))
% 198.04/198.41 Found (fun (Xx1:a) (x6:(X09 Xx1))=> x6) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 198.04/198.41 Found ((x3110 (fun (Xx1:a) (x6:(X09 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X08) Xx0)
% 198.04/198.41 Found (((x311 X08) (fun (Xx1:a) (x6:(X09 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X08) Xx0)
% 198.04/198.41 Found ((((x3 x4) X08) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X08) Xx0)
% 198.04/198.41 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> ((((x3 x4) X08) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))))) as proof of ((cK X08) Xx0)
% 198.04/198.41 Found x4:(X09 Xx1)
% 198.04/198.41 Found x4 as proof of (X08 Xx1)
% 198.04/198.41 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X08 Xx1)
% 198.04/198.41 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X08 Xx1))
% 198.04/198.41 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X08 Xx1)))
% 198.04/198.41 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X08 Xx1)
% 198.04/198.41 Found ((and_rect0 (X08 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X08 Xx1)
% 198.04/198.41 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X08 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X08 Xx1)
% 198.04/198.41 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X08 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X08 Xx1)
% 198.04/198.41 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 199.67/199.99 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 199.67/199.99 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 199.67/199.99 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 199.67/199.99 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X09) Xx0)))
% 199.67/199.99 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 199.67/199.99 Found ((and_rect0 ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 199.67/199.99 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 199.67/199.99 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X09) Xx0)
% 199.67/199.99 Found x4:(X08 Xx1)
% 199.67/199.99 Instantiate: X08:=(cK x5):(a->Prop)
% 199.67/199.99 Found x4 as proof of (X07 Xx1)
% 199.67/199.99 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X07 Xx1)
% 199.67/199.99 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X07 Xx1))
% 199.67/199.99 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X07 Xx1)))
% 199.67/199.99 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X07 Xx1)
% 199.67/199.99 Found ((and_rect0 (X07 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X07 Xx1)
% 199.67/199.99 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X07 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X07 Xx1)
% 199.67/199.99 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X07 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X07 Xx1)
% 199.67/199.99 Found x4:(X09 Xx1)
% 199.67/199.99 Instantiate: X09:=(cK x5):(a->Prop)
% 199.67/199.99 Found x4 as proof of (X08 Xx1)
% 199.67/199.99 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X08 Xx1)
% 199.67/199.99 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X08 Xx1))
% 199.67/199.99 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X08 Xx1)))
% 199.67/199.99 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X08 Xx1)
% 199.67/199.99 Found ((and_rect0 (X08 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X08 Xx1)
% 199.67/199.99 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X08 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X08 Xx1)
% 199.67/199.99 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X08 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X08 Xx1)
% 199.67/199.99 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 199.67/199.99 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 199.67/199.99 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 199.67/199.99 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 199.91/200.25 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X09) Xx0)))
% 199.91/200.25 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 199.91/200.25 Found ((and_rect0 ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 199.91/200.25 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 199.91/200.25 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 199.91/200.25 Found x6:(X09 Xx1)
% 199.91/200.25 Instantiate: X08:=X09:(a->Prop)
% 199.91/200.25 Found (fun (x6:(X09 Xx1))=> x6) as proof of (X08 Xx1)
% 199.91/200.25 Found (fun (Xx1:a) (x6:(X09 Xx1))=> x6) as proof of ((X09 Xx1)->(X08 Xx1))
% 199.91/200.25 Found (fun (Xx1:a) (x6:(X09 Xx1))=> x6) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 199.91/200.25 Found ((x3110 (fun (Xx1:a) (x6:(X09 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X08) Xx0)
% 199.91/200.25 Found (((x311 X08) (fun (Xx1:a) (x6:(X09 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X08) Xx0)
% 199.91/200.25 Found ((((x3 x4) X08) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X08) Xx0)
% 199.91/200.25 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> ((((x3 x4) X08) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))))) as proof of ((cK X08) Xx0)
% 199.91/200.25 Found x4:(X09 Xx1)
% 199.91/200.25 Found x4 as proof of (X08 Xx1)
% 199.91/200.25 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X08 Xx1)
% 199.91/200.25 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X08 Xx1))
% 199.91/200.25 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X08 Xx1)))
% 199.91/200.25 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X08 Xx1)
% 199.91/200.25 Found ((and_rect0 (X08 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X08 Xx1)
% 199.91/200.25 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X08 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X08 Xx1)
% 199.91/200.25 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X08 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X08 Xx1)
% 199.91/200.25 Found x4:(X08 Xx1)
% 199.91/200.25 Found x4 as proof of (X07 Xx1)
% 199.91/200.25 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X07 Xx1)
% 199.91/200.25 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X07 Xx1))
% 201.60/201.90 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X07 Xx1)))
% 201.60/201.90 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X07 Xx1)
% 201.60/201.90 Found ((and_rect0 (X07 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X07 Xx1)
% 201.60/201.90 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X07 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X07 Xx1)
% 201.60/201.90 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X07 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X07 Xx1)
% 201.60/201.90 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 201.60/201.90 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 201.60/201.90 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 201.60/201.90 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 201.60/201.90 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X09) Xx0)))
% 201.60/201.90 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 201.60/201.90 Found ((and_rect0 ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 201.60/201.90 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 201.60/201.90 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X09) Xx0)
% 201.60/201.90 Found x4:(X09 Xx1)
% 201.60/201.90 Instantiate: X09:=(cK x5):(a->Prop)
% 201.60/201.90 Found x4 as proof of (X08 Xx1)
% 201.60/201.90 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X08 Xx1)
% 201.60/201.90 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X08 Xx1))
% 201.60/201.90 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X08 Xx1)))
% 201.60/201.90 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X08 Xx1)
% 201.60/201.90 Found ((and_rect0 (X08 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X08 Xx1)
% 201.60/201.90 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X08 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X08 Xx1)
% 201.60/201.90 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X08 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X08 Xx1)
% 201.60/201.90 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 201.60/201.90 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 201.60/201.90 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 201.60/201.90 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 201.60/201.90 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X09) Xx0)))
% 202.01/202.33 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 202.01/202.33 Found ((and_rect0 ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 202.01/202.33 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 202.01/202.33 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 202.01/202.33 Found x6:(X09 Xx1)
% 202.01/202.33 Instantiate: X08:=X09:(a->Prop)
% 202.01/202.33 Found (fun (x6:(X09 Xx1))=> x6) as proof of (X08 Xx1)
% 202.01/202.33 Found (fun (Xx1:a) (x6:(X09 Xx1))=> x6) as proof of ((X09 Xx1)->(X08 Xx1))
% 202.01/202.33 Found (fun (Xx1:a) (x6:(X09 Xx1))=> x6) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 202.01/202.33 Found ((x3110 (fun (Xx1:a) (x6:(X09 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X08) Xx0)
% 202.01/202.33 Found (((x311 X08) (fun (Xx1:a) (x6:(X09 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X08) Xx0)
% 202.01/202.33 Found ((((x3 x4) X08) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X08) Xx0)
% 202.01/202.33 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> ((((x3 x4) X08) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))))) as proof of ((cK X08) Xx0)
% 202.01/202.33 Found x4:(X09 Xx1)
% 202.01/202.33 Found x4 as proof of (X08 Xx1)
% 202.01/202.33 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X08 Xx1)
% 202.01/202.33 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X08 Xx1))
% 202.01/202.33 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X08 Xx1)))
% 202.01/202.33 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X08 Xx1)
% 202.01/202.33 Found ((and_rect0 (X08 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X08 Xx1)
% 202.01/202.33 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X08 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X08 Xx1)
% 202.01/202.33 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X08 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X08 Xx1)
% 202.01/202.33 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 202.01/202.33 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 202.01/202.33 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 202.01/202.33 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 203.50/203.84 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X09) Xx0)))
% 203.50/203.84 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 203.50/203.84 Found ((and_rect0 ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 203.50/203.84 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 203.50/203.84 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X09) Xx0)
% 203.50/203.84 Found x4:(X09 Xx1)
% 203.50/203.84 Instantiate: X09:=(cK x5):(a->Prop)
% 203.50/203.84 Found x4 as proof of (X08 Xx1)
% 203.50/203.84 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X08 Xx1)
% 203.50/203.84 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X08 Xx1))
% 203.50/203.84 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X08 Xx1)))
% 203.50/203.84 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X08 Xx1)
% 203.50/203.84 Found ((and_rect0 (X08 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X08 Xx1)
% 203.50/203.84 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X08 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X08 Xx1)
% 203.50/203.84 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X08 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X08 Xx1)
% 203.50/203.84 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 203.50/203.84 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 203.50/203.84 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 203.50/203.84 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 203.50/203.84 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X09) Xx0)))
% 203.50/203.84 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 203.50/203.84 Found ((and_rect0 ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 203.50/203.84 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 203.50/203.84 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 203.50/203.84 Found x6:(X09 Xx1)
% 203.50/203.84 Instantiate: X08:=X09:(a->Prop)
% 203.50/203.84 Found (fun (x6:(X09 Xx1))=> x6) as proof of (X08 Xx1)
% 203.50/203.84 Found (fun (Xx1:a) (x6:(X09 Xx1))=> x6) as proof of ((X09 Xx1)->(X08 Xx1))
% 203.50/203.84 Found (fun (Xx1:a) (x6:(X09 Xx1))=> x6) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 203.50/203.84 Found ((x3110 (fun (Xx1:a) (x6:(X09 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X08) Xx0)
% 207.89/208.24 Found (((x311 X08) (fun (Xx1:a) (x6:(X09 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X08) Xx0)
% 207.89/208.24 Found ((((x3 x4) X08) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X08) Xx0)
% 207.89/208.24 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> ((((x3 x4) X08) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))))) as proof of ((cK X08) Xx0)
% 207.89/208.24 Found x4:(X09 Xx1)
% 207.89/208.24 Found x4 as proof of (X08 Xx1)
% 207.89/208.24 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X08 Xx1)
% 207.89/208.24 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X08 Xx1))
% 207.89/208.24 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X08 Xx1)))
% 207.89/208.24 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X08 Xx1)
% 207.89/208.24 Found ((and_rect0 (X08 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X08 Xx1)
% 207.89/208.24 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X08 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X08 Xx1)
% 207.89/208.24 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X08 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X08 Xx1)
% 207.89/208.24 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 207.89/208.24 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 207.89/208.24 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 207.89/208.24 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 207.89/208.24 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X09) Xx0)))
% 207.89/208.24 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 207.89/208.24 Found ((and_rect0 ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 207.89/208.24 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 207.89/208.24 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X09) Xx0)
% 207.89/208.24 Found x4:(X010 Xx1)
% 207.89/208.24 Found x4 as proof of (X09 Xx1)
% 207.89/208.24 Found (fun (x4:(X010 Xx1))=> x4) as proof of (X09 Xx1)
% 207.89/208.24 Found (fun (Xx1:a) (x4:(X010 Xx1))=> x4) as proof of ((X010 Xx1)->(X09 Xx1))
% 207.89/208.24 Found (fun (Xx1:a) (x4:(X010 Xx1))=> x4) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 207.89/208.24 Found x6:(X010 Xx1)
% 207.89/208.24 Found x6 as proof of (X09 Xx1)
% 207.89/208.24 Found (fun (x6:(X010 Xx1))=> x6) as proof of (X09 Xx1)
% 221.70/222.03 Found (fun (Xx1:a) (x6:(X010 Xx1))=> x6) as proof of ((X010 Xx1)->(X09 Xx1))
% 221.70/222.03 Found (fun (Xx1:a) (x6:(X010 Xx1))=> x6) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 221.70/222.03 Found x6:(X010 Xx1)
% 221.70/222.03 Found x6 as proof of (X09 Xx1)
% 221.70/222.03 Found (fun (x6:(X010 Xx1))=> x6) as proof of (X09 Xx1)
% 221.70/222.03 Found (fun (Xx1:a) (x6:(X010 Xx1))=> x6) as proof of ((X010 Xx1)->(X09 Xx1))
% 221.70/222.03 Found (fun (Xx1:a) (x6:(X010 Xx1))=> x6) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 221.70/222.03 Found x6:(X010 Xx1)
% 221.70/222.03 Found x6 as proof of (X09 Xx1)
% 221.70/222.03 Found (fun (x6:(X010 Xx1))=> x6) as proof of (X09 Xx1)
% 221.70/222.03 Found (fun (Xx1:a) (x6:(X010 Xx1))=> x6) as proof of ((X010 Xx1)->(X09 Xx1))
% 221.70/222.03 Found (fun (Xx1:a) (x6:(X010 Xx1))=> x6) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 221.70/222.03 Found x6:(X010 Xx1)
% 221.70/222.03 Found x6 as proof of (X09 Xx1)
% 221.70/222.03 Found (fun (x6:(X010 Xx1))=> x6) as proof of (X09 Xx1)
% 221.70/222.03 Found (fun (Xx1:a) (x6:(X010 Xx1))=> x6) as proof of ((X010 Xx1)->(X09 Xx1))
% 221.70/222.03 Found (fun (Xx1:a) (x6:(X010 Xx1))=> x6) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 221.70/222.03 Found x6:(X010 Xx1)
% 221.70/222.03 Found x6 as proof of (X09 Xx1)
% 221.70/222.03 Found (fun (x6:(X010 Xx1))=> x6) as proof of (X09 Xx1)
% 221.70/222.03 Found (fun (Xx1:a) (x6:(X010 Xx1))=> x6) as proof of ((X010 Xx1)->(X09 Xx1))
% 221.70/222.03 Found (fun (Xx1:a) (x6:(X010 Xx1))=> x6) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 221.70/222.03 Found x6:(X010 Xx1)
% 221.70/222.03 Found x6 as proof of (X09 Xx1)
% 221.70/222.03 Found (fun (x6:(X010 Xx1))=> x6) as proof of (X09 Xx1)
% 221.70/222.03 Found (fun (Xx1:a) (x6:(X010 Xx1))=> x6) as proof of ((X010 Xx1)->(X09 Xx1))
% 221.70/222.03 Found (fun (Xx1:a) (x6:(X010 Xx1))=> x6) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 221.70/222.03 Found x4:(X09 Xx1)
% 221.70/222.03 Instantiate: X09:=(cK x5):(a->Prop)
% 221.70/222.03 Found x4 as proof of (X08 Xx1)
% 221.70/222.03 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X08 Xx1)
% 221.70/222.03 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X08 Xx1))
% 221.70/222.03 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X08 Xx1)))
% 221.70/222.03 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X08 Xx1)
% 221.70/222.03 Found ((and_rect0 (X08 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X08 Xx1)
% 221.70/222.03 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X08 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X08 Xx1)
% 221.70/222.03 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X08 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X08 Xx1)
% 221.70/222.03 Found x6:(X010 Xx1)
% 221.70/222.03 Found x6 as proof of (X09 Xx1)
% 221.70/222.03 Found (fun (x6:(X010 Xx1))=> x6) as proof of (X09 Xx1)
% 221.70/222.03 Found (fun (Xx1:a) (x6:(X010 Xx1))=> x6) as proof of ((X010 Xx1)->(X09 Xx1))
% 221.70/222.03 Found (fun (Xx1:a) (x6:(X010 Xx1))=> x6) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 221.70/222.03 Found x6:(X010 Xx1)
% 221.70/222.03 Found x6 as proof of (X09 Xx1)
% 221.70/222.03 Found (fun (x6:(X010 Xx1))=> x6) as proof of (X09 Xx1)
% 221.70/222.03 Found (fun (Xx1:a) (x6:(X010 Xx1))=> x6) as proof of ((X010 Xx1)->(X09 Xx1))
% 221.70/222.03 Found (fun (Xx1:a) (x6:(X010 Xx1))=> x6) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 221.70/222.03 Found x6:(X010 Xx1)
% 221.70/222.03 Found x6 as proof of (X09 Xx1)
% 221.70/222.03 Found (fun (x6:(X010 Xx1))=> x6) as proof of (X09 Xx1)
% 221.70/222.03 Found (fun (Xx1:a) (x6:(X010 Xx1))=> x6) as proof of ((X010 Xx1)->(X09 Xx1))
% 221.70/222.03 Found (fun (Xx1:a) (x6:(X010 Xx1))=> x6) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 221.70/222.03 Found x6:(X010 Xx1)
% 221.70/222.03 Found x6 as proof of (X09 Xx1)
% 221.70/222.03 Found (fun (x6:(X010 Xx1))=> x6) as proof of (X09 Xx1)
% 221.70/222.03 Found (fun (Xx1:a) (x6:(X010 Xx1))=> x6) as proof of ((X010 Xx1)->(X09 Xx1))
% 221.70/222.03 Found (fun (Xx1:a) (x6:(X010 Xx1))=> x6) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 221.70/222.03 Found x6:(X010 Xx1)
% 221.70/222.03 Found x6 as proof of (X09 Xx1)
% 221.70/222.03 Found (fun (x6:(X010 Xx1))=> x6) as proof of (X09 Xx1)
% 230.28/230.60 Found (fun (Xx1:a) (x6:(X010 Xx1))=> x6) as proof of ((X010 Xx1)->(X09 Xx1))
% 230.28/230.60 Found (fun (Xx1:a) (x6:(X010 Xx1))=> x6) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 230.28/230.60 Found x8:(X010 Xx1)
% 230.28/230.60 Found x8 as proof of (X09 Xx1)
% 230.28/230.60 Found (fun (x8:(X010 Xx1))=> x8) as proof of (X09 Xx1)
% 230.28/230.60 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of ((X010 Xx1)->(X09 Xx1))
% 230.28/230.60 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 230.28/230.60 Found x600:=(x60 x7):((cK x4) Xx0)
% 230.28/230.60 Found (x60 x7) as proof of ((cK X010) Xx0)
% 230.28/230.60 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 230.28/230.60 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 230.28/230.60 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 230.28/230.60 Found x6:(X010 Xx1)
% 230.28/230.60 Found x6 as proof of (X09 Xx1)
% 230.28/230.60 Found (fun (x6:(X010 Xx1))=> x6) as proof of (X09 Xx1)
% 230.28/230.60 Found (fun (Xx1:a) (x6:(X010 Xx1))=> x6) as proof of ((X010 Xx1)->(X09 Xx1))
% 230.28/230.60 Found (fun (Xx1:a) (x6:(X010 Xx1))=> x6) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 230.28/230.60 Found x8:(X010 Xx1)
% 230.28/230.60 Found x8 as proof of (X09 Xx1)
% 230.28/230.60 Found (fun (x8:(X010 Xx1))=> x8) as proof of (X09 Xx1)
% 230.28/230.60 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of ((X010 Xx1)->(X09 Xx1))
% 230.28/230.60 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 230.28/230.60 Found x600:=(x60 x7):((cK x4) Xx0)
% 230.28/230.60 Found (x60 x7) as proof of ((cK X010) Xx0)
% 230.28/230.60 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 230.28/230.60 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 230.28/230.60 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 230.28/230.60 Found x8:(X010 Xx1)
% 230.28/230.60 Found x8 as proof of (X09 Xx1)
% 230.28/230.60 Found (fun (x8:(X010 Xx1))=> x8) as proof of (X09 Xx1)
% 230.28/230.60 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of ((X010 Xx1)->(X09 Xx1))
% 230.28/230.60 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 230.28/230.60 Found x600:=(x60 x7):((cK x4) Xx0)
% 230.28/230.60 Found (x60 x7) as proof of ((cK X010) Xx0)
% 230.28/230.60 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 230.28/230.60 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 230.28/230.60 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 230.28/230.60 Found x8:(X010 Xx1)
% 230.28/230.60 Found x8 as proof of (X09 Xx1)
% 230.28/230.60 Found (fun (x8:(X010 Xx1))=> x8) as proof of (X09 Xx1)
% 230.28/230.60 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of ((X010 Xx1)->(X09 Xx1))
% 230.28/230.60 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 230.28/230.60 Found x600:=(x60 x7):((cK x3) Xx0)
% 230.28/230.60 Found (x60 x7) as proof of ((cK X010) Xx0)
% 230.28/230.60 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 230.28/230.60 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 230.28/230.60 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 230.28/230.60 Found x8:(X010 Xx1)
% 230.28/230.60 Found x8 as proof of (X09 Xx1)
% 230.28/230.60 Found (fun (x8:(X010 Xx1))=> x8) as proof of (X09 Xx1)
% 230.28/230.60 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of ((X010 Xx1)->(X09 Xx1))
% 230.28/230.60 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 230.28/230.60 Found x600:=(x60 x7):((cK x4) Xx0)
% 230.28/230.60 Found (x60 x7) as proof of ((cK X010) Xx0)
% 230.28/230.60 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 230.28/230.60 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 230.28/230.60 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 230.28/230.60 Found x8:(X010 Xx1)
% 230.28/230.60 Found x8 as proof of (X09 Xx1)
% 230.28/230.60 Found (fun (x8:(X010 Xx1))=> x8) as proof of (X09 Xx1)
% 230.28/230.60 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of ((X010 Xx1)->(X09 Xx1))
% 230.28/230.60 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 230.28/230.60 Found x600:=(x60 x7):((cK x4) Xx0)
% 230.28/230.60 Found (x60 x7) as proof of ((cK X010) Xx0)
% 230.28/230.60 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 230.28/230.60 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 230.28/230.60 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 230.28/230.60 Found x8:(X010 Xx1)
% 230.28/230.60 Found x8 as proof of (X09 Xx1)
% 230.28/230.60 Found (fun (x8:(X010 Xx1))=> x8) as proof of (X09 Xx1)
% 230.28/230.60 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of ((X010 Xx1)->(X09 Xx1))
% 230.28/230.60 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 230.28/230.60 Found x600:=(x60 x7):((cK x4) Xx0)
% 230.28/230.60 Found (x60 x7) as proof of ((cK X010) Xx0)
% 230.28/230.60 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 230.28/230.60 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 230.28/230.60 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 230.28/230.60 Found x8:(X010 Xx1)
% 230.28/230.60 Found x8 as proof of (X09 Xx1)
% 230.28/230.60 Found (fun (x8:(X010 Xx1))=> x8) as proof of (X09 Xx1)
% 230.28/230.60 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of ((X010 Xx1)->(X09 Xx1))
% 231.38/231.70 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 231.38/231.70 Found x600:=(x60 x7):((cK x4) Xx0)
% 231.38/231.70 Found (x60 x7) as proof of ((cK X010) Xx0)
% 231.38/231.70 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 231.38/231.70 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 231.38/231.70 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 231.38/231.70 Found x4:(X09 Xx1)
% 231.38/231.70 Found x4 as proof of (X08 Xx1)
% 231.38/231.70 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X08 Xx1)
% 231.38/231.70 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X08 Xx1))
% 231.38/231.70 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X08 Xx1)))
% 231.38/231.70 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X08 Xx1)
% 231.38/231.70 Found ((and_rect0 (X08 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X08 Xx1)
% 231.38/231.70 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X08 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X08 Xx1)
% 231.38/231.70 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X08 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X08 Xx1)
% 231.38/231.70 Found x8:(X010 Xx1)
% 231.38/231.70 Found x8 as proof of (X09 Xx1)
% 231.38/231.70 Found (fun (x8:(X010 Xx1))=> x8) as proof of (X09 Xx1)
% 231.38/231.70 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of ((X010 Xx1)->(X09 Xx1))
% 231.38/231.70 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 231.38/231.70 Found x600:=(x60 x7):((cK x3) Xx0)
% 231.38/231.70 Found (x60 x7) as proof of ((cK X010) Xx0)
% 231.38/231.70 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 231.38/231.70 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 231.38/231.70 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 231.38/231.70 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 231.38/231.70 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 231.38/231.70 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 231.38/231.70 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 231.38/231.70 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X09) Xx0)))
% 231.38/231.70 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 231.38/231.70 Found ((and_rect0 ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 231.38/231.70 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 231.38/231.70 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 231.38/231.70 Found x6:(X09 Xx1)
% 231.38/231.70 Instantiate: X08:=X09:(a->Prop)
% 231.38/231.70 Found (fun (x6:(X09 Xx1))=> x6) as proof of (X08 Xx1)
% 231.38/231.70 Found (fun (Xx1:a) (x6:(X09 Xx1))=> x6) as proof of ((X09 Xx1)->(X08 Xx1))
% 231.38/231.70 Found (fun (Xx1:a) (x6:(X09 Xx1))=> x6) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 231.38/231.70 Found ((x3110 (fun (Xx1:a) (x6:(X09 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X08) Xx0)
% 231.38/231.70 Found (((x311 X08) (fun (Xx1:a) (x6:(X09 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X08) Xx0)
% 233.56/233.93 Found ((((x3 x4) X08) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X08) Xx0)
% 233.56/233.93 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> ((((x3 x4) X08) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))))) as proof of ((cK X08) Xx0)
% 233.56/233.93 Found x8:(X010 Xx1)
% 233.56/233.93 Found x8 as proof of (X09 Xx1)
% 233.56/233.93 Found (fun (x8:(X010 Xx1))=> x8) as proof of (X09 Xx1)
% 233.56/233.93 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of ((X010 Xx1)->(X09 Xx1))
% 233.56/233.93 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 233.56/233.93 Found x600:=(x60 x7):((cK x4) Xx0)
% 233.56/233.93 Found (x60 x7) as proof of ((cK X010) Xx0)
% 233.56/233.93 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 233.56/233.93 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 233.56/233.93 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 233.56/233.93 Found x8:(X010 Xx1)
% 233.56/233.93 Found x8 as proof of (X09 Xx1)
% 233.56/233.93 Found (fun (x8:(X010 Xx1))=> x8) as proof of (X09 Xx1)
% 233.56/233.93 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of ((X010 Xx1)->(X09 Xx1))
% 233.56/233.93 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 233.56/233.93 Found x500:=(x50 x6):((cK x3) Xx0)
% 233.56/233.93 Found (x50 x6) as proof of ((cK X010) Xx0)
% 233.56/233.93 Found ((x5 Xx0) x6) as proof of ((cK X010) Xx0)
% 233.56/233.93 Found ((x5 Xx0) x6) as proof of ((cK X010) Xx0)
% 233.56/233.93 Found ((x5 Xx0) x6) as proof of ((cK X010) Xx0)
% 233.56/233.93 Found x8:(X010 Xx1)
% 233.56/233.93 Found x8 as proof of (X09 Xx1)
% 233.56/233.93 Found (fun (x8:(X010 Xx1))=> x8) as proof of (X09 Xx1)
% 233.56/233.93 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of ((X010 Xx1)->(X09 Xx1))
% 233.56/233.93 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 233.56/233.93 Found x600:=(x60 x7):((cK x4) Xx0)
% 233.56/233.93 Found (x60 x7) as proof of ((cK X010) Xx0)
% 233.56/233.93 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 233.56/233.93 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 233.56/233.93 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 233.56/233.93 Found x8:(X010 Xx1)
% 233.56/233.93 Found x8 as proof of (X09 Xx1)
% 233.56/233.93 Found (fun (x8:(X010 Xx1))=> x8) as proof of (X09 Xx1)
% 233.56/233.93 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of ((X010 Xx1)->(X09 Xx1))
% 233.56/233.93 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 233.56/233.93 Found x600:=(x60 x7):((cK x4) Xx0)
% 233.56/233.93 Found (x60 x7) as proof of ((cK X010) Xx0)
% 233.56/233.93 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 233.56/233.93 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 233.56/233.93 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 233.56/233.93 Found x8:(X010 Xx1)
% 233.56/233.93 Found x8 as proof of (X09 Xx1)
% 233.56/233.93 Found (fun (x8:(X010 Xx1))=> x8) as proof of (X09 Xx1)
% 233.56/233.93 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of ((X010 Xx1)->(X09 Xx1))
% 233.56/233.93 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 233.56/233.93 Found x600:=(x60 x7):((cK x4) Xx0)
% 233.56/233.93 Found (x60 x7) as proof of ((cK X010) Xx0)
% 233.56/233.93 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 233.56/233.93 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 233.56/233.93 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 233.56/233.93 Found x8:(X010 Xx1)
% 233.56/233.93 Found x8 as proof of (X09 Xx1)
% 233.56/233.93 Found (fun (x8:(X010 Xx1))=> x8) as proof of (X09 Xx1)
% 233.56/233.93 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of ((X010 Xx1)->(X09 Xx1))
% 233.56/233.93 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 233.56/233.93 Found x600:=(x60 x7):((cK x4) Xx0)
% 233.56/233.93 Found (x60 x7) as proof of ((cK X010) Xx0)
% 233.56/233.93 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 233.56/233.93 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 233.56/233.93 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 233.56/233.93 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 233.56/233.93 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 233.56/233.93 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 233.56/233.93 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 233.95/234.33 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X010) Xx0)))
% 233.95/234.33 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 233.95/234.33 Found ((and_rect0 ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 233.95/234.33 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 233.95/234.33 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 233.95/234.33 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 233.95/234.33 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 233.95/234.33 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 233.95/234.33 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 233.95/234.33 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X010) Xx0)))
% 233.95/234.33 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 233.95/234.33 Found ((and_rect0 ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 233.95/234.33 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 233.95/234.33 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 233.95/234.33 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 233.95/234.33 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 233.95/234.33 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 233.95/234.33 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 233.95/234.33 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X010) Xx0)))
% 233.95/234.33 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 233.95/234.33 Found ((and_rect0 ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 233.95/234.33 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 233.95/234.33 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 233.95/234.33 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 233.95/234.33 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 233.95/234.33 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 233.95/234.33 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 233.95/234.33 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X010) Xx0)))
% 233.95/234.33 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 233.95/234.33 Found ((and_rect0 ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 234.42/234.80 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 234.42/234.80 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 234.42/234.80 Found x8:(X010 Xx1)
% 234.42/234.80 Found x8 as proof of (X09 Xx1)
% 234.42/234.80 Found (fun (x8:(X010 Xx1))=> x8) as proof of (X09 Xx1)
% 234.42/234.80 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of ((X010 Xx1)->(X09 Xx1))
% 234.42/234.80 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 234.42/234.80 Found x600:=(x60 x7):((cK x3) Xx0)
% 234.42/234.80 Found (x60 x7) as proof of ((cK X010) Xx0)
% 234.42/234.80 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 234.42/234.80 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 234.42/234.80 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 234.42/234.80 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 234.42/234.80 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 234.42/234.80 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 234.42/234.80 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 234.42/234.80 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X010) Xx0)))
% 234.42/234.80 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 234.42/234.80 Found ((and_rect0 ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 234.42/234.80 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 234.42/234.80 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 234.42/234.80 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 234.42/234.80 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 234.42/234.80 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 234.42/234.80 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 234.42/234.80 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X010) Xx0)))
% 234.42/234.80 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 234.42/234.80 Found ((and_rect0 ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 234.42/234.80 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 234.42/234.80 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 234.42/234.80 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 234.42/234.80 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 234.42/234.80 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 234.42/234.80 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 234.42/234.80 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X010) Xx0)))
% 234.42/234.80 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 235.04/235.43 Found ((and_rect0 ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 235.04/235.43 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 235.04/235.43 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 235.04/235.43 Found x8:(X010 Xx1)
% 235.04/235.43 Found x8 as proof of (X09 Xx1)
% 235.04/235.43 Found (fun (x8:(X010 Xx1))=> x8) as proof of (X09 Xx1)
% 235.04/235.43 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of ((X010 Xx1)->(X09 Xx1))
% 235.04/235.43 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 235.04/235.43 Found x600:=(x60 x7):((cK x4) Xx0)
% 235.04/235.43 Found (x60 x7) as proof of ((cK X010) Xx0)
% 235.04/235.43 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 235.04/235.43 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 235.04/235.43 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 235.04/235.43 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 235.04/235.43 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 235.04/235.43 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 235.04/235.43 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 235.04/235.43 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X010) Xx0)))
% 235.04/235.43 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 235.04/235.43 Found ((and_rect0 ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 235.04/235.43 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 235.04/235.43 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 235.04/235.43 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 235.04/235.43 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 235.04/235.43 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 235.04/235.43 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 235.04/235.43 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X010) Xx0)))
% 235.04/235.43 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 235.04/235.43 Found ((and_rect0 ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 235.04/235.43 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 235.04/235.43 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 235.04/235.43 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 235.04/235.43 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 235.04/235.43 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 235.04/235.43 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 235.04/235.43 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X010) Xx0)))
% 237.70/238.02 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 237.70/238.02 Found ((and_rect0 ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 237.70/238.02 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 237.70/238.02 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 237.70/238.02 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 237.70/238.02 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 237.70/238.02 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 237.70/238.02 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 237.70/238.02 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X010) Xx0)))
% 237.70/238.02 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 237.70/238.02 Found ((and_rect0 ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 237.70/238.02 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 237.70/238.02 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 237.70/238.02 Found x8:(X010 Xx1)
% 237.70/238.02 Found x8 as proof of (X09 Xx1)
% 237.70/238.02 Found (fun (x8:(X010 Xx1))=> x8) as proof of (X09 Xx1)
% 237.70/238.02 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of ((X010 Xx1)->(X09 Xx1))
% 237.70/238.02 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 237.70/238.02 Found x600:=(x60 x7):((cK x4) Xx0)
% 237.70/238.02 Found (x60 x7) as proof of ((cK X010) Xx0)
% 237.70/238.02 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 237.70/238.02 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 237.70/238.02 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 237.70/238.02 Found x8:(X010 Xx1)
% 237.70/238.02 Found x8 as proof of (X09 Xx1)
% 237.70/238.02 Found (fun (x8:(X010 Xx1))=> x8) as proof of (X09 Xx1)
% 237.70/238.02 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of ((X010 Xx1)->(X09 Xx1))
% 237.70/238.02 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 237.70/238.02 Found x600:=(x60 x7):((cK x4) Xx0)
% 237.70/238.02 Found (x60 x7) as proof of ((cK X010) Xx0)
% 237.70/238.02 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 237.70/238.02 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 237.70/238.02 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 237.70/238.02 Found x8:(X010 Xx1)
% 237.70/238.02 Found x8 as proof of (X09 Xx1)
% 237.70/238.02 Found (fun (x8:(X010 Xx1))=> x8) as proof of (X09 Xx1)
% 237.70/238.02 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of ((X010 Xx1)->(X09 Xx1))
% 237.70/238.02 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 237.70/238.02 Found x600:=(x60 x7):((cK x4) Xx0)
% 237.70/238.02 Found (x60 x7) as proof of ((cK X010) Xx0)
% 237.70/238.02 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 237.70/238.02 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 237.70/238.02 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 237.70/238.02 Found x8:(X010 Xx1)
% 237.70/238.02 Found x8 as proof of (X09 Xx1)
% 237.70/238.02 Found (fun (x8:(X010 Xx1))=> x8) as proof of (X09 Xx1)
% 237.70/238.02 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of ((X010 Xx1)->(X09 Xx1))
% 237.70/238.02 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 237.70/238.02 Found x600:=(x60 x7):((cK x4) Xx0)
% 237.70/238.02 Found (x60 x7) as proof of ((cK X010) Xx0)
% 237.70/238.02 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 237.70/238.02 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 237.70/238.02 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 240.22/240.60 Found x8:(X010 Xx1)
% 240.22/240.60 Found x8 as proof of (X09 Xx1)
% 240.22/240.60 Found (fun (x8:(X010 Xx1))=> x8) as proof of (X09 Xx1)
% 240.22/240.60 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of ((X010 Xx1)->(X09 Xx1))
% 240.22/240.60 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 240.22/240.60 Found x600:=(x60 x7):((cK x4) Xx0)
% 240.22/240.60 Found (x60 x7) as proof of ((cK X010) Xx0)
% 240.22/240.60 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 240.22/240.60 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 240.22/240.60 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 240.22/240.60 Found x8:(X010 Xx1)
% 240.22/240.60 Found x8 as proof of (X09 Xx1)
% 240.22/240.60 Found (fun (x8:(X010 Xx1))=> x8) as proof of (X09 Xx1)
% 240.22/240.60 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of ((X010 Xx1)->(X09 Xx1))
% 240.22/240.60 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 240.22/240.60 Found x600:=(x60 x7):((cK x3) Xx0)
% 240.22/240.60 Found (x60 x7) as proof of ((cK X010) Xx0)
% 240.22/240.60 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 240.22/240.60 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 240.22/240.60 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 240.22/240.60 Found x8:(X010 Xx1)
% 240.22/240.60 Found x8 as proof of (X09 Xx1)
% 240.22/240.60 Found (fun (x8:(X010 Xx1))=> x8) as proof of (X09 Xx1)
% 240.22/240.60 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of ((X010 Xx1)->(X09 Xx1))
% 240.22/240.60 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 240.22/240.60 Found x600:=(x60 x7):((cK x4) Xx0)
% 240.22/240.60 Found (x60 x7) as proof of ((cK X010) Xx0)
% 240.22/240.60 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 240.22/240.60 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 240.22/240.60 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 240.22/240.60 Found x8:(X010 Xx1)
% 240.22/240.60 Found x8 as proof of (X09 Xx1)
% 240.22/240.60 Found (fun (x8:(X010 Xx1))=> x8) as proof of (X09 Xx1)
% 240.22/240.60 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of ((X010 Xx1)->(X09 Xx1))
% 240.22/240.60 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 240.22/240.60 Found x600:=(x60 x7):((cK x4) Xx0)
% 240.22/240.60 Found (x60 x7) as proof of ((cK X010) Xx0)
% 240.22/240.60 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 240.22/240.60 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 240.22/240.60 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 240.22/240.60 Found x8:(X010 Xx1)
% 240.22/240.60 Found x8 as proof of (X09 Xx1)
% 240.22/240.60 Found (fun (x8:(X010 Xx1))=> x8) as proof of (X09 Xx1)
% 240.22/240.60 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of ((X010 Xx1)->(X09 Xx1))
% 240.22/240.60 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 240.22/240.60 Found x600:=(x60 x7):((cK x4) Xx0)
% 240.22/240.60 Found (x60 x7) as proof of ((cK X010) Xx0)
% 240.22/240.60 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 240.22/240.60 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 240.22/240.60 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 240.22/240.60 Found x8:(X010 Xx1)
% 240.22/240.60 Found x8 as proof of (X09 Xx1)
% 240.22/240.60 Found (fun (x8:(X010 Xx1))=> x8) as proof of (X09 Xx1)
% 240.22/240.60 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of ((X010 Xx1)->(X09 Xx1))
% 240.22/240.60 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 240.22/240.60 Found x600:=(x60 x7):((cK x4) Xx0)
% 240.22/240.60 Found (x60 x7) as proof of ((cK X010) Xx0)
% 240.22/240.60 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 240.22/240.60 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 240.22/240.60 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 240.22/240.60 Found x8:(X010 Xx1)
% 240.22/240.60 Found x8 as proof of (X09 Xx1)
% 240.22/240.60 Found (fun (x8:(X010 Xx1))=> x8) as proof of (X09 Xx1)
% 240.22/240.60 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of ((X010 Xx1)->(X09 Xx1))
% 240.22/240.60 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 240.22/240.60 Found x600:=(x60 x7):((cK x4) Xx0)
% 240.22/240.60 Found (x60 x7) as proof of ((cK X010) Xx0)
% 240.22/240.60 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 240.22/240.60 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 240.22/240.60 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 240.22/240.60 Found x8:(X010 Xx1)
% 240.22/240.60 Found x8 as proof of (X09 Xx1)
% 240.22/240.60 Found (fun (x8:(X010 Xx1))=> x8) as proof of (X09 Xx1)
% 240.22/240.60 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of ((X010 Xx1)->(X09 Xx1))
% 240.22/240.60 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 240.22/240.60 Found x600:=(x60 x7):((cK x4) Xx0)
% 240.22/240.60 Found (x60 x7) as proof of ((cK X010) Xx0)
% 240.22/240.60 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 240.22/240.60 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 240.22/240.60 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 240.22/240.60 Found x8:(X010 Xx1)
% 240.22/240.60 Found x8 as proof of (X09 Xx1)
% 240.22/240.60 Found (fun (x8:(X010 Xx1))=> x8) as proof of (X09 Xx1)
% 240.22/240.60 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of ((X010 Xx1)->(X09 Xx1))
% 242.53/242.86 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 242.53/242.86 Found x600:=(x60 x7):((cK x4) Xx0)
% 242.53/242.86 Found (x60 x7) as proof of ((cK X010) Xx0)
% 242.53/242.86 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 242.53/242.86 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 242.53/242.86 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 242.53/242.86 Found x8:(X010 Xx1)
% 242.53/242.86 Found x8 as proof of (X09 Xx1)
% 242.53/242.86 Found (fun (x8:(X010 Xx1))=> x8) as proof of (X09 Xx1)
% 242.53/242.86 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of ((X010 Xx1)->(X09 Xx1))
% 242.53/242.86 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 242.53/242.86 Found x600:=(x60 x7):((cK x3) Xx0)
% 242.53/242.86 Found (x60 x7) as proof of ((cK X010) Xx0)
% 242.53/242.86 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 242.53/242.86 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 242.53/242.86 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 242.53/242.86 Found x8:(X010 Xx1)
% 242.53/242.86 Found x8 as proof of (X09 Xx1)
% 242.53/242.86 Found (fun (x8:(X010 Xx1))=> x8) as proof of (X09 Xx1)
% 242.53/242.86 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of ((X010 Xx1)->(X09 Xx1))
% 242.53/242.86 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 242.53/242.86 Found x600:=(x60 x7):((cK x4) Xx0)
% 242.53/242.86 Found (x60 x7) as proof of ((cK X010) Xx0)
% 242.53/242.86 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 242.53/242.86 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 242.53/242.86 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 242.53/242.86 Found x60:=(x6 Xx0):((x3 Xx0)->((cK x3) Xx0))
% 242.53/242.86 Found (x6 Xx0) as proof of ((x3 Xx0)->((cK X010) Xx0))
% 242.53/242.86 Found (x6 Xx0) as proof of ((x3 Xx0)->((cK X010) Xx0))
% 242.53/242.86 Found (fun (x6:(forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1))))=> (x6 Xx0)) as proof of ((x3 Xx0)->((cK X010) Xx0))
% 242.53/242.86 Found (fun (x6:(forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1)))->((x3 Xx0)->((cK X010) Xx0)))
% 242.53/242.86 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 242.53/242.86 Found ((and_rect0 ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 242.53/242.86 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1)))->((x3 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1)))) (x3 Xx0)) P) x6) x4)) ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 242.53/242.86 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1)))->((x3 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1)))) (x3 Xx0)) P) x6) x4)) ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x3 Xx1)->((cK x3) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 242.53/242.86 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 242.53/242.86 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 242.53/242.86 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 242.53/242.86 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 242.53/242.86 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X010) Xx0)))
% 242.53/242.86 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 242.53/242.86 Found ((and_rect0 ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 242.53/242.86 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 242.53/242.86 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X010) Xx0)
% 242.53/242.86 Found x8:(X010 Xx1)
% 242.53/242.86 Found x8 as proof of (X09 Xx1)
% 242.53/242.86 Found (fun (x8:(X010 Xx1))=> x8) as proof of (X09 Xx1)
% 242.53/242.86 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of ((X010 Xx1)->(X09 Xx1))
% 244.26/244.58 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 244.26/244.58 Found x600:=(x60 x7):((cK x4) Xx0)
% 244.26/244.58 Found (x60 x7) as proof of ((cK X010) Xx0)
% 244.26/244.58 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 244.26/244.58 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 244.26/244.58 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 244.26/244.58 Found x8:(X010 Xx1)
% 244.26/244.58 Found x8 as proof of (X09 Xx1)
% 244.26/244.58 Found (fun (x8:(X010 Xx1))=> x8) as proof of (X09 Xx1)
% 244.26/244.58 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of ((X010 Xx1)->(X09 Xx1))
% 244.26/244.58 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 244.26/244.58 Found x600:=(x60 x7):((cK x4) Xx0)
% 244.26/244.58 Found (x60 x7) as proof of ((cK X010) Xx0)
% 244.26/244.58 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 244.26/244.58 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 244.26/244.58 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 244.26/244.58 Found x8:(X010 Xx1)
% 244.26/244.58 Found x8 as proof of (X09 Xx1)
% 244.26/244.58 Found (fun (x8:(X010 Xx1))=> x8) as proof of (X09 Xx1)
% 244.26/244.58 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of ((X010 Xx1)->(X09 Xx1))
% 244.26/244.58 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 244.26/244.58 Found x600:=(x60 x7):((cK x4) Xx0)
% 244.26/244.58 Found (x60 x7) as proof of ((cK X010) Xx0)
% 244.26/244.58 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 244.26/244.58 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 244.26/244.58 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 244.26/244.58 Found x8:(X010 Xx1)
% 244.26/244.58 Found x8 as proof of (X09 Xx1)
% 244.26/244.58 Found (fun (x8:(X010 Xx1))=> x8) as proof of (X09 Xx1)
% 244.26/244.58 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of ((X010 Xx1)->(X09 Xx1))
% 244.26/244.58 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 244.26/244.58 Found x600:=(x60 x7):((cK x4) Xx0)
% 244.26/244.58 Found (x60 x7) as proof of ((cK X010) Xx0)
% 244.26/244.58 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 244.26/244.58 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 244.26/244.58 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 244.26/244.58 Found x8:(X010 Xx1)
% 244.26/244.58 Found x8 as proof of (X09 Xx1)
% 244.26/244.58 Found (fun (x8:(X010 Xx1))=> x8) as proof of (X09 Xx1)
% 244.26/244.58 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of ((X010 Xx1)->(X09 Xx1))
% 244.26/244.58 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 244.26/244.58 Found x600:=(x60 x7):((cK x4) Xx0)
% 244.26/244.58 Found (x60 x7) as proof of ((cK X010) Xx0)
% 244.26/244.58 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 244.26/244.58 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 244.26/244.58 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 244.26/244.58 Found x8:(X010 Xx1)
% 244.26/244.58 Found x8 as proof of (X09 Xx1)
% 244.26/244.58 Found (fun (x8:(X010 Xx1))=> x8) as proof of (X09 Xx1)
% 244.26/244.58 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of ((X010 Xx1)->(X09 Xx1))
% 244.26/244.58 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 244.26/244.58 Found x600:=(x60 x7):((cK x4) Xx0)
% 244.26/244.58 Found (x60 x7) as proof of ((cK X010) Xx0)
% 244.26/244.58 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 244.26/244.58 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 244.26/244.58 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 244.26/244.58 Found x8:(X010 Xx1)
% 244.26/244.58 Found x8 as proof of (X09 Xx1)
% 244.26/244.58 Found (fun (x8:(X010 Xx1))=> x8) as proof of (X09 Xx1)
% 244.26/244.58 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of ((X010 Xx1)->(X09 Xx1))
% 244.26/244.58 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 244.26/244.58 Found x600:=(x60 x7):((cK x4) Xx0)
% 244.26/244.58 Found (x60 x7) as proof of ((cK X010) Xx0)
% 244.26/244.58 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 244.26/244.58 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 244.26/244.58 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 244.26/244.58 Found x8:(X010 Xx1)
% 244.26/244.58 Found x8 as proof of (X09 Xx1)
% 244.26/244.58 Found (fun (x8:(X010 Xx1))=> x8) as proof of (X09 Xx1)
% 244.26/244.58 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of ((X010 Xx1)->(X09 Xx1))
% 244.26/244.58 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 244.26/244.58 Found x600:=(x60 x7):((cK x3) Xx0)
% 244.26/244.58 Found (x60 x7) as proof of ((cK X010) Xx0)
% 244.26/244.58 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 244.26/244.58 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 244.26/244.58 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 244.26/244.58 Found x8:(X010 Xx1)
% 244.26/244.58 Found x8 as proof of (X09 Xx1)
% 244.26/244.58 Found (fun (x8:(X010 Xx1))=> x8) as proof of (X09 Xx1)
% 244.26/244.58 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of ((X010 Xx1)->(X09 Xx1))
% 244.26/244.58 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 244.26/244.58 Found x600:=(x60 x7):((cK x4) Xx0)
% 245.37/245.74 Found (x60 x7) as proof of ((cK X010) Xx0)
% 245.37/245.74 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 245.37/245.74 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 245.37/245.74 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 245.37/245.74 Found x8:(X010 Xx1)
% 245.37/245.74 Found x8 as proof of (X09 Xx1)
% 245.37/245.74 Found (fun (x8:(X010 Xx1))=> x8) as proof of (X09 Xx1)
% 245.37/245.74 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of ((X010 Xx1)->(X09 Xx1))
% 245.37/245.74 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 245.37/245.74 Found x600:=(x60 x7):((cK x4) Xx0)
% 245.37/245.74 Found (x60 x7) as proof of ((cK X010) Xx0)
% 245.37/245.74 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 245.37/245.74 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 245.37/245.74 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 245.37/245.74 Found x8:(X010 Xx1)
% 245.37/245.74 Found x8 as proof of (X09 Xx1)
% 245.37/245.74 Found (fun (x8:(X010 Xx1))=> x8) as proof of (X09 Xx1)
% 245.37/245.74 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of ((X010 Xx1)->(X09 Xx1))
% 245.37/245.74 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 245.37/245.74 Found x600:=(x60 x7):((cK x4) Xx0)
% 245.37/245.74 Found (x60 x7) as proof of ((cK X010) Xx0)
% 245.37/245.74 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 245.37/245.74 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 245.37/245.74 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 245.37/245.74 Found x8:(X010 Xx1)
% 245.37/245.74 Found x8 as proof of (X09 Xx1)
% 245.37/245.74 Found (fun (x8:(X010 Xx1))=> x8) as proof of (X09 Xx1)
% 245.37/245.74 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of ((X010 Xx1)->(X09 Xx1))
% 245.37/245.74 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 245.37/245.74 Found x600:=(x60 x7):((cK x4) Xx0)
% 245.37/245.74 Found (x60 x7) as proof of ((cK X010) Xx0)
% 245.37/245.74 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 245.37/245.74 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 245.37/245.74 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 245.37/245.74 Found x8:(X010 Xx1)
% 245.37/245.74 Found x8 as proof of (X09 Xx1)
% 245.37/245.74 Found (fun (x8:(X010 Xx1))=> x8) as proof of (X09 Xx1)
% 245.37/245.74 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of ((X010 Xx1)->(X09 Xx1))
% 245.37/245.74 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 245.37/245.74 Found x600:=(x60 x7):((cK x4) Xx0)
% 245.37/245.74 Found (x60 x7) as proof of ((cK X010) Xx0)
% 245.37/245.74 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 245.37/245.74 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 245.37/245.74 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 245.37/245.74 Found x8:(X010 Xx1)
% 245.37/245.74 Found x8 as proof of (X09 Xx1)
% 245.37/245.74 Found (fun (x8:(X010 Xx1))=> x8) as proof of (X09 Xx1)
% 245.37/245.74 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of ((X010 Xx1)->(X09 Xx1))
% 245.37/245.74 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 245.37/245.74 Found x600:=(x60 x7):((cK x4) Xx0)
% 245.37/245.74 Found (x60 x7) as proof of ((cK X010) Xx0)
% 245.37/245.74 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 245.37/245.74 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 245.37/245.74 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 245.37/245.74 Found x8:(X010 Xx1)
% 245.37/245.74 Found x8 as proof of (X09 Xx1)
% 245.37/245.74 Found (fun (x8:(X010 Xx1))=> x8) as proof of (X09 Xx1)
% 245.37/245.74 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of ((X010 Xx1)->(X09 Xx1))
% 245.37/245.74 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 245.37/245.74 Found x600:=(x60 x7):((cK x4) Xx0)
% 245.37/245.74 Found (x60 x7) as proof of ((cK X010) Xx0)
% 245.37/245.74 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 245.37/245.74 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 245.37/245.74 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 245.37/245.74 Found x8:(X010 Xx1)
% 245.37/245.74 Found x8 as proof of (X09 Xx1)
% 245.37/245.74 Found (fun (x8:(X010 Xx1))=> x8) as proof of (X09 Xx1)
% 245.37/245.74 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of ((X010 Xx1)->(X09 Xx1))
% 245.37/245.74 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 245.37/245.74 Found x600:=(x60 x7):((cK x4) Xx0)
% 245.37/245.74 Found (x60 x7) as proof of ((cK X010) Xx0)
% 245.37/245.74 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 245.37/245.74 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 245.37/245.74 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 245.37/245.74 Found x8:(X010 Xx1)
% 245.37/245.74 Found x8 as proof of (X09 Xx1)
% 245.37/245.74 Found (fun (x8:(X010 Xx1))=> x8) as proof of (X09 Xx1)
% 245.37/245.74 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of ((X010 Xx1)->(X09 Xx1))
% 245.37/245.74 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 245.37/245.74 Found x600:=(x60 x7):((cK x4) Xx0)
% 245.37/245.74 Found (x60 x7) as proof of ((cK X010) Xx0)
% 245.37/245.74 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 245.37/245.74 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 246.36/246.72 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 246.36/246.72 Found x8:(X010 Xx1)
% 246.36/246.72 Found x8 as proof of (X09 Xx1)
% 246.36/246.72 Found (fun (x8:(X010 Xx1))=> x8) as proof of (X09 Xx1)
% 246.36/246.72 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of ((X010 Xx1)->(X09 Xx1))
% 246.36/246.72 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 246.36/246.72 Found x600:=(x60 x7):((cK x3) Xx0)
% 246.36/246.72 Found (x60 x7) as proof of ((cK X010) Xx0)
% 246.36/246.72 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 246.36/246.72 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 246.36/246.72 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 246.36/246.72 Found x8:(X010 Xx1)
% 246.36/246.72 Found x8 as proof of (X09 Xx1)
% 246.36/246.72 Found (fun (x8:(X010 Xx1))=> x8) as proof of (X09 Xx1)
% 246.36/246.72 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of ((X010 Xx1)->(X09 Xx1))
% 246.36/246.72 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 246.36/246.72 Found x600:=(x60 x7):((cK x4) Xx0)
% 246.36/246.72 Found (x60 x7) as proof of ((cK X010) Xx0)
% 246.36/246.72 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 246.36/246.72 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 246.36/246.72 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 246.36/246.72 Found x8:(X010 Xx1)
% 246.36/246.72 Found x8 as proof of (X09 Xx1)
% 246.36/246.72 Found (fun (x8:(X010 Xx1))=> x8) as proof of (X09 Xx1)
% 246.36/246.72 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of ((X010 Xx1)->(X09 Xx1))
% 246.36/246.72 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 246.36/246.72 Found x600:=(x60 x7):((cK x4) Xx0)
% 246.36/246.72 Found (x60 x7) as proof of ((cK X010) Xx0)
% 246.36/246.72 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 246.36/246.72 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 246.36/246.72 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 246.36/246.72 Found x8:(X010 Xx1)
% 246.36/246.72 Found x8 as proof of (X09 Xx1)
% 246.36/246.72 Found (fun (x8:(X010 Xx1))=> x8) as proof of (X09 Xx1)
% 246.36/246.72 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of ((X010 Xx1)->(X09 Xx1))
% 246.36/246.72 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 246.36/246.72 Found x600:=(x60 x7):((cK x4) Xx0)
% 246.36/246.72 Found (x60 x7) as proof of ((cK X010) Xx0)
% 246.36/246.72 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 246.36/246.72 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 246.36/246.72 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 246.36/246.72 Found x8:(X010 Xx1)
% 246.36/246.72 Found x8 as proof of (X09 Xx1)
% 246.36/246.72 Found (fun (x8:(X010 Xx1))=> x8) as proof of (X09 Xx1)
% 246.36/246.72 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of ((X010 Xx1)->(X09 Xx1))
% 246.36/246.72 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 246.36/246.72 Found x600:=(x60 x7):((cK x4) Xx0)
% 246.36/246.72 Found (x60 x7) as proof of ((cK X010) Xx0)
% 246.36/246.72 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 246.36/246.72 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 246.36/246.72 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 246.36/246.72 Found x8:(X010 Xx1)
% 246.36/246.72 Found x8 as proof of (X09 Xx1)
% 246.36/246.72 Found (fun (x8:(X010 Xx1))=> x8) as proof of (X09 Xx1)
% 246.36/246.72 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of ((X010 Xx1)->(X09 Xx1))
% 246.36/246.72 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 246.36/246.72 Found x600:=(x60 x7):((cK x4) Xx0)
% 246.36/246.72 Found (x60 x7) as proof of ((cK X010) Xx0)
% 246.36/246.72 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 246.36/246.72 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 246.36/246.72 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 246.36/246.72 Found x8:(X010 Xx1)
% 246.36/246.72 Found x8 as proof of (X09 Xx1)
% 246.36/246.72 Found (fun (x8:(X010 Xx1))=> x8) as proof of (X09 Xx1)
% 246.36/246.72 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of ((X010 Xx1)->(X09 Xx1))
% 246.36/246.72 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 246.36/246.72 Found x600:=(x60 x7):((cK x4) Xx0)
% 246.36/246.72 Found (x60 x7) as proof of ((cK X010) Xx0)
% 246.36/246.72 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 246.36/246.72 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 246.36/246.72 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 246.36/246.72 Found x8:(X010 Xx1)
% 246.36/246.72 Found x8 as proof of (X09 Xx1)
% 246.36/246.72 Found (fun (x8:(X010 Xx1))=> x8) as proof of (X09 Xx1)
% 246.36/246.72 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of ((X010 Xx1)->(X09 Xx1))
% 246.36/246.72 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 246.36/246.72 Found x600:=(x60 x7):((cK x4) Xx0)
% 246.36/246.72 Found (x60 x7) as proof of ((cK X010) Xx0)
% 246.36/246.72 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 246.36/246.72 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 246.36/246.72 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 246.36/246.72 Found x8:(X010 Xx1)
% 246.36/246.72 Found x8 as proof of (X09 Xx1)
% 247.15/247.50 Found (fun (x8:(X010 Xx1))=> x8) as proof of (X09 Xx1)
% 247.15/247.50 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of ((X010 Xx1)->(X09 Xx1))
% 247.15/247.50 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 247.15/247.50 Found x600:=(x60 x7):((cK x4) Xx0)
% 247.15/247.50 Found (x60 x7) as proof of ((cK X010) Xx0)
% 247.15/247.50 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 247.15/247.50 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 247.15/247.50 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 247.15/247.50 Found x8:(X010 Xx1)
% 247.15/247.50 Found x8 as proof of (X09 Xx1)
% 247.15/247.50 Found (fun (x8:(X010 Xx1))=> x8) as proof of (X09 Xx1)
% 247.15/247.50 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of ((X010 Xx1)->(X09 Xx1))
% 247.15/247.50 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 247.15/247.50 Found x600:=(x60 x7):((cK x4) Xx0)
% 247.15/247.50 Found (x60 x7) as proof of ((cK X010) Xx0)
% 247.15/247.50 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 247.15/247.50 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 247.15/247.50 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 247.15/247.50 Found x8:(X010 Xx1)
% 247.15/247.50 Found x8 as proof of (X09 Xx1)
% 247.15/247.50 Found (fun (x8:(X010 Xx1))=> x8) as proof of (X09 Xx1)
% 247.15/247.50 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of ((X010 Xx1)->(X09 Xx1))
% 247.15/247.50 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 247.15/247.50 Found x600:=(x60 x7):((cK x4) Xx0)
% 247.15/247.50 Found (x60 x7) as proof of ((cK X010) Xx0)
% 247.15/247.50 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 247.15/247.50 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 247.15/247.50 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 247.15/247.50 Found x8:(X010 Xx1)
% 247.15/247.50 Found x8 as proof of (X09 Xx1)
% 247.15/247.50 Found (fun (x8:(X010 Xx1))=> x8) as proof of (X09 Xx1)
% 247.15/247.50 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of ((X010 Xx1)->(X09 Xx1))
% 247.15/247.50 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 247.15/247.50 Found x600:=(x60 x7):((cK x3) Xx0)
% 247.15/247.50 Found (x60 x7) as proof of ((cK X010) Xx0)
% 247.15/247.50 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 247.15/247.50 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 247.15/247.50 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 247.15/247.50 Found x8:(X010 Xx1)
% 247.15/247.50 Found x8 as proof of (X09 Xx1)
% 247.15/247.50 Found (fun (x8:(X010 Xx1))=> x8) as proof of (X09 Xx1)
% 247.15/247.50 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of ((X010 Xx1)->(X09 Xx1))
% 247.15/247.50 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 247.15/247.50 Found x600:=(x60 x7):((cK x4) Xx0)
% 247.15/247.50 Found (x60 x7) as proof of ((cK X010) Xx0)
% 247.15/247.50 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 247.15/247.50 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 247.15/247.50 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 247.15/247.50 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 247.15/247.50 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 247.15/247.50 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 247.15/247.50 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 247.15/247.50 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X010) Xx0)))
% 247.15/247.50 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 247.15/247.50 Found ((and_rect0 ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 247.15/247.50 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 247.15/247.50 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 247.15/247.50 Found x6:(X010 Xx1)
% 247.15/247.50 Instantiate: X09:=X010:(a->Prop)
% 247.15/247.50 Found (fun (x6:(X010 Xx1))=> x6) as proof of (X09 Xx1)
% 247.15/247.50 Found (fun (Xx1:a) (x6:(X010 Xx1))=> x6) as proof of ((X010 Xx1)->(X09 Xx1))
% 247.15/247.50 Found (fun (Xx1:a) (x6:(X010 Xx1))=> x6) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 247.15/247.50 Found ((x3120 (fun (Xx1:a) (x6:(X010 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X09) Xx0)
% 247.69/248.07 Found (((x312 X09) (fun (Xx1:a) (x6:(X010 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X09) Xx0)
% 247.69/248.07 Found ((((x3 x4) X09) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X09) Xx0)
% 247.69/248.07 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> ((((x3 x4) X09) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))))) as proof of ((cK X09) Xx0)
% 247.69/248.07 Found x8:(X010 Xx1)
% 247.69/248.07 Found x8 as proof of (X09 Xx1)
% 247.69/248.07 Found (fun (x8:(X010 Xx1))=> x8) as proof of (X09 Xx1)
% 247.69/248.07 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of ((X010 Xx1)->(X09 Xx1))
% 247.69/248.07 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 247.69/248.07 Found x600:=(x60 x7):((cK x4) Xx0)
% 247.69/248.07 Found (x60 x7) as proof of ((cK X010) Xx0)
% 247.69/248.07 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 247.69/248.07 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 247.69/248.07 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 247.69/248.07 Found x8:(X010 Xx1)
% 247.69/248.07 Found x8 as proof of (X09 Xx1)
% 247.69/248.07 Found (fun (x8:(X010 Xx1))=> x8) as proof of (X09 Xx1)
% 247.69/248.07 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of ((X010 Xx1)->(X09 Xx1))
% 247.69/248.07 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 247.69/248.07 Found x600:=(x60 x7):((cK x4) Xx0)
% 247.69/248.07 Found (x60 x7) as proof of ((cK X010) Xx0)
% 247.69/248.07 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 247.69/248.07 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 247.69/248.07 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 247.69/248.07 Found x8:(X010 Xx1)
% 247.69/248.07 Found x8 as proof of (X09 Xx1)
% 247.69/248.07 Found (fun (x8:(X010 Xx1))=> x8) as proof of (X09 Xx1)
% 247.69/248.07 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of ((X010 Xx1)->(X09 Xx1))
% 247.69/248.07 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 247.69/248.07 Found x600:=(x60 x7):((cK x4) Xx0)
% 247.69/248.07 Found (x60 x7) as proof of ((cK X010) Xx0)
% 247.69/248.07 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 247.69/248.07 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 247.69/248.07 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 247.69/248.07 Found x8:(X010 Xx1)
% 247.69/248.07 Found x8 as proof of (X09 Xx1)
% 247.69/248.07 Found (fun (x8:(X010 Xx1))=> x8) as proof of (X09 Xx1)
% 247.69/248.07 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of ((X010 Xx1)->(X09 Xx1))
% 247.69/248.07 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 247.69/248.07 Found x600:=(x60 x7):((cK x4) Xx0)
% 247.69/248.07 Found (x60 x7) as proof of ((cK X010) Xx0)
% 247.69/248.07 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 247.69/248.07 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 247.69/248.07 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 247.69/248.07 Found x8:(X010 Xx1)
% 247.69/248.07 Found x8 as proof of (X09 Xx1)
% 247.69/248.07 Found (fun (x8:(X010 Xx1))=> x8) as proof of (X09 Xx1)
% 247.69/248.07 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of ((X010 Xx1)->(X09 Xx1))
% 247.69/248.07 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 247.69/248.07 Found x600:=(x60 x7):((cK x4) Xx0)
% 247.69/248.07 Found (x60 x7) as proof of ((cK X010) Xx0)
% 247.69/248.07 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 247.69/248.07 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 247.69/248.07 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 247.69/248.07 Found x8:(X010 Xx1)
% 247.69/248.07 Found x8 as proof of (X09 Xx1)
% 247.69/248.07 Found (fun (x8:(X010 Xx1))=> x8) as proof of (X09 Xx1)
% 247.69/248.07 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of ((X010 Xx1)->(X09 Xx1))
% 247.69/248.07 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 247.69/248.07 Found x600:=(x60 x7):((cK x4) Xx0)
% 247.69/248.07 Found (x60 x7) as proof of ((cK X010) Xx0)
% 248.20/248.56 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 248.20/248.56 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 248.20/248.56 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 248.20/248.56 Found x8:(X010 Xx1)
% 248.20/248.56 Found x8 as proof of (X09 Xx1)
% 248.20/248.56 Found (fun (x8:(X010 Xx1))=> x8) as proof of (X09 Xx1)
% 248.20/248.56 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of ((X010 Xx1)->(X09 Xx1))
% 248.20/248.56 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 248.20/248.56 Found x600:=(x60 x7):((cK x4) Xx0)
% 248.20/248.56 Found (x60 x7) as proof of ((cK X010) Xx0)
% 248.20/248.56 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 248.20/248.56 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 248.20/248.56 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 248.20/248.56 Found x8:(X010 Xx1)
% 248.20/248.56 Found x8 as proof of (X09 Xx1)
% 248.20/248.56 Found (fun (x8:(X010 Xx1))=> x8) as proof of (X09 Xx1)
% 248.20/248.56 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of ((X010 Xx1)->(X09 Xx1))
% 248.20/248.56 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 248.20/248.56 Found x600:=(x60 x7):((cK x4) Xx0)
% 248.20/248.56 Found (x60 x7) as proof of ((cK X010) Xx0)
% 248.20/248.56 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 248.20/248.56 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 248.20/248.56 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 248.20/248.56 Found x8:(X010 Xx1)
% 248.20/248.56 Found x8 as proof of (X09 Xx1)
% 248.20/248.56 Found (fun (x8:(X010 Xx1))=> x8) as proof of (X09 Xx1)
% 248.20/248.56 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of ((X010 Xx1)->(X09 Xx1))
% 248.20/248.56 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 248.20/248.56 Found x600:=(x60 x7):((cK x4) Xx0)
% 248.20/248.56 Found (x60 x7) as proof of ((cK X010) Xx0)
% 248.20/248.56 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 248.20/248.56 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 248.20/248.56 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 248.20/248.56 Found x8:(X010 Xx1)
% 248.20/248.56 Found x8 as proof of (X09 Xx1)
% 248.20/248.56 Found (fun (x8:(X010 Xx1))=> x8) as proof of (X09 Xx1)
% 248.20/248.56 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of ((X010 Xx1)->(X09 Xx1))
% 248.20/248.56 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 248.20/248.56 Found x600:=(x60 x7):((cK x4) Xx0)
% 248.20/248.56 Found (x60 x7) as proof of ((cK X010) Xx0)
% 248.20/248.56 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 248.20/248.56 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 248.20/248.56 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 248.20/248.56 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 248.20/248.56 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 248.20/248.56 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 248.20/248.56 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 248.20/248.56 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X09) Xx0)))
% 248.20/248.56 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 248.20/248.56 Found ((and_rect0 ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 248.20/248.56 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 248.20/248.56 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X09) Xx0)
% 248.20/248.56 Found x8:(X010 Xx1)
% 248.20/248.56 Found x8 as proof of (X09 Xx1)
% 248.20/248.56 Found (fun (x8:(X010 Xx1))=> x8) as proof of (X09 Xx1)
% 248.20/248.56 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of ((X010 Xx1)->(X09 Xx1))
% 248.20/248.56 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 248.20/248.56 Found x600:=(x60 x7):((cK x3) Xx0)
% 248.20/248.56 Found (x60 x7) as proof of ((cK X010) Xx0)
% 248.20/248.56 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 248.20/248.56 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 248.20/248.56 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 248.20/248.56 Found x8:(X010 Xx1)
% 248.20/248.56 Found x8 as proof of (X09 Xx1)
% 248.20/248.56 Found (fun (x8:(X010 Xx1))=> x8) as proof of (X09 Xx1)
% 248.20/248.56 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of ((X010 Xx1)->(X09 Xx1))
% 251.27/251.65 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 251.27/251.65 Found x600:=(x60 x7):((cK x4) Xx0)
% 251.27/251.65 Found (x60 x7) as proof of ((cK X010) Xx0)
% 251.27/251.65 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 251.27/251.65 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 251.27/251.65 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 251.27/251.65 Found x8:(X010 Xx1)
% 251.27/251.65 Found x8 as proof of (X09 Xx1)
% 251.27/251.65 Found (fun (x8:(X010 Xx1))=> x8) as proof of (X09 Xx1)
% 251.27/251.65 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of ((X010 Xx1)->(X09 Xx1))
% 251.27/251.65 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 251.27/251.65 Found x600:=(x60 x7):((cK x3) Xx0)
% 251.27/251.65 Found (x60 x7) as proof of ((cK X010) Xx0)
% 251.27/251.65 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 251.27/251.65 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 251.27/251.65 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 251.27/251.65 Found x8:(X010 Xx1)
% 251.27/251.65 Found x8 as proof of (X09 Xx1)
% 251.27/251.65 Found (fun (x8:(X010 Xx1))=> x8) as proof of (X09 Xx1)
% 251.27/251.65 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of ((X010 Xx1)->(X09 Xx1))
% 251.27/251.65 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 251.27/251.65 Found x600:=(x60 x7):((cK x4) Xx0)
% 251.27/251.65 Found (x60 x7) as proof of ((cK X010) Xx0)
% 251.27/251.65 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 251.27/251.65 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 251.27/251.65 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 251.27/251.65 Found x8:(X010 Xx1)
% 251.27/251.65 Found x8 as proof of (X09 Xx1)
% 251.27/251.65 Found (fun (x8:(X010 Xx1))=> x8) as proof of (X09 Xx1)
% 251.27/251.65 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of ((X010 Xx1)->(X09 Xx1))
% 251.27/251.65 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 251.27/251.65 Found x600:=(x60 x7):((cK x3) Xx0)
% 251.27/251.65 Found (x60 x7) as proof of ((cK X010) Xx0)
% 251.27/251.65 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 251.27/251.65 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 251.27/251.65 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 251.27/251.65 Found x8:(X010 Xx1)
% 251.27/251.65 Found x8 as proof of (X09 Xx1)
% 251.27/251.65 Found (fun (x8:(X010 Xx1))=> x8) as proof of (X09 Xx1)
% 251.27/251.65 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of ((X010 Xx1)->(X09 Xx1))
% 251.27/251.65 Found (fun (Xx1:a) (x8:(X010 Xx1))=> x8) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 251.27/251.65 Found x600:=(x60 x7):((cK x4) Xx0)
% 251.27/251.65 Found (x60 x7) as proof of ((cK X010) Xx0)
% 251.27/251.65 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 251.27/251.65 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 251.27/251.65 Found ((x6 Xx0) x7) as proof of ((cK X010) Xx0)
% 251.27/251.65 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 251.27/251.65 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 251.27/251.65 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 251.27/251.65 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 251.27/251.65 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X010) Xx0)))
% 251.27/251.65 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 251.27/251.65 Found ((and_rect0 ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 251.27/251.65 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 251.27/251.65 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X010) Xx0)
% 251.27/251.65 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 251.27/251.65 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 251.27/251.65 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 251.27/251.65 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 251.27/251.65 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X010) Xx0)))
% 251.27/251.65 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 252.01/252.39 Found ((and_rect0 ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 252.01/252.39 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 252.01/252.39 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 252.01/252.39 Found x6:(X010 Xx1)
% 252.01/252.39 Instantiate: X09:=X010:(a->Prop)
% 252.01/252.39 Found (fun (x6:(X010 Xx1))=> x6) as proof of (X09 Xx1)
% 252.01/252.39 Found (fun (Xx1:a) (x6:(X010 Xx1))=> x6) as proof of ((X010 Xx1)->(X09 Xx1))
% 252.01/252.39 Found (fun (Xx1:a) (x6:(X010 Xx1))=> x6) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 252.01/252.39 Found ((x3120 (fun (Xx1:a) (x6:(X010 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X09) Xx0)
% 252.01/252.39 Found (((x312 X09) (fun (Xx1:a) (x6:(X010 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X09) Xx0)
% 252.01/252.39 Found ((((x3 x4) X09) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X09) Xx0)
% 252.01/252.39 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> ((((x3 x4) X09) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))))) as proof of ((cK X09) Xx0)
% 252.01/252.39 Found x4:(X010 Xx1)
% 252.01/252.39 Instantiate: X010:=(cK x5):(a->Prop)
% 252.01/252.39 Found x4 as proof of (X09 Xx1)
% 252.01/252.39 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X09 Xx1)
% 252.01/252.39 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X09 Xx1))
% 252.01/252.39 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X09 Xx1)))
% 252.01/252.39 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X09 Xx1)
% 252.01/252.39 Found ((and_rect0 (X09 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X09 Xx1)
% 252.01/252.39 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X09 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X09 Xx1)
% 252.01/252.39 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X09 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X09 Xx1)
% 252.01/252.39 Found x4:(X010 Xx1)
% 252.01/252.39 Found x4 as proof of (X09 Xx1)
% 252.01/252.39 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X09 Xx1)
% 252.01/252.39 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X09 Xx1))
% 252.01/252.39 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X09 Xx1)))
% 253.61/253.96 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X09 Xx1)
% 253.61/253.96 Found ((and_rect0 (X09 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X09 Xx1)
% 253.61/253.96 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X09 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X09 Xx1)
% 253.61/253.96 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X09 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X09 Xx1)
% 253.61/253.96 Found x4:(X09 Xx1)
% 253.61/253.96 Instantiate: X09:=(cK x5):(a->Prop)
% 253.61/253.96 Found x4 as proof of (X08 Xx1)
% 253.61/253.96 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X08 Xx1)
% 253.61/253.96 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X08 Xx1))
% 253.61/253.96 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X08 Xx1)))
% 253.61/253.96 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X08 Xx1)
% 253.61/253.96 Found ((and_rect0 (X08 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X08 Xx1)
% 253.61/253.96 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X08 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X08 Xx1)
% 253.61/253.96 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X08 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X08 Xx1)
% 253.61/253.96 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 253.61/253.96 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 253.61/253.96 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 253.61/253.96 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 253.61/253.96 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X010) Xx0)))
% 253.61/253.96 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 253.61/253.96 Found ((and_rect0 ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 253.61/253.96 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 253.61/253.96 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X010) Xx0)
% 253.61/253.96 Found x4:(X09 Xx1)
% 253.61/253.96 Found x4 as proof of (X08 Xx1)
% 253.61/253.96 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X08 Xx1)
% 253.61/253.96 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X08 Xx1))
% 253.61/253.96 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X08 Xx1)))
% 253.61/253.96 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X08 Xx1)
% 254.29/254.68 Found ((and_rect0 (X08 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X08 Xx1)
% 254.29/254.68 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X08 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X08 Xx1)
% 254.29/254.68 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X08 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X08 Xx1)
% 254.29/254.68 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 254.29/254.68 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 254.29/254.68 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 254.29/254.68 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 254.29/254.68 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X09) Xx0)))
% 254.29/254.68 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 254.29/254.68 Found ((and_rect0 ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 254.29/254.68 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 254.29/254.68 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 254.29/254.68 Found x6:(X09 Xx1)
% 254.29/254.68 Instantiate: X08:=X09:(a->Prop)
% 254.29/254.68 Found (fun (x6:(X09 Xx1))=> x6) as proof of (X08 Xx1)
% 254.29/254.68 Found (fun (Xx1:a) (x6:(X09 Xx1))=> x6) as proof of ((X09 Xx1)->(X08 Xx1))
% 254.29/254.68 Found (fun (Xx1:a) (x6:(X09 Xx1))=> x6) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 254.29/254.68 Found ((x3110 (fun (Xx1:a) (x6:(X09 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X08) Xx0)
% 254.29/254.68 Found (((x311 X08) (fun (Xx1:a) (x6:(X09 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X08) Xx0)
% 254.29/254.68 Found ((((x3 x4) X08) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X08) Xx0)
% 254.29/254.68 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> ((((x3 x4) X08) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))))) as proof of ((cK X08) Xx0)
% 254.29/254.68 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 254.29/254.68 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 254.29/254.68 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 254.29/254.68 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 254.29/254.68 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X010) Xx0)))
% 254.89/255.23 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 254.89/255.23 Found ((and_rect0 ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 254.89/255.23 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 254.89/255.23 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 254.89/255.23 Found x6:(X010 Xx1)
% 254.89/255.23 Instantiate: X09:=X010:(a->Prop)
% 254.89/255.23 Found (fun (x6:(X010 Xx1))=> x6) as proof of (X09 Xx1)
% 254.89/255.23 Found (fun (Xx1:a) (x6:(X010 Xx1))=> x6) as proof of ((X010 Xx1)->(X09 Xx1))
% 254.89/255.23 Found (fun (Xx1:a) (x6:(X010 Xx1))=> x6) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 254.89/255.23 Found ((x3120 (fun (Xx1:a) (x6:(X010 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X09) Xx0)
% 254.89/255.23 Found (((x312 X09) (fun (Xx1:a) (x6:(X010 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X09) Xx0)
% 254.89/255.23 Found ((((x3 x4) X09) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X09) Xx0)
% 254.89/255.23 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> ((((x3 x4) X09) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))))) as proof of ((cK X09) Xx0)
% 254.89/255.23 Found x4:(X010 Xx1)
% 254.89/255.23 Instantiate: X010:=(cK x5):(a->Prop)
% 254.89/255.23 Found x4 as proof of (X09 Xx1)
% 254.89/255.23 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X09 Xx1)
% 254.89/255.23 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X09 Xx1))
% 254.89/255.23 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X09 Xx1)))
% 254.89/255.23 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X09 Xx1)
% 254.89/255.23 Found ((and_rect0 (X09 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X09 Xx1)
% 254.89/255.23 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X09 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X09 Xx1)
% 254.89/255.23 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X09 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X09 Xx1)
% 254.89/255.23 Found x4:(X010 Xx1)
% 254.89/255.23 Found x4 as proof of (X09 Xx1)
% 254.89/255.23 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X09 Xx1)
% 254.89/255.23 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X09 Xx1))
% 254.89/255.23 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X09 Xx1)))
% 256.62/256.97 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X09 Xx1)
% 256.62/256.97 Found ((and_rect0 (X09 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X09 Xx1)
% 256.62/256.97 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X09 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X09 Xx1)
% 256.62/256.97 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X09 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X09 Xx1)
% 256.62/256.97 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 256.62/256.97 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 256.62/256.97 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 256.62/256.97 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 256.62/256.97 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X09) Xx0)))
% 256.62/256.97 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 256.62/256.97 Found ((and_rect0 ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 256.62/256.97 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 256.62/256.97 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X09) Xx0)
% 256.62/256.97 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 256.62/256.97 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 256.62/256.97 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 256.62/256.97 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 256.62/256.97 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X010) Xx0)))
% 256.62/256.97 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 256.62/256.97 Found ((and_rect0 ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 256.62/256.97 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 256.62/256.97 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X010) Xx0)
% 256.62/256.97 Found x4:(X010 Xx1)
% 256.62/256.97 Instantiate: X010:=(cK x5):(a->Prop)
% 256.62/256.97 Found x4 as proof of (X09 Xx1)
% 256.62/256.97 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X09 Xx1)
% 256.62/256.97 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X09 Xx1))
% 256.62/256.97 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X09 Xx1)))
% 256.62/256.97 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X09 Xx1)
% 257.04/257.45 Found ((and_rect0 (X09 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X09 Xx1)
% 257.04/257.45 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X09 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X09 Xx1)
% 257.04/257.45 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X09 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X09 Xx1)
% 257.04/257.45 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 257.04/257.45 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 257.04/257.45 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 257.04/257.45 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 257.04/257.45 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X010) Xx0)))
% 257.04/257.45 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 257.04/257.45 Found ((and_rect0 ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 257.04/257.45 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 257.04/257.45 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 257.04/257.45 Found x6:(X010 Xx1)
% 257.04/257.45 Instantiate: X09:=X010:(a->Prop)
% 257.04/257.45 Found (fun (x6:(X010 Xx1))=> x6) as proof of (X09 Xx1)
% 257.04/257.45 Found (fun (Xx1:a) (x6:(X010 Xx1))=> x6) as proof of ((X010 Xx1)->(X09 Xx1))
% 257.04/257.45 Found (fun (Xx1:a) (x6:(X010 Xx1))=> x6) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 257.04/257.45 Found ((x3120 (fun (Xx1:a) (x6:(X010 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X09) Xx0)
% 257.04/257.45 Found (((x312 X09) (fun (Xx1:a) (x6:(X010 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X09) Xx0)
% 257.04/257.45 Found ((((x3 x4) X09) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X09) Xx0)
% 257.04/257.45 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> ((((x3 x4) X09) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))))) as proof of ((cK X09) Xx0)
% 257.04/257.45 Found x4:(X010 Xx1)
% 257.04/257.45 Found x4 as proof of (X09 Xx1)
% 257.04/257.45 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X09 Xx1)
% 257.04/257.45 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X09 Xx1))
% 257.04/257.45 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X09 Xx1)))
% 258.38/258.78 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X09 Xx1)
% 258.38/258.78 Found ((and_rect0 (X09 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X09 Xx1)
% 258.38/258.78 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X09 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X09 Xx1)
% 258.38/258.78 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X09 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X09 Xx1)
% 258.38/258.78 Found x4:(X09 Xx1)
% 258.38/258.78 Instantiate: X09:=(cK x5):(a->Prop)
% 258.38/258.78 Found x4 as proof of (X08 Xx1)
% 258.38/258.78 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X08 Xx1)
% 258.38/258.78 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X08 Xx1))
% 258.38/258.78 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X08 Xx1)))
% 258.38/258.78 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X08 Xx1)
% 258.38/258.78 Found ((and_rect0 (X08 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X08 Xx1)
% 258.38/258.78 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X08 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X08 Xx1)
% 258.38/258.78 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X08 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X08 Xx1)
% 258.38/258.78 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 258.38/258.78 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 258.38/258.78 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 258.38/258.78 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 258.38/258.78 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X010) Xx0)))
% 258.38/258.78 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 258.38/258.78 Found ((and_rect0 ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 258.38/258.78 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 258.38/258.78 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X010) Xx0)
% 258.38/258.78 Found x4:(X09 Xx1)
% 258.38/258.78 Found x4 as proof of (X08 Xx1)
% 258.38/258.78 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X08 Xx1)
% 258.38/258.78 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X08 Xx1))
% 258.38/258.78 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X08 Xx1)))
% 258.38/258.78 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X08 Xx1)
% 258.38/258.78 Found ((and_rect0 (X08 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X08 Xx1)
% 259.06/259.45 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X08 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X08 Xx1)
% 259.06/259.45 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X08 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X08 Xx1)
% 259.06/259.45 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 259.06/259.45 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 259.06/259.45 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 259.06/259.45 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 259.06/259.45 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X09) Xx0)))
% 259.06/259.45 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 259.06/259.45 Found ((and_rect0 ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 259.06/259.45 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 259.06/259.45 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 259.06/259.45 Found x6:(X09 Xx1)
% 259.06/259.45 Instantiate: X08:=X09:(a->Prop)
% 259.06/259.45 Found (fun (x6:(X09 Xx1))=> x6) as proof of (X08 Xx1)
% 259.06/259.45 Found (fun (Xx1:a) (x6:(X09 Xx1))=> x6) as proof of ((X09 Xx1)->(X08 Xx1))
% 259.06/259.45 Found (fun (Xx1:a) (x6:(X09 Xx1))=> x6) as proof of (forall (Xx:a), ((X09 Xx)->(X08 Xx)))
% 259.06/259.45 Found ((x3110 (fun (Xx1:a) (x6:(X09 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X08) Xx0)
% 259.06/259.45 Found (((x311 X08) (fun (Xx1:a) (x6:(X09 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X08) Xx0)
% 259.06/259.45 Found ((((x3 x4) X08) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X08) Xx0)
% 259.06/259.45 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> ((((x3 x4) X08) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))))) as proof of ((cK X08) Xx0)
% 259.06/259.45 Found x4:(X010 Xx1)
% 259.06/259.45 Instantiate: X010:=(cK x5):(a->Prop)
% 259.06/259.45 Found x4 as proof of (X09 Xx1)
% 259.06/259.45 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X09 Xx1)
% 259.06/259.45 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X09 Xx1))
% 259.06/259.45 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X09 Xx1)))
% 259.06/259.45 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X09 Xx1)
% 259.52/259.89 Found ((and_rect0 (X09 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X09 Xx1)
% 259.52/259.89 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X09 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X09 Xx1)
% 259.52/259.89 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X09 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X09 Xx1)
% 259.52/259.89 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 259.52/259.89 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 259.52/259.89 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 259.52/259.89 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X09) Xx0))
% 259.52/259.89 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X09) Xx0)))
% 259.52/259.89 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 259.52/259.89 Found ((and_rect0 ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 259.52/259.89 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X09) Xx0)
% 259.52/259.89 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X09) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X09) Xx0)
% 259.52/259.89 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 259.52/259.89 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 259.52/259.89 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 259.52/259.89 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 259.52/259.89 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X010) Xx0)))
% 259.52/259.89 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 259.52/259.89 Found ((and_rect0 ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 259.52/259.89 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 259.52/259.89 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 259.52/259.89 Found x6:(X010 Xx1)
% 259.52/259.89 Instantiate: X09:=X010:(a->Prop)
% 259.52/259.89 Found (fun (x6:(X010 Xx1))=> x6) as proof of (X09 Xx1)
% 259.52/259.89 Found (fun (Xx1:a) (x6:(X010 Xx1))=> x6) as proof of ((X010 Xx1)->(X09 Xx1))
% 259.52/259.89 Found (fun (Xx1:a) (x6:(X010 Xx1))=> x6) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 259.52/259.89 Found ((x3120 (fun (Xx1:a) (x6:(X010 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X09) Xx0)
% 259.52/259.89 Found (((x312 X09) (fun (Xx1:a) (x6:(X010 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X09) Xx0)
% 261.10/261.48 Found ((((x3 x4) X09) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X09) Xx0)
% 261.10/261.48 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> ((((x3 x4) X09) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))))) as proof of ((cK X09) Xx0)
% 261.10/261.48 Found x4:(X010 Xx1)
% 261.10/261.48 Found x4 as proof of (X09 Xx1)
% 261.10/261.48 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X09 Xx1)
% 261.10/261.48 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X09 Xx1))
% 261.10/261.48 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X09 Xx1)))
% 261.10/261.48 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X09 Xx1)
% 261.10/261.48 Found ((and_rect0 (X09 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X09 Xx1)
% 261.10/261.48 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X09 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X09 Xx1)
% 261.10/261.48 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X09 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X09 Xx1)
% 261.10/261.48 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 261.10/261.48 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 261.10/261.48 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 261.10/261.48 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 261.10/261.48 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X010) Xx0)))
% 261.10/261.48 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 261.10/261.48 Found ((and_rect0 ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 261.10/261.48 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 261.10/261.48 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X010) Xx0)
% 261.10/261.48 Found x4:(X010 Xx1)
% 261.10/261.48 Instantiate: X010:=(cK x5):(a->Prop)
% 261.10/261.48 Found x4 as proof of (X09 Xx1)
% 261.10/261.48 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X09 Xx1)
% 261.10/261.48 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X09 Xx1))
% 261.10/261.48 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X09 Xx1)))
% 261.10/261.48 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X09 Xx1)
% 261.78/262.18 Found ((and_rect0 (X09 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X09 Xx1)
% 261.78/262.18 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X09 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X09 Xx1)
% 261.78/262.18 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X09 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X09 Xx1)
% 261.78/262.18 Found x4:(X09 Xx1)
% 261.78/262.18 Instantiate: X09:=(cK x5):(a->Prop)
% 261.78/262.18 Found x4 as proof of (X08 Xx1)
% 261.78/262.18 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X08 Xx1)
% 261.78/262.18 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X08 Xx1))
% 261.78/262.18 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X08 Xx1)))
% 261.78/262.18 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X08 Xx1)
% 261.78/262.18 Found ((and_rect0 (X08 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X08 Xx1)
% 261.78/262.18 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X08 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X08 Xx1)
% 261.78/262.18 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X08 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X08 Xx1)
% 261.78/262.18 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 261.78/262.18 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 261.78/262.18 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 261.78/262.18 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 261.78/262.18 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X010) Xx0)))
% 261.78/262.18 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 261.78/262.18 Found ((and_rect0 ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 261.78/262.18 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 261.78/262.18 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 261.78/262.18 Found x6:(X010 Xx1)
% 261.78/262.18 Instantiate: X09:=X010:(a->Prop)
% 261.78/262.18 Found (fun (x6:(X010 Xx1))=> x6) as proof of (X09 Xx1)
% 261.78/262.18 Found (fun (Xx1:a) (x6:(X010 Xx1))=> x6) as proof of ((X010 Xx1)->(X09 Xx1))
% 261.78/262.18 Found (fun (Xx1:a) (x6:(X010 Xx1))=> x6) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 261.78/262.18 Found ((x3120 (fun (Xx1:a) (x6:(X010 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X09) Xx0)
% 261.78/262.18 Found (((x312 X09) (fun (Xx1:a) (x6:(X010 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X09) Xx0)
% 262.24/262.60 Found ((((x3 x4) X09) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X09) Xx0)
% 262.24/262.60 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> ((((x3 x4) X09) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))))) as proof of ((cK X09) Xx0)
% 262.24/262.60 Found x4:(X010 Xx1)
% 262.24/262.60 Found x4 as proof of (X09 Xx1)
% 262.24/262.60 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X09 Xx1)
% 262.24/262.60 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X09 Xx1))
% 262.24/262.60 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X09 Xx1)))
% 262.24/262.60 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X09 Xx1)
% 262.24/262.60 Found ((and_rect0 (X09 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X09 Xx1)
% 262.24/262.60 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X09 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X09 Xx1)
% 262.24/262.60 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X09 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X09 Xx1)
% 262.24/262.60 Found x4:(X09 Xx1)
% 262.24/262.60 Found x4 as proof of (X08 Xx1)
% 262.24/262.60 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X08 Xx1)
% 262.24/262.60 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X08 Xx1))
% 262.24/262.60 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X08 Xx1)))
% 262.24/262.60 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X08 Xx1)
% 262.24/262.60 Found ((and_rect0 (X08 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X08 Xx1)
% 262.24/262.60 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X08 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X08 Xx1)
% 262.24/262.60 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X08 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X08 Xx1)
% 262.24/262.60 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 262.24/262.60 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 262.24/262.60 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 262.24/262.60 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 262.24/262.60 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X010) Xx0)))
% 262.24/262.60 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 262.24/262.60 Found ((and_rect0 ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 263.80/264.14 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 263.80/264.14 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X010) Xx0)
% 263.80/264.14 Found x4:(X010 Xx1)
% 263.80/264.14 Instantiate: X010:=(cK x5):(a->Prop)
% 263.80/264.14 Found x4 as proof of (X09 Xx1)
% 263.80/264.14 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X09 Xx1)
% 263.80/264.14 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X09 Xx1))
% 263.80/264.14 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X09 Xx1)))
% 263.80/264.14 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X09 Xx1)
% 263.80/264.14 Found ((and_rect0 (X09 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X09 Xx1)
% 263.80/264.14 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X09 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X09 Xx1)
% 263.80/264.14 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X09 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X09 Xx1)
% 263.80/264.14 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 263.80/264.14 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 263.80/264.14 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 263.80/264.14 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 263.80/264.14 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X010) Xx0)))
% 263.80/264.14 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 263.80/264.14 Found ((and_rect0 ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 263.80/264.14 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 263.80/264.14 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 263.80/264.14 Found x6:(X010 Xx1)
% 263.80/264.14 Instantiate: X09:=X010:(a->Prop)
% 263.80/264.14 Found (fun (x6:(X010 Xx1))=> x6) as proof of (X09 Xx1)
% 263.80/264.14 Found (fun (Xx1:a) (x6:(X010 Xx1))=> x6) as proof of ((X010 Xx1)->(X09 Xx1))
% 263.80/264.14 Found (fun (Xx1:a) (x6:(X010 Xx1))=> x6) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 263.80/264.14 Found ((x3120 (fun (Xx1:a) (x6:(X010 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X09) Xx0)
% 263.80/264.14 Found (((x312 X09) (fun (Xx1:a) (x6:(X010 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X09) Xx0)
% 266.31/266.68 Found ((((x3 x4) X09) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X09) Xx0)
% 266.31/266.68 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> ((((x3 x4) X09) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))))) as proof of ((cK X09) Xx0)
% 266.31/266.68 Found x4:(X010 Xx1)
% 266.31/266.68 Found x4 as proof of (X09 Xx1)
% 266.31/266.68 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X09 Xx1)
% 266.31/266.68 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X09 Xx1))
% 266.31/266.68 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X09 Xx1)))
% 266.31/266.68 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X09 Xx1)
% 266.31/266.68 Found ((and_rect0 (X09 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X09 Xx1)
% 266.31/266.68 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X09 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X09 Xx1)
% 266.31/266.68 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X09 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X09 Xx1)
% 266.31/266.68 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 266.31/266.68 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 266.31/266.68 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 266.31/266.68 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 266.31/266.68 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X010) Xx0)))
% 266.31/266.68 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 266.31/266.68 Found ((and_rect0 ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 266.31/266.68 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 266.31/266.68 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X010) Xx0)
% 266.31/266.68 Found x4:(X011 Xx1)
% 266.31/266.68 Found x4 as proof of (X010 Xx1)
% 266.31/266.68 Found (fun (x4:(X011 Xx1))=> x4) as proof of (X010 Xx1)
% 266.31/266.68 Found (fun (Xx1:a) (x4:(X011 Xx1))=> x4) as proof of ((X011 Xx1)->(X010 Xx1))
% 266.31/266.68 Found (fun (Xx1:a) (x4:(X011 Xx1))=> x4) as proof of (forall (Xx:a), ((X011 Xx)->(X010 Xx)))
% 266.31/266.68 Found x4:(X010 Xx1)
% 266.31/266.68 Instantiate: X010:=(cK x5):(a->Prop)
% 266.31/266.68 Found x4 as proof of (X09 Xx1)
% 266.31/266.68 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X09 Xx1)
% 266.31/266.68 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X09 Xx1))
% 266.31/266.68 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X09 Xx1)))
% 269.70/270.10 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X09 Xx1)
% 269.70/270.10 Found ((and_rect0 (X09 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X09 Xx1)
% 269.70/270.10 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X09 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X09 Xx1)
% 269.70/270.10 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X09 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X09 Xx1)
% 269.70/270.10 Found x6:(X011 Xx1)
% 269.70/270.10 Found x6 as proof of (X010 Xx1)
% 269.70/270.10 Found (fun (x6:(X011 Xx1))=> x6) as proof of (X010 Xx1)
% 269.70/270.10 Found (fun (Xx1:a) (x6:(X011 Xx1))=> x6) as proof of ((X011 Xx1)->(X010 Xx1))
% 269.70/270.10 Found (fun (Xx1:a) (x6:(X011 Xx1))=> x6) as proof of (forall (Xx:a), ((X011 Xx)->(X010 Xx)))
% 269.70/270.10 Found x4:(X010 Xx1)
% 269.70/270.10 Found x4 as proof of (X09 Xx1)
% 269.70/270.10 Found (fun (x8:(x5 Xx0))=> x4) as proof of (X09 Xx1)
% 269.70/270.10 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((x5 Xx0)->(X09 Xx1))
% 269.70/270.10 Found (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4) as proof of ((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->(X09 Xx1)))
% 269.70/270.10 Found (and_rect00 (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X09 Xx1)
% 269.70/270.10 Found ((and_rect0 (X09 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X09 Xx1)
% 269.70/270.10 Found (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X09 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4)) as proof of (X09 Xx1)
% 269.70/270.10 Found (fun (x6:((and (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)))=> (((fun (P:Type) (x7:((forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))->((x5 Xx0)->P)))=> (((((and_rect (forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x5 Xx0)) P) x7) x6)) (X09 Xx1)) (fun (x7:(forall (Xx10:a), ((x5 Xx10)->((cK x5) Xx10)))) (x8:(x5 Xx0))=> x4))) as proof of (X09 Xx1)
% 269.70/270.10 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 269.70/270.10 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 269.70/270.10 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 269.70/270.10 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 269.70/270.10 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X010) Xx0)))
% 269.70/270.10 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 269.70/270.10 Found ((and_rect0 ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 269.70/270.10 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 269.70/270.10 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 269.70/270.10 Found x6:(X010 Xx1)
% 269.70/270.10 Instantiate: X09:=X010:(a->Prop)
% 269.70/270.10 Found (fun (x6:(X010 Xx1))=> x6) as proof of (X09 Xx1)
% 269.70/270.10 Found (fun (Xx1:a) (x6:(X010 Xx1))=> x6) as proof of ((X010 Xx1)->(X09 Xx1))
% 269.70/270.10 Found (fun (Xx1:a) (x6:(X010 Xx1))=> x6) as proof of (forall (Xx:a), ((X010 Xx)->(X09 Xx)))
% 269.70/270.10 Found ((x3120 (fun (Xx1:a) (x6:(X010 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X09) Xx0)
% 279.19/279.59 Found (((x312 X09) (fun (Xx1:a) (x6:(X010 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X09) Xx0)
% 279.19/279.59 Found ((((x3 x4) X09) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X09) Xx0)
% 279.19/279.59 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> ((((x3 x4) X09) (fun (Xx1:a) (x6:(x4 Xx1))=> x6)) (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK x4) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))))) as proof of ((cK X09) Xx0)
% 279.19/279.59 Found x6:(X011 Xx1)
% 279.19/279.59 Found x6 as proof of (X010 Xx1)
% 279.19/279.59 Found (fun (x6:(X011 Xx1))=> x6) as proof of (X010 Xx1)
% 279.19/279.59 Found (fun (Xx1:a) (x6:(X011 Xx1))=> x6) as proof of ((X011 Xx1)->(X010 Xx1))
% 279.19/279.59 Found (fun (Xx1:a) (x6:(X011 Xx1))=> x6) as proof of (forall (Xx:a), ((X011 Xx)->(X010 Xx)))
% 279.19/279.59 Found x6:(X011 Xx1)
% 279.19/279.59 Found x6 as proof of (X010 Xx1)
% 279.19/279.59 Found (fun (x6:(X011 Xx1))=> x6) as proof of (X010 Xx1)
% 279.19/279.59 Found (fun (Xx1:a) (x6:(X011 Xx1))=> x6) as proof of ((X011 Xx1)->(X010 Xx1))
% 279.19/279.59 Found (fun (Xx1:a) (x6:(X011 Xx1))=> x6) as proof of (forall (Xx:a), ((X011 Xx)->(X010 Xx)))
% 279.19/279.59 Found x6:(X011 Xx1)
% 279.19/279.59 Found x6 as proof of (X010 Xx1)
% 279.19/279.59 Found (fun (x6:(X011 Xx1))=> x6) as proof of (X010 Xx1)
% 279.19/279.59 Found (fun (Xx1:a) (x6:(X011 Xx1))=> x6) as proof of ((X011 Xx1)->(X010 Xx1))
% 279.19/279.59 Found (fun (Xx1:a) (x6:(X011 Xx1))=> x6) as proof of (forall (Xx:a), ((X011 Xx)->(X010 Xx)))
% 279.19/279.59 Found x6:(X011 Xx1)
% 279.19/279.59 Found x6 as proof of (X010 Xx1)
% 279.19/279.59 Found (fun (x6:(X011 Xx1))=> x6) as proof of (X010 Xx1)
% 279.19/279.59 Found (fun (Xx1:a) (x6:(X011 Xx1))=> x6) as proof of ((X011 Xx1)->(X010 Xx1))
% 279.19/279.59 Found (fun (Xx1:a) (x6:(X011 Xx1))=> x6) as proof of (forall (Xx:a), ((X011 Xx)->(X010 Xx)))
% 279.19/279.59 Found x6:(X011 Xx1)
% 279.19/279.59 Found x6 as proof of (X010 Xx1)
% 279.19/279.59 Found (fun (x6:(X011 Xx1))=> x6) as proof of (X010 Xx1)
% 279.19/279.59 Found (fun (Xx1:a) (x6:(X011 Xx1))=> x6) as proof of ((X011 Xx1)->(X010 Xx1))
% 279.19/279.59 Found (fun (Xx1:a) (x6:(X011 Xx1))=> x6) as proof of (forall (Xx:a), ((X011 Xx)->(X010 Xx)))
% 279.19/279.59 Found x6:(X011 Xx1)
% 279.19/279.59 Found x6 as proof of (X010 Xx1)
% 279.19/279.59 Found (fun (x6:(X011 Xx1))=> x6) as proof of (X010 Xx1)
% 279.19/279.59 Found (fun (Xx1:a) (x6:(X011 Xx1))=> x6) as proof of ((X011 Xx1)->(X010 Xx1))
% 279.19/279.59 Found (fun (Xx1:a) (x6:(X011 Xx1))=> x6) as proof of (forall (Xx:a), ((X011 Xx)->(X010 Xx)))
% 279.19/279.59 Found x6:(X011 Xx1)
% 279.19/279.59 Found x6 as proof of (X010 Xx1)
% 279.19/279.59 Found (fun (x6:(X011 Xx1))=> x6) as proof of (X010 Xx1)
% 279.19/279.59 Found (fun (Xx1:a) (x6:(X011 Xx1))=> x6) as proof of ((X011 Xx1)->(X010 Xx1))
% 279.19/279.59 Found (fun (Xx1:a) (x6:(X011 Xx1))=> x6) as proof of (forall (Xx:a), ((X011 Xx)->(X010 Xx)))
% 279.19/279.59 Found x6:(X011 Xx1)
% 279.19/279.59 Found x6 as proof of (X010 Xx1)
% 279.19/279.59 Found (fun (x6:(X011 Xx1))=> x6) as proof of (X010 Xx1)
% 279.19/279.59 Found (fun (Xx1:a) (x6:(X011 Xx1))=> x6) as proof of ((X011 Xx1)->(X010 Xx1))
% 279.19/279.59 Found (fun (Xx1:a) (x6:(X011 Xx1))=> x6) as proof of (forall (Xx:a), ((X011 Xx)->(X010 Xx)))
% 279.19/279.59 Found x60:=(x6 Xx0):((x4 Xx0)->((cK x4) Xx0))
% 279.19/279.59 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 279.19/279.59 Found (x6 Xx0) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 279.19/279.59 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((x4 Xx0)->((cK X010) Xx0))
% 279.19/279.59 Found (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)) as proof of ((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->((cK X010) Xx0)))
% 279.19/279.59 Found (and_rect00 (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 291.94/292.30 Found ((and_rect0 ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 291.94/292.30 Found (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0))) as proof of ((cK X010) Xx0)
% 291.94/292.30 Found (fun (x5:((and (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)))=> (((fun (P:Type) (x6:((forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))->((x4 Xx0)->P)))=> (((((and_rect (forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1)))) (x4 Xx0)) P) x6) x5)) ((cK X010) Xx0)) (fun (x6:(forall (Xx1:a), ((x4 Xx1)->((cK x4) Xx1))))=> (x6 Xx0)))) as proof of ((cK X010) Xx0)
% 291.94/292.30 Found x6:(X011 Xx1)
% 291.94/292.30 Found x6 as proof of (X010 Xx1)
% 291.94/292.30 Found (fun (x6:(X011 Xx1))=> x6) as proof of (X010 Xx1)
% 291.94/292.30 Found (fun (Xx1:a) (x6:(X011 Xx1))=> x6) as proof of ((X011 Xx1)->(X010 Xx1))
% 291.94/292.30 Found (fun (Xx1:a) (x6:(X011 Xx1))=> x6) as proof of (forall (Xx:a), ((X011 Xx)->(X010 Xx)))
% 291.94/292.30 Found x6:(X011 Xx1)
% 291.94/292.30 Found x6 as proof of (X010 Xx1)
% 291.94/292.30 Found (fun (x6:(X011 Xx1))=> x6) as proof of (X010 Xx1)
% 291.94/292.30 Found (fun (Xx1:a) (x6:(X011 Xx1))=> x6) as proof of ((X011 Xx1)->(X010 Xx1))
% 291.94/292.30 Found (fun (Xx1:a) (x6:(X011 Xx1))=> x6) as proof of (forall (Xx:a), ((X011 Xx)->(X010 Xx)))
% 291.94/292.30 Found x6:(X011 Xx1)
% 291.94/292.30 Found x6 as proof of (X010 Xx1)
% 291.94/292.30 Found (fun (x6:(X011 Xx1))=> x6) as proof of (X010 Xx1)
% 291.94/292.30 Found (fun (Xx1:a) (x6:(X011 Xx1))=> x6) as proof of ((X011 Xx1)->(X010 Xx1))
% 291.94/292.30 Found (fun (Xx1:a) (x6:(X011 Xx1))=> x6) as proof of (forall (Xx:a), ((X011 Xx)->(X010 Xx)))
% 291.94/292.30 Found x8:(X011 Xx1)
% 291.94/292.30 Found x8 as proof of (X010 Xx1)
% 291.94/292.30 Found (fun (x8:(X011 Xx1))=> x8) as proof of (X010 Xx1)
% 291.94/292.30 Found (fun (Xx1:a) (x8:(X011 Xx1))=> x8) as proof of ((X011 Xx1)->(X010 Xx1))
% 291.94/292.30 Found (fun (Xx1:a) (x8:(X011 Xx1))=> x8) as proof of (forall (Xx:a), ((X011 Xx)->(X010 Xx)))
% 291.94/292.30 Found x600:=(x60 x7):((cK x4) Xx0)
% 291.94/292.30 Found (x60 x7) as proof of ((cK X011) Xx0)
% 291.94/292.30 Found ((x6 Xx0) x7) as proof of ((cK X011) Xx0)
% 291.94/292.30 Found ((x6 Xx0) x7) as proof of ((cK X011) Xx0)
% 291.94/292.30 Found ((x6 Xx0) x7) as proof of ((cK X011) Xx0)
% 291.94/292.30 Found x6:(X011 Xx1)
% 291.94/292.30 Found x6 as proof of (X010 Xx1)
% 291.94/292.30 Found (fun (x6:(X011 Xx1))=> x6) as proof of (X010 Xx1)
% 291.94/292.30 Found (fun (Xx1:a) (x6:(X011 Xx1))=> x6) as proof of ((X011 Xx1)->(X010 Xx1))
% 291.94/292.30 Found (fun (Xx1:a) (x6:(X011 Xx1))=> x6) as proof of (forall (Xx:a), ((X011 Xx)->(X010 Xx)))
% 291.94/292.30 Found x8:(X011 Xx1)
% 291.94/292.30 Found x8 as proof of (X010 Xx1)
% 291.94/292.30 Found (fun (x8:(X011 Xx1))=> x8) as proof of (X010 Xx1)
% 291.94/292.30 Found (fun (Xx1:a) (x8:(X011 Xx1))=> x8) as proof of ((X011 Xx1)->(X010 Xx1))
% 291.94/292.30 Found (fun (Xx1:a) (x8:(X011 Xx1))=> x8) as proof of (forall (Xx:a), ((X011 Xx)->(X010 Xx)))
% 291.94/292.30 Found x600:=(x60 x7):((cK x4) Xx0)
% 291.94/292.30 Found (x60 x7) as proof of ((cK X011) Xx0)
% 291.94/292.30 Found ((x6 Xx0) x7) as proof of ((cK X011) Xx0)
% 291.94/292.30 Found ((x6 Xx0) x7) as proof of ((cK X011) Xx0)
% 291.94/292.30 Found ((x6 Xx0) x7) as proof of ((cK X011) Xx0)
% 291.94/292.30 Found x8:(X011 Xx1)
% 291.94/292.30 Found x8 as proof of (X010 Xx1)
% 291.94/292.30 Found (fun (x8:(X011 Xx1))=> x8) as proof of (X010 Xx1)
% 291.94/292.30 Found (fun (Xx1:a) (x8:(X011 Xx1))=> x8) as proof of ((X011 Xx1)->(X010 Xx1))
% 291.94/292.30 Found (fun (Xx1:a) (x8:(X011 Xx1))=> x8) as proof of (forall (Xx:a), ((X011 Xx)->(X010 Xx)))
% 291.94/292.30 Found x600:=(x60 x7):((cK x4) Xx0)
% 291.94/292.30 Found (x60 x7) as proof of ((cK X011) Xx0)
% 291.94/292.30 Found ((x6 Xx0) x7) as proof of ((cK X011) Xx0)
% 291.94/292.30 Found ((x6 Xx0) x7) as proof of ((cK X011) Xx0)
% 291.94/292.30 Found ((x6 Xx0) x7) as proof of ((cK X011) Xx0)
% 291.94/292.30 Found x8:(X011 Xx1)
% 291.94/292.30 Found x8 as proof of (X010 Xx1)
% 291.94/292.30 Found (fun (x8:(X011 Xx1))=> x8) as proof of (X010 Xx1)
% 291.94/292.30 Found (fun (Xx1:a) (x8:(X011 Xx1))=> x8) as proof of ((X011 Xx1)->(X010 Xx1))
% 291.94/292.30 Found (fun (Xx1:a) (x8:(X011 Xx1))=> x8) as proof of (forall (Xx:a), ((X011 Xx)->(X010 Xx)))
% 291.94/292.30 Found x600:=(x60 x7):((cK x3) Xx0)
% 291.94/292.30 Found (x60 x7) as proof of ((cK X011) Xx0)
% 291.94/292.30 Found ((x6 Xx0) x7) as proof of ((cK X011) Xx0)
% 291.94/292.30 Found ((x6 Xx0) x7) as proof of ((cK X011) Xx0)
% 291.94/292.30 Found ((x6 Xx0) x7) as proof of ((cK X011) Xx0)
% 291.94/292.30 Found x8:(X011 Xx1)
% 291.94/292.30 Found x8 as proof of (X010 Xx1)
% 291.94/292.30 Found (fun (x8:(X011 Xx1))=> x8) as proof of (X010 Xx1)
% 291.94/292.30 Found (fun (Xx1:a) (x8:(X011 Xx1))=> x8) as proof of ((X011 Xx1)->(X010 Xx1))
% 299.17/299.55 Found (fun (Xx1:a) (x8:(X011 Xx1))=> x8) as proof of (forall (Xx:a), ((X011 Xx)->(X010 Xx)))
% 299.17/299.55 Found x600:=(x60 x7):((cK x4) Xx0)
% 299.17/299.55 Found (x60 x7) as proof of ((cK X011) Xx0)
% 299.17/299.55 Found ((x6 Xx0) x7) as proof of ((cK X011) Xx0)
% 299.17/299.55 Found ((x6 Xx0) x7) as proof of ((cK X011) Xx0)
% 299.17/299.55 Found ((x6 Xx0) x7) as proof of ((cK X011) Xx0)
% 299.17/299.55 Found x8:(X011 Xx1)
% 299.17/299.55 Found x8 as proof of (X010 Xx1)
% 299.17/299.55 Found (fun (x8:(X011 Xx1))=> x8) as proof of (X010 Xx1)
% 299.17/299.55 Found (fun (Xx1:a) (x8:(X011 Xx1))=> x8) as proof of ((X011 Xx1)->(X010 Xx1))
% 299.17/299.55 Found (fun (Xx1:a) (x8:(X011 Xx1))=> x8) as proof of (forall (Xx:a), ((X011 Xx)->(X010 Xx)))
% 299.17/299.55 Found x600:=(x60 x7):((cK x4) Xx0)
% 299.17/299.55 Found (x60 x7) as proof of ((cK X011) Xx0)
% 299.17/299.55 Found ((x6 Xx0) x7) as proof of ((cK X011) Xx0)
% 299.17/299.55 Found ((x6 Xx0) x7) as proof of ((cK X011) Xx0)
% 299.17/299.55 Found ((x6 Xx0) x7) as proof of ((cK X011) Xx0)
% 299.17/299.55 Found x8:(X011 Xx1)
% 299.17/299.55 Found x8 as proof of (X010 Xx1)
% 299.17/299.55 Found (fun (x8:(X011 Xx1))=> x8) as proof of (X010 Xx1)
% 299.17/299.55 Found (fun (Xx1:a) (x8:(X011 Xx1))=> x8) as proof of ((X011 Xx1)->(X010 Xx1))
% 299.17/299.55 Found (fun (Xx1:a) (x8:(X011 Xx1))=> x8) as proof of (forall (Xx:a), ((X011 Xx)->(X010 Xx)))
% 299.17/299.55 Found x600:=(x60 x7):((cK x4) Xx0)
% 299.17/299.55 Found (x60 x7) as proof of ((cK X011) Xx0)
% 299.17/299.55 Found ((x6 Xx0) x7) as proof of ((cK X011) Xx0)
% 299.17/299.55 Found ((x6 Xx0) x7) as proof of ((cK X011) Xx0)
% 299.17/299.55 Found ((x6 Xx0) x7) as proof of ((cK X011) Xx0)
% 299.17/299.55 Found x8:(X011 Xx1)
% 299.17/299.55 Found x8 as proof of (X010 Xx1)
% 299.17/299.55 Found (fun (x8:(X011 Xx1))=> x8) as proof of (X010 Xx1)
% 299.17/299.55 Found (fun (Xx1:a) (x8:(X011 Xx1))=> x8) as proof of ((X011 Xx1)->(X010 Xx1))
% 299.17/299.55 Found (fun (Xx1:a) (x8:(X011 Xx1))=> x8) as proof of (forall (Xx:a), ((X011 Xx)->(X010 Xx)))
% 299.17/299.55 Found x600:=(x60 x7):((cK x4) Xx0)
% 299.17/299.55 Found (x60 x7) as proof of ((cK X011) Xx0)
% 299.17/299.55 Found ((x6 Xx0) x7) as proof of ((cK X011) Xx0)
% 299.17/299.55 Found ((x6 Xx0) x7) as proof of ((cK X011) Xx0)
% 299.17/299.55 Found ((x6 Xx0) x7) as proof of ((cK X011) Xx0)
% 299.17/299.55 Found x8:(X011 Xx1)
% 299.17/299.55 Found x8 as proof of (X010 Xx1)
% 299.17/299.55 Found (fun (x8:(X011 Xx1))=> x8) as proof of (X010 Xx1)
% 299.17/299.55 Found (fun (Xx1:a) (x8:(X011 Xx1))=> x8) as proof of ((X011 Xx1)->(X010 Xx1))
% 299.17/299.55 Found (fun (Xx1:a) (x8:(X011 Xx1))=> x8) as proof of (forall (Xx:a), ((X011 Xx)->(X010 Xx)))
% 299.17/299.55 Found x600:=(x60 x7):((cK x3) Xx0)
% 299.17/299.55 Found (x60 x7) as proof of ((cK X011) Xx0)
% 299.17/299.55 Found ((x6 Xx0) x7) as proof of ((cK X011) Xx0)
% 299.17/299.55 Found ((x6 Xx0) x7) as proof of ((cK X011) Xx0)
% 299.17/299.55 Found ((x6 Xx0) x7) as proof of ((cK X011) Xx0)
% 299.17/299.55 Found x8:(X011 Xx1)
% 299.17/299.55 Found x8 as proof of (X010 Xx1)
% 299.17/299.55 Found (fun (x8:(X011 Xx1))=> x8) as proof of (X010 Xx1)
% 299.17/299.55 Found (fun (Xx1:a) (x8:(X011 Xx1))=> x8) as proof of ((X011 Xx1)->(X010 Xx1))
% 299.17/299.55 Found (fun (Xx1:a) (x8:(X011 Xx1))=> x8) as proof of (forall (Xx:a), ((X011 Xx)->(X010 Xx)))
% 299.17/299.55 Found x600:=(x60 x7):((cK x4) Xx0)
% 299.17/299.55 Found (x60 x7) as proof of ((cK X011) Xx0)
% 299.17/299.55 Found ((x6 Xx0) x7) as proof of ((cK X011) Xx0)
% 299.17/299.55 Found ((x6 Xx0) x7) as proof of ((cK X011) Xx0)
% 299.17/299.55 Found ((x6 Xx0) x7) as proof of ((cK X011) Xx0)
% 299.17/299.55 Found x8:(X011 Xx1)
% 299.17/299.55 Found x8 as proof of (X010 Xx1)
% 299.17/299.55 Found (fun (x8:(X011 Xx1))=> x8) as proof of (X010 Xx1)
% 299.17/299.55 Found (fun (Xx1:a) (x8:(X011 Xx1))=> x8) as proof of ((X011 Xx1)->(X010 Xx1))
% 299.17/299.55 Found (fun (Xx1:a) (x8:(X011 Xx1))=> x8) as proof of (forall (Xx:a), ((X011 Xx)->(X010 Xx)))
% 299.17/299.55 Found x500:=(x50 x6):((cK x3) Xx0)
% 299.17/299.55 Found (x50 x6) as proof of ((cK X011) Xx0)
% 299.17/299.55 Found ((x5 Xx0) x6) as proof of ((cK X011) Xx0)
% 299.17/299.55 Found ((x5 Xx0) x6) as proof of ((cK X011) Xx0)
% 299.17/299.55 Found ((x5 Xx0) x6) as proof of ((cK X011) Xx0)
% 299.17/299.55 Found x8:(X011 Xx1)
% 299.17/299.55 Found x8 as proof of (X010 Xx1)
% 299.17/299.55 Found (fun (x8:(X011 Xx1))=> x8) as proof of (X010 Xx1)
% 299.17/299.55 Found (fun (Xx1:a) (x8:(X011 Xx1))=> x8) as proof of ((X011 Xx1)->(X010 Xx1))
% 299.17/299.55 Found (fun (Xx1:a) (x8:(X011 Xx1))=> x8) as proof of (forall (Xx:a), ((X011 Xx)->(X010 Xx)))
% 299.17/299.55 Found x600:=(x60 x7):((cK x4) Xx0)
% 299.17/299.55 Found (x60 x7) as proof of ((cK X011) Xx0)
% 299.17/299.55 Found ((x6 Xx0) x7) as proof of ((cK X011) Xx0)
% 299.17/299.55 Found ((x6 Xx0) x7) as proof of ((cK X011) Xx0)
% 299.17/299.55 Found ((x6 Xx0) x7) as proof of ((cK X011) Xx0)
% 299.17/299.55 Found x8:(X011 Xx1)
% 299.17/299.55 Found x8 as proof of (X010 Xx1)
% 299.17/299.55 Found (fun (x8:(X011 Xx1))=> x8) as proof of (X010 Xx1)
% 299.17/299.55 Found (fun (Xx1:a) (x8:(X011 Xx1))=> x8) as proof of ((X011 Xx1)->(X010 Xx1))
% 299.17/299.55 Found (fun (Xx1:a) (x8:(X011 Xx1))=> x8) as proof of (forall (Xx:a), (
%------------------------------------------------------------------------------