%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SEV252^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n106.star.cs.uiowa.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory   : 32286.75MB
% OS       : Linux 2.6.32-431.20.3.el6.x86_64
% CPULimit : 300s
% DateTime : Thu Jul 17 13:33:57 EDT 2014

% Result   : Timeout 300.00s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SEV252^5 : TPTP v6.1.0. Released v4.0.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n106.star.cs.uiowa.edu
% % Model    : x86_64 x86_64
% % CPU      : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% % Memory   : 32286.75MB
% % OS       : Linux 2.6.32-431.20.3.el6.x86_64
% % CPULimit : 300
% % DateTime : Thu Jul 17 08:37:46 CDT 2014
% % CPUTime  : 300.00 
% Python 2.7.5
% Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% FOF formula (forall (K:((fofType->Prop)->(fofType->Prop))), (((and (forall (Xx:(fofType->Prop)) (Xy:(fofType->Prop)), ((forall (Xx0:fofType), ((Xx Xx0)->(Xy Xx0)))->(forall (Xx0:fofType), (((K Xx) Xx0)->((K Xy) Xx0)))))) (forall (Xx:(fofType->Prop)) (Xy:(fofType->Prop)), ((forall (Xx0:fofType), ((Xx Xx0)->(Xy Xx0)))->(forall (Xx0:fofType), (((K Xx) Xx0)->((K Xy) Xx0))))))->(forall (Xx:fofType), ((iff ((K (fun (Xx0:fofType)=> ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx0)))))) Xx)) ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))))))) of role conjecture named cTHM2A_EXPANDED_pme
% Conjecture to prove = (forall (K:((fofType->Prop)->(fofType->Prop))), (((and (forall (Xx:(fofType->Prop)) (Xy:(fofType->Prop)), ((forall (Xx0:fofType), ((Xx Xx0)->(Xy Xx0)))->(forall (Xx0:fofType), (((K Xx) Xx0)->((K Xy) Xx0)))))) (forall (Xx:(fofType->Prop)) (Xy:(fofType->Prop)), ((forall (Xx0:fofType), ((Xx Xx0)->(Xy Xx0)))->(forall (Xx0:fofType), (((K Xx) Xx0)->((K Xy) Xx0))))))->(forall (Xx:fofType), ((iff ((K (fun (Xx0:fofType)=> ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx0)))))) Xx)) ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))))))):Prop
% Parameter fofType_DUMMY:fofType.
% We need to prove ['(forall (K:((fofType->Prop)->(fofType->Prop))), (((and (forall (Xx:(fofType->Prop)) (Xy:(fofType->Prop)), ((forall (Xx0:fofType), ((Xx Xx0)->(Xy Xx0)))->(forall (Xx0:fofType), (((K Xx) Xx0)->((K Xy) Xx0)))))) (forall (Xx:(fofType->Prop)) (Xy:(fofType->Prop)), ((forall (Xx0:fofType), ((Xx Xx0)->(Xy Xx0)))->(forall (Xx0:fofType), (((K Xx) Xx0)->((K Xy) Xx0))))))->(forall (Xx:fofType), ((iff ((K (fun (Xx0:fofType)=> ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx0)))))) Xx)) ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx))))))))']
% Parameter fofType:Type.
% Trying to prove (forall (K:((fofType->Prop)->(fofType->Prop))), (((and (forall (Xx:(fofType->Prop)) (Xy:(fofType->Prop)), ((forall (Xx0:fofType), ((Xx Xx0)->(Xy Xx0)))->(forall (Xx0:fofType), (((K Xx) Xx0)->((K Xy) Xx0)))))) (forall (Xx:(fofType->Prop)) (Xy:(fofType->Prop)), ((forall (Xx0:fofType), ((Xx Xx0)->(Xy Xx0)))->(forall (Xx0:fofType), (((K Xx) Xx0)->((K Xy) Xx0))))))->(forall (Xx:fofType), ((iff ((K (fun (Xx0:fofType)=> ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx0)))))) Xx)) ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx))))))))
% Found x3:(Xx0 Xx00)
% Found x3 as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (x3:(Xx0 Xx00))=> x3) as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (Xx00:fofType) (x3:(Xx0 Xx00))=> x3) as proof of ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00)))))
% Found (fun (Xx00:fofType) (x3:(Xx0 Xx00))=> x3) as proof of (forall (Xx00:fofType), ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))))
% Found x3:(Xx0 Xx00)
% Found x3 as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (x3:(Xx0 Xx00))=> x3) as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (Xx00:fofType) (x3:(Xx0 Xx00))=> x3) as proof of ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00)))))
% Found (fun (Xx00:fofType) (x3:(Xx0 Xx00))=> x3) as proof of (forall (Xx00:fofType), ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))))
% Found x3:(Xx0 Xx00)
% Found x3 as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (x3:(Xx0 Xx00))=> x3) as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (Xx00:fofType) (x3:(Xx0 Xx00))=> x3) as proof of ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00)))))
% Found (fun (Xx00:fofType) (x3:(Xx0 Xx00))=> x3) as proof of (forall (Xx00:fofType), ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))))
% Found x3:(Xx0 Xx00)
% Found x3 as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (x3:(Xx0 Xx00))=> x3) as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (Xx00:fofType) (x3:(Xx0 Xx00))=> x3) as proof of ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00)))))
% Found (fun (Xx00:fofType) (x3:(Xx0 Xx00))=> x3) as proof of (forall (Xx00:fofType), ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))))
% Found x3:(Xx0 Xx00)
% Found x3 as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (x3:(Xx0 Xx00))=> x3) as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (Xx00:fofType) (x3:(Xx0 Xx00))=> x3) as proof of ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00)))))
% Found (fun (Xx00:fofType) (x3:(Xx0 Xx00))=> x3) as proof of (forall (Xx00:fofType), ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))))
% Found x3:(Xx0 Xx00)
% Found x3 as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (x3:(Xx0 Xx00))=> x3) as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (Xx00:fofType) (x3:(Xx0 Xx00))=> x3) as proof of ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00)))))
% Found (fun (Xx00:fofType) (x3:(Xx0 Xx00))=> x3) as proof of (forall (Xx00:fofType), ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))))
% Found x3:(Xx0 Xx00)
% Found x3 as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (x3:(Xx0 Xx00))=> x3) as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (Xx00:fofType) (x3:(Xx0 Xx00))=> x3) as proof of ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00)))))
% Found (fun (Xx00:fofType) (x3:(Xx0 Xx00))=> x3) as proof of (forall (Xx00:fofType), ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))))
% Found x3:(Xx0 Xx00)
% Found x3 as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (x3:(Xx0 Xx00))=> x3) as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (Xx00:fofType) (x3:(Xx0 Xx00))=> x3) as proof of ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00)))))
% Found (fun (Xx00:fofType) (x3:(Xx0 Xx00))=> x3) as proof of (forall (Xx00:fofType), ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))))
% Found x5:(Xx0 Xx00)
% Found x5 as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (x5:(Xx0 Xx00))=> x5) as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (Xx00:fofType) (x5:(Xx0 Xx00))=> x5) as proof of ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00)))))
% Found (fun (Xx00:fofType) (x5:(Xx0 Xx00))=> x5) as proof of (forall (Xx00:fofType), ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))))
% Found x5:(Xx0 Xx00)
% Found x5 as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (x5:(Xx0 Xx00))=> x5) as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (Xx00:fofType) (x5:(Xx0 Xx00))=> x5) as proof of ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00)))))
% Found (fun (Xx00:fofType) (x5:(Xx0 Xx00))=> x5) as proof of (forall (Xx00:fofType), ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))))
% Found x3:(Xx0 Xx00)
% Found x3 as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (x3:(Xx0 Xx00))=> x3) as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (Xx00:fofType) (x3:(Xx0 Xx00))=> x3) as proof of ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00)))))
% Found (fun (Xx00:fofType) (x3:(Xx0 Xx00))=> x3) as proof of (forall (Xx00:fofType), ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))))
% Found x3:(Xx0 Xx00)
% Found x3 as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (x3:(Xx0 Xx00))=> x3) as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (Xx00:fofType) (x3:(Xx0 Xx00))=> x3) as proof of ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00)))))
% Found (fun (Xx00:fofType) (x3:(Xx0 Xx00))=> x3) as proof of (forall (Xx00:fofType), ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))))
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx0) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx0) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx0) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)) as proof of ((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->((K Xx0) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found ((and_rect1 ((K Xx0) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx0) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found (fun (x4:((and (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx0) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)))) as proof of ((K Xx0) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx0) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx0) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx0) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)) as proof of ((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->((K Xx0) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found ((and_rect1 ((K Xx0) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx0) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found (fun (x4:((and (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx0) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)))) as proof of ((K Xx0) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx0) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx0) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx0) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)) as proof of ((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->((K Xx0) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found ((and_rect1 ((K Xx0) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx0) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx0) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx0) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx0) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx0) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)) as proof of ((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->((K Xx0) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found ((and_rect1 ((K Xx0) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx0) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx0) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found x5:(Xx0 Xx00)
% Found x5 as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (x5:(Xx0 Xx00))=> x5) as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (Xx00:fofType) (x5:(Xx0 Xx00))=> x5) as proof of ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00)))))
% Found (fun (Xx00:fofType) (x5:(Xx0 Xx00))=> x5) as proof of (forall (Xx00:fofType), ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))))
% Found x5:(Xx0 Xx00)
% Found x5 as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (x5:(Xx0 Xx00))=> x5) as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (Xx00:fofType) (x5:(Xx0 Xx00))=> x5) as proof of ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00)))))
% Found (fun (Xx00:fofType) (x5:(Xx0 Xx00))=> x5) as proof of (forall (Xx00:fofType), ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))))
% Found x5:(Xx0 Xx00)
% Found x5 as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (x5:(Xx0 Xx00))=> x5) as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (Xx00:fofType) (x5:(Xx0 Xx00))=> x5) as proof of ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00)))))
% Found (fun (Xx00:fofType) (x5:(Xx0 Xx00))=> x5) as proof of (forall (Xx00:fofType), ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))))
% Found x5:(Xx0 Xx00)
% Found x5 as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (x5:(Xx0 Xx00))=> x5) as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (Xx00:fofType) (x5:(Xx0 Xx00))=> x5) as proof of ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00)))))
% Found (fun (Xx00:fofType) (x5:(Xx0 Xx00))=> x5) as proof of (forall (Xx00:fofType), ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))))
% Found x5:(Xx0 Xx00)
% Found x5 as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (x5:(Xx0 Xx00))=> x5) as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (Xx00:fofType) (x5:(Xx0 Xx00))=> x5) as proof of ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00)))))
% Found (fun (Xx00:fofType) (x5:(Xx0 Xx00))=> x5) as proof of (forall (Xx00:fofType), ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))))
% Found x5:(Xx0 Xx00)
% Found x5 as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (x5:(Xx0 Xx00))=> x5) as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (Xx00:fofType) (x5:(Xx0 Xx00))=> x5) as proof of ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00)))))
% Found (fun (Xx00:fofType) (x5:(Xx0 Xx00))=> x5) as proof of (forall (Xx00:fofType), ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))))
% Found x5:(Xx0 Xx00)
% Found x5 as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (x5:(Xx0 Xx00))=> x5) as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (Xx00:fofType) (x5:(Xx0 Xx00))=> x5) as proof of ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00)))))
% Found (fun (Xx00:fofType) (x5:(Xx0 Xx00))=> x5) as proof of (forall (Xx00:fofType), ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))))
% Found x5:(Xx0 Xx00)
% Found x5 as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (x5:(Xx0 Xx00))=> x5) as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (Xx00:fofType) (x5:(Xx0 Xx00))=> x5) as proof of ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00)))))
% Found (fun (Xx00:fofType) (x5:(Xx0 Xx00))=> x5) as proof of (forall (Xx00:fofType), ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))))
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx0) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx0) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx0) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)) as proof of ((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->((K Xx0) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found ((and_rect1 ((K Xx0) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx0) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found (fun (x4:((and (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx0) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)))) as proof of ((K Xx0) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx0) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx0) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx0) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)) as proof of ((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->((K Xx0) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found ((and_rect1 ((K Xx0) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx0) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found (fun (x4:((and (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx0) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)))) as proof of ((K Xx0) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx0) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx0) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx0) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)) as proof of ((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->((K Xx0) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found ((and_rect1 ((K Xx0) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx0) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx0) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx0) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx0) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx0) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)) as proof of ((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->((K Xx0) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found ((and_rect1 ((K Xx0) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx0) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx0) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx0) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx0) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx0) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)) as proof of ((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->((K Xx0) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found ((and_rect1 ((K Xx0) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx0) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found (fun (x4:((and (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx0) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)))) as proof of ((K Xx0) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx0) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx0) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx0) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)) as proof of ((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->((K Xx0) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found ((and_rect1 ((K Xx0) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx0) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found (fun (x4:((and (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx0) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)))) as proof of ((K Xx0) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx0) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx0) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx0) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)) as proof of ((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->((K Xx0) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found ((and_rect1 ((K Xx0) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx0) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx0) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx0) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx0) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx0) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)) as proof of ((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->((K Xx0) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found ((and_rect1 ((K Xx0) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx0) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx0) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx0) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx0) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx0) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)) as proof of ((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->((K Xx0) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found ((and_rect1 ((K Xx0) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx0) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found (fun (x4:((and (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx0) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)))) as proof of ((K Xx0) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx0) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx0) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx0) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)) as proof of ((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->((K Xx0) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found ((and_rect1 ((K Xx0) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx0) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found (fun (x4:((and (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx0) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)))) as proof of ((K Xx0) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx0) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx0) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx0) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)) as proof of ((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->((K Xx0) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found ((and_rect1 ((K Xx0) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx0) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx0) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx0) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx0) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx0) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)) as proof of ((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->((K Xx0) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found ((and_rect1 ((K Xx0) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx0) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx0) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found x7:(Xx0 Xx00)
% Found x7 as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (x7:(Xx0 Xx00))=> x7) as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (Xx00:fofType) (x7:(Xx0 Xx00))=> x7) as proof of ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00)))))
% Found (fun (Xx00:fofType) (x7:(Xx0 Xx00))=> x7) as proof of (forall (Xx00:fofType), ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx0) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx0) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx0) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx0) Xx)
% Found x7:(Xx0 Xx00)
% Found x7 as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (x7:(Xx0 Xx00))=> x7) as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (Xx00:fofType) (x7:(Xx0 Xx00))=> x7) as proof of ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00)))))
% Found (fun (Xx00:fofType) (x7:(Xx0 Xx00))=> x7) as proof of (forall (Xx00:fofType), ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx0) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx0) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx0) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx0) Xx)
% Found x50:=(x5 Xx):((x1 Xx)->((K x1) Xx))
% Found (x5 Xx) as proof of ((x1 Xx)->((K Xx0) Xx))
% Found (x5 Xx) as proof of ((x1 Xx)->((K Xx0) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x1 Xx00)->((K x1) Xx00))))=> (x5 Xx)) as proof of ((x1 Xx)->((K Xx0) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x1 Xx00)->((K x1) Xx00))))=> (x5 Xx)) as proof of ((forall (Xx00:fofType), ((x1 Xx00)->((K x1) Xx00)))->((x1 Xx)->((K Xx0) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx00:fofType), ((x1 Xx00)->((K x1) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found ((and_rect1 ((K Xx0) Xx)) (fun (x5:(forall (Xx00:fofType), ((x1 Xx00)->((K x1) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x5) x2)) ((K Xx0) Xx)) (fun (x5:(forall (Xx00:fofType), ((x1 Xx00)->((K x1) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x5) x2)) ((K Xx0) Xx)) (fun (x5:(forall (Xx00:fofType), ((x1 Xx00)->((K x1) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found x50:=(x5 Xx):((x1 Xx)->((K x1) Xx))
% Found (x5 Xx) as proof of ((x1 Xx)->((K Xx0) Xx))
% Found (x5 Xx) as proof of ((x1 Xx)->((K Xx0) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x1 Xx00)->((K x1) Xx00))))=> (x5 Xx)) as proof of ((x1 Xx)->((K Xx0) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x1 Xx00)->((K x1) Xx00))))=> (x5 Xx)) as proof of ((forall (Xx00:fofType), ((x1 Xx00)->((K x1) Xx00)))->((x1 Xx)->((K Xx0) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx00:fofType), ((x1 Xx00)->((K x1) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found ((and_rect1 ((K Xx0) Xx)) (fun (x5:(forall (Xx00:fofType), ((x1 Xx00)->((K x1) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x5) x2)) ((K Xx0) Xx)) (fun (x5:(forall (Xx00:fofType), ((x1 Xx00)->((K x1) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x5) x2)) ((K Xx0) Xx)) (fun (x5:(forall (Xx00:fofType), ((x1 Xx00)->((K x1) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found x5:(Xx0 Xx00)
% Found x5 as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (x5:(Xx0 Xx00))=> x5) as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (Xx00:fofType) (x5:(Xx0 Xx00))=> x5) as proof of ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00)))))
% Found (fun (Xx00:fofType) (x5:(Xx0 Xx00))=> x5) as proof of (forall (Xx00:fofType), ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))))
% Found x5:(Xx0 Xx00)
% Found x5 as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (x5:(Xx0 Xx00))=> x5) as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (Xx00:fofType) (x5:(Xx0 Xx00))=> x5) as proof of ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00)))))
% Found (fun (Xx00:fofType) (x5:(Xx0 Xx00))=> x5) as proof of (forall (Xx00:fofType), ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))))
% Found x5:(Xx0 Xx00)
% Found x5 as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (x5:(Xx0 Xx00))=> x5) as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (Xx00:fofType) (x5:(Xx0 Xx00))=> x5) as proof of ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00)))))
% Found (fun (Xx00:fofType) (x5:(Xx0 Xx00))=> x5) as proof of (forall (Xx00:fofType), ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))))
% Found x5:(Xx0 Xx00)
% Found x5 as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (x5:(Xx0 Xx00))=> x5) as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (Xx00:fofType) (x5:(Xx0 Xx00))=> x5) as proof of ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00)))))
% Found (fun (Xx00:fofType) (x5:(Xx0 Xx00))=> x5) as proof of (forall (Xx00:fofType), ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))))
% Found x7:(Xx0 Xx00)
% Found x7 as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (x7:(Xx0 Xx00))=> x7) as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (Xx00:fofType) (x7:(Xx0 Xx00))=> x7) as proof of ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00)))))
% Found (fun (Xx00:fofType) (x7:(Xx0 Xx00))=> x7) as proof of (forall (Xx00:fofType), ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx0) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx0) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx0) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx0) Xx)
% Found x7:(Xx0 Xx00)
% Found x7 as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (x7:(Xx0 Xx00))=> x7) as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (Xx00:fofType) (x7:(Xx0 Xx00))=> x7) as proof of ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00)))))
% Found (fun (Xx00:fofType) (x7:(Xx0 Xx00))=> x7) as proof of (forall (Xx00:fofType), ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx0) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx0) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx0) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx0) Xx)
% Found x3:(Xx00 Xx000)
% Found x3 as proof of (Xx0 Xx000)
% Found (fun (x3:(Xx00 Xx000))=> x3) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx00 Xx000))=> x3) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx00 Xx000))=> x3) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x3:(Xx00 Xx000)
% Found x3 as proof of (Xx0 Xx000)
% Found (fun (x3:(Xx00 Xx000))=> x3) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx00 Xx000))=> x3) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx00 Xx000))=> x3) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx0) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx0) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx0) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)) as proof of ((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->((K Xx0) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found ((and_rect1 ((K Xx0) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx0) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found (fun (x4:((and (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx0) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)))) as proof of ((K Xx0) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx0) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx0) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx0) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)) as proof of ((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->((K Xx0) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found ((and_rect1 ((K Xx0) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx0) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found (fun (x4:((and (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx0) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)))) as proof of ((K Xx0) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx0) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx0) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx0) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)) as proof of ((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->((K Xx0) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found ((and_rect1 ((K Xx0) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx0) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx0) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx0) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx0) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx0) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)) as proof of ((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->((K Xx0) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found ((and_rect1 ((K Xx0) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx0) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx0) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found x7:(Xx0 Xx00)
% Found x7 as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (x7:(Xx0 Xx00))=> x7) as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (Xx00:fofType) (x7:(Xx0 Xx00))=> x7) as proof of ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00)))))
% Found (fun (Xx00:fofType) (x7:(Xx0 Xx00))=> x7) as proof of (forall (Xx00:fofType), ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx0) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx0) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx0) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx0) Xx)
% Found x7:(Xx0 Xx00)
% Found x7 as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (x7:(Xx0 Xx00))=> x7) as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (Xx00:fofType) (x7:(Xx0 Xx00))=> x7) as proof of ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00)))))
% Found (fun (Xx00:fofType) (x7:(Xx0 Xx00))=> x7) as proof of (forall (Xx00:fofType), ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx0) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx0) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx0) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx0) Xx)
% Found x7:(Xx0 Xx00)
% Found x7 as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (x7:(Xx0 Xx00))=> x7) as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (Xx00:fofType) (x7:(Xx0 Xx00))=> x7) as proof of ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00)))))
% Found (fun (Xx00:fofType) (x7:(Xx0 Xx00))=> x7) as proof of (forall (Xx00:fofType), ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx0) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx0) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx0) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx0) Xx)
% Found x7:(Xx0 Xx00)
% Found x7 as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (x7:(Xx0 Xx00))=> x7) as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (Xx00:fofType) (x7:(Xx0 Xx00))=> x7) as proof of ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00)))))
% Found (fun (Xx00:fofType) (x7:(Xx0 Xx00))=> x7) as proof of (forall (Xx00:fofType), ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx0) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx0) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx0) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx0) Xx)
% Found x50:=(x5 Xx):((x1 Xx)->((K x1) Xx))
% Found (x5 Xx) as proof of ((x1 Xx)->((K Xx0) Xx))
% Found (x5 Xx) as proof of ((x1 Xx)->((K Xx0) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x1 Xx00)->((K x1) Xx00))))=> (x5 Xx)) as proof of ((x1 Xx)->((K Xx0) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x1 Xx00)->((K x1) Xx00))))=> (x5 Xx)) as proof of ((forall (Xx00:fofType), ((x1 Xx00)->((K x1) Xx00)))->((x1 Xx)->((K Xx0) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx00:fofType), ((x1 Xx00)->((K x1) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found ((and_rect1 ((K Xx0) Xx)) (fun (x5:(forall (Xx00:fofType), ((x1 Xx00)->((K x1) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x5) x2)) ((K Xx0) Xx)) (fun (x5:(forall (Xx00:fofType), ((x1 Xx00)->((K x1) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x5) x2)) ((K Xx0) Xx)) (fun (x5:(forall (Xx00:fofType), ((x1 Xx00)->((K x1) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found x50:=(x5 Xx):((x1 Xx)->((K x1) Xx))
% Found (x5 Xx) as proof of ((x1 Xx)->((K Xx0) Xx))
% Found (x5 Xx) as proof of ((x1 Xx)->((K Xx0) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x1 Xx00)->((K x1) Xx00))))=> (x5 Xx)) as proof of ((x1 Xx)->((K Xx0) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x1 Xx00)->((K x1) Xx00))))=> (x5 Xx)) as proof of ((forall (Xx00:fofType), ((x1 Xx00)->((K x1) Xx00)))->((x1 Xx)->((K Xx0) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx00:fofType), ((x1 Xx00)->((K x1) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found ((and_rect1 ((K Xx0) Xx)) (fun (x5:(forall (Xx00:fofType), ((x1 Xx00)->((K x1) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x5) x2)) ((K Xx0) Xx)) (fun (x5:(forall (Xx00:fofType), ((x1 Xx00)->((K x1) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x5) x2)) ((K Xx0) Xx)) (fun (x5:(forall (Xx00:fofType), ((x1 Xx00)->((K x1) Xx00))))=> (x5 Xx))) as proof of ((K Xx0) Xx)
% Found x7:(Xx0 Xx00)
% Found x7 as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (x7:(Xx0 Xx00))=> x7) as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (Xx00:fofType) (x7:(Xx0 Xx00))=> x7) as proof of ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00)))))
% Found (fun (Xx00:fofType) (x7:(Xx0 Xx00))=> x7) as proof of (forall (Xx00:fofType), ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))))
% Found x300:=(x30 x4):((K x1) Xx)
% Found (x30 x4) as proof of ((K Xx0) Xx)
% Found ((x3 Xx) x4) as proof of ((K Xx0) Xx)
% Found ((x3 Xx) x4) as proof of ((K Xx0) Xx)
% Found ((x3 Xx) x4) as proof of ((K Xx0) Xx)
% Found x7:(Xx0 Xx00)
% Found x7 as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (x7:(Xx0 Xx00))=> x7) as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (Xx00:fofType) (x7:(Xx0 Xx00))=> x7) as proof of ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00)))))
% Found (fun (Xx00:fofType) (x7:(Xx0 Xx00))=> x7) as proof of (forall (Xx00:fofType), ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))))
% Found x300:=(x30 x4):((K x1) Xx)
% Found (x30 x4) as proof of ((K Xx0) Xx)
% Found ((x3 Xx) x4) as proof of ((K Xx0) Xx)
% Found ((x3 Xx) x4) as proof of ((K Xx0) Xx)
% Found ((x3 Xx) x4) as proof of ((K Xx0) Xx)
% Found x7:(Xx0 Xx00)
% Found x7 as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (x7:(Xx0 Xx00))=> x7) as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (Xx00:fofType) (x7:(Xx0 Xx00))=> x7) as proof of ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00)))))
% Found (fun (Xx00:fofType) (x7:(Xx0 Xx00))=> x7) as proof of (forall (Xx00:fofType), ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))))
% Found x500:=(x50 x6):((K x1) Xx)
% Found (x50 x6) as proof of ((K Xx0) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx0) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx0) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx0) Xx)
% Found x7:(Xx0 Xx00)
% Found x7 as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (x7:(Xx0 Xx00))=> x7) as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (Xx00:fofType) (x7:(Xx0 Xx00))=> x7) as proof of ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00)))))
% Found (fun (Xx00:fofType) (x7:(Xx0 Xx00))=> x7) as proof of (forall (Xx00:fofType), ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))))
% Found x500:=(x50 x6):((K x1) Xx)
% Found (x50 x6) as proof of ((K Xx0) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx0) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx0) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx0) Xx)
% Found x3:(Xx00 Xx000)
% Found x3 as proof of (Xx0 Xx000)
% Found (fun (x3:(Xx00 Xx000))=> x3) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx00 Xx000))=> x3) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx00 Xx000))=> x3) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x3:(Xx00 Xx000)
% Found x3 as proof of (Xx0 Xx000)
% Found (fun (x3:(Xx00 Xx000))=> x3) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx00 Xx000))=> x3) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx00 Xx000))=> x3) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x3:(Xx00 Xx000)
% Found x3 as proof of (Xx0 Xx000)
% Found (fun (x3:(Xx00 Xx000))=> x3) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx00 Xx000))=> x3) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx00 Xx000))=> x3) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x3:(Xx00 Xx000)
% Found x3 as proof of (Xx0 Xx000)
% Found (fun (x3:(Xx00 Xx000))=> x3) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx00 Xx000))=> x3) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx00 Xx000))=> x3) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x3:(Xx00 Xx000)
% Found x3 as proof of (Xx0 Xx000)
% Found (fun (x3:(Xx00 Xx000))=> x3) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx00 Xx000))=> x3) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx00 Xx000))=> x3) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x3:(Xx00 Xx000)
% Found x3 as proof of (Xx0 Xx000)
% Found (fun (x3:(Xx00 Xx000))=> x3) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx00 Xx000))=> x3) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx00 Xx000))=> x3) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x7:(Xx0 Xx00)
% Found x7 as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (x7:(Xx0 Xx00))=> x7) as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (Xx00:fofType) (x7:(Xx0 Xx00))=> x7) as proof of ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00)))))
% Found (fun (Xx00:fofType) (x7:(Xx0 Xx00))=> x7) as proof of (forall (Xx00:fofType), ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx0) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx0) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx0) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx0) Xx)
% Found x7:(Xx0 Xx00)
% Found x7 as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (x7:(Xx0 Xx00))=> x7) as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (Xx00:fofType) (x7:(Xx0 Xx00))=> x7) as proof of ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00)))))
% Found (fun (Xx00:fofType) (x7:(Xx0 Xx00))=> x7) as proof of (forall (Xx00:fofType), ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx0) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx0) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx0) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx0) Xx)
% Found x5:(Xx00 Xx000)
% Found x5 as proof of (Xx0 Xx000)
% Found (fun (x5:(Xx00 Xx000))=> x5) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x5:(Xx00 Xx000)
% Found x5 as proof of (Xx0 Xx000)
% Found (fun (x5:(Xx00 Xx000))=> x5) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x7:(Xx0 Xx00)
% Found x7 as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (x7:(Xx0 Xx00))=> x7) as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (Xx00:fofType) (x7:(Xx0 Xx00))=> x7) as proof of ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00)))))
% Found (fun (Xx00:fofType) (x7:(Xx0 Xx00))=> x7) as proof of (forall (Xx00:fofType), ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))))
% Found x300:=(x30 x4):((K x1) Xx)
% Found (x30 x4) as proof of ((K Xx0) Xx)
% Found ((x3 Xx) x4) as proof of ((K Xx0) Xx)
% Found ((x3 Xx) x4) as proof of ((K Xx0) Xx)
% Found ((x3 Xx) x4) as proof of ((K Xx0) Xx)
% Found x7:(Xx0 Xx00)
% Found x7 as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (x7:(Xx0 Xx00))=> x7) as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (Xx00:fofType) (x7:(Xx0 Xx00))=> x7) as proof of ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00)))))
% Found (fun (Xx00:fofType) (x7:(Xx0 Xx00))=> x7) as proof of (forall (Xx00:fofType), ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))))
% Found x300:=(x30 x4):((K x1) Xx)
% Found (x30 x4) as proof of ((K Xx0) Xx)
% Found ((x3 Xx) x4) as proof of ((K Xx0) Xx)
% Found ((x3 Xx) x4) as proof of ((K Xx0) Xx)
% Found ((x3 Xx) x4) as proof of ((K Xx0) Xx)
% Found x7:(Xx0 Xx00)
% Found x7 as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (x7:(Xx0 Xx00))=> x7) as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (Xx00:fofType) (x7:(Xx0 Xx00))=> x7) as proof of ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00)))))
% Found (fun (Xx00:fofType) (x7:(Xx0 Xx00))=> x7) as proof of (forall (Xx00:fofType), ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))))
% Found x500:=(x50 x6):((K x1) Xx)
% Found (x50 x6) as proof of ((K Xx0) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx0) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx0) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx0) Xx)
% Found x7:(Xx0 Xx00)
% Found x7 as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (x7:(Xx0 Xx00))=> x7) as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (Xx00:fofType) (x7:(Xx0 Xx00))=> x7) as proof of ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00)))))
% Found (fun (Xx00:fofType) (x7:(Xx0 Xx00))=> x7) as proof of (forall (Xx00:fofType), ((Xx0 Xx00)->((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))))
% Found x500:=(x50 x6):((K x1) Xx)
% Found (x50 x6) as proof of ((K Xx0) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx0) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx0) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx0) Xx)
% Found x5:(Xx00 Xx000)
% Found x5 as proof of (Xx0 Xx000)
% Found (fun (x5:(Xx00 Xx000))=> x5) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x5:(Xx00 Xx000)
% Found x5 as proof of (Xx0 Xx000)
% Found (fun (x5:(Xx00 Xx000))=> x5) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x00:(x3 Xx0)
% Instantiate: x3:=(K Xx00):(fofType->Prop)
% Found x00 as proof of ((K Xx00) Xx0)
% Found x00:(x3 Xx0)
% Instantiate: x3:=(K Xx00):(fofType->Prop)
% Found x00 as proof of ((K Xx00) Xx0)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx)) as proof of ((forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000)))->((x3 Xx)->((K Xx00) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found ((and_rect1 ((K Xx00) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx)) as proof of ((forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000)))->((x3 Xx)->((K Xx00) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found ((and_rect1 ((K Xx00) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found x3:(Xx00 Xx000)
% Found x3 as proof of (Xx0 Xx000)
% Found (fun (x3:(Xx00 Xx000))=> x3) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx00 Xx000))=> x3) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx00 Xx000))=> x3) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x3:(Xx00 Xx000)
% Found x3 as proof of (Xx0 Xx000)
% Found (fun (x3:(Xx00 Xx000))=> x3) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx00 Xx000))=> x3) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx00 Xx000))=> x3) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx00) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found ((and_rect1 ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx00) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx00) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found ((and_rect1 ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx00) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found ((and_rect1 ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx00) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx00) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found ((and_rect1 ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found x5:(Xx00 Xx000)
% Found x5 as proof of (Xx0 Xx000)
% Found (fun (x5:(Xx00 Xx000))=> x5) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x5:(Xx00 Xx000)
% Found x5 as proof of (Xx0 Xx000)
% Found (fun (x5:(Xx00 Xx000))=> x5) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x5:(Xx00 Xx000)
% Found x5 as proof of (Xx0 Xx000)
% Found (fun (x5:(Xx00 Xx000))=> x5) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x5:(Xx00 Xx000)
% Found x5 as proof of (Xx0 Xx000)
% Found (fun (x5:(Xx00 Xx000))=> x5) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x00:(x3 Xx0)
% Instantiate: x3:=(K Xx00):(fofType->Prop)
% Found x00 as proof of ((K Xx00) Xx0)
% Found x00:(x3 Xx0)
% Instantiate: x3:=(K Xx00):(fofType->Prop)
% Found x00 as proof of ((K Xx00) Xx0)
% Found x5:(Xx00 Xx000)
% Found x5 as proof of (Xx0 Xx000)
% Found (fun (x5:(Xx00 Xx000))=> x5) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x5:(Xx00 Xx000)
% Found x5 as proof of (Xx0 Xx000)
% Found (fun (x5:(Xx00 Xx000))=> x5) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x00:(x3 Xx0)
% Instantiate: x3:=(K Xx00):(fofType->Prop)
% Found x00 as proof of ((K Xx00) Xx0)
% Found x00:(x3 Xx0)
% Instantiate: x3:=(K Xx00):(fofType->Prop)
% Found x00 as proof of ((K Xx00) Xx0)
% Found x5:(Xx00 Xx000)
% Found x5 as proof of (Xx0 Xx000)
% Found (fun (x5:(Xx00 Xx000))=> x5) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x5:(Xx00 Xx000)
% Found x5 as proof of (Xx0 Xx000)
% Found (fun (x5:(Xx00 Xx000))=> x5) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x00:(x3 Xx0)
% Instantiate: x3:=(K Xx00):(fofType->Prop)
% Found x00 as proof of ((K Xx00) Xx0)
% Found x00:(x3 Xx0)
% Instantiate: x3:=(K Xx00):(fofType->Prop)
% Found x00 as proof of ((K Xx00) Xx0)
% Found x5:(Xx00 Xx000)
% Found x5 as proof of (Xx0 Xx000)
% Found (fun (x5:(Xx00 Xx000))=> x5) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x5:(Xx00 Xx000)
% Found x5 as proof of (Xx0 Xx000)
% Found (fun (x5:(Xx00 Xx000))=> x5) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx)) as proof of ((forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000)))->((x3 Xx)->((K Xx00) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found ((and_rect1 ((K Xx00) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found x5:(Xx00 Xx000)
% Instantiate: Xx0:=Xx00:(fofType->Prop)
% Found (fun (x5:(Xx00 Xx000))=> x5) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found ((x0010 (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx)))) as proof of ((K Xx0) Xx)
% Found (((x001 Xx0) (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx)))) as proof of ((K Xx0) Xx)
% Found ((((x00 x3) Xx0) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx)))) as proof of ((K Xx0) Xx)
% Found (fun (x4:((and (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)))=> ((((x00 x3) Xx0) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))))) as proof of ((K Xx0) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx)) as proof of ((forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000)))->((x3 Xx)->((K Xx00) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found ((and_rect1 ((K Xx00) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found x5:(Xx00 Xx000)
% Instantiate: Xx0:=Xx00:(fofType->Prop)
% Found (fun (x5:(Xx00 Xx000))=> x5) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found ((x1010 (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx)))) as proof of ((K Xx0) Xx)
% Found (((x101 Xx0) (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx)))) as proof of ((K Xx0) Xx)
% Found ((((x10 x3) Xx0) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx)))) as proof of ((K Xx0) Xx)
% Found (fun (x4:((and (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)))=> ((((x10 x3) Xx0) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))))) as proof of ((K Xx0) Xx)
% Found x00:(x1 Xx0)
% Instantiate: x1:=(K Xx00):(fofType->Prop)
% Found x00 as proof of ((K Xx00) Xx0)
% Found x00:(x1 Xx0)
% Instantiate: x1:=(K Xx00):(fofType->Prop)
% Found x00 as proof of ((K Xx00) Xx0)
% Found x5:(Xx00 Xx000)
% Found x5 as proof of (Xx0 Xx000)
% Found (fun (x5:(Xx00 Xx000))=> x5) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x5:(Xx00 Xx000)
% Found x5 as proof of (Xx0 Xx000)
% Found (fun (x5:(Xx00 Xx000))=> x5) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x5:(Xx00 Xx000)
% Found x5 as proof of (Xx0 Xx000)
% Found (fun (x5:(Xx00 Xx000))=> x5) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x5:(Xx00 Xx000)
% Found x5 as proof of (Xx0 Xx000)
% Found (fun (x5:(Xx00 Xx000))=> x5) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx)) as proof of ((forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000)))->((x3 Xx)->((K Xx00) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found ((and_rect1 ((K Xx00) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx)) as proof of ((forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000)))->((x3 Xx)->((K Xx00) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found ((and_rect1 ((K Xx00) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx)) as proof of ((forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000)))->((x3 Xx)->((K Xx00) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found ((and_rect1 ((K Xx00) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx)) as proof of ((forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000)))->((x3 Xx)->((K Xx00) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found ((and_rect1 ((K Xx00) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx)) as proof of ((forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000)))->((x3 Xx)->((K Xx00) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found ((and_rect1 ((K Xx00) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx)) as proof of ((forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000)))->((x3 Xx)->((K Xx00) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found ((and_rect1 ((K Xx00) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found x7:(Xx00 Xx000)
% Found x7 as proof of (Xx0 Xx000)
% Found (fun (x7:(Xx00 Xx000))=> x7) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found x7:(Xx00 Xx000)
% Found x7 as proof of (Xx0 Xx000)
% Found (fun (x7:(Xx00 Xx000))=> x7) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found x7:(Xx00 Xx000)
% Found x7 as proof of (Xx0 Xx000)
% Found (fun (x7:(Xx00 Xx000))=> x7) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found x7:(Xx00 Xx000)
% Found x7 as proof of (Xx0 Xx000)
% Found (fun (x7:(Xx00 Xx000))=> x7) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx00) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found ((and_rect1 ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx00) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx00) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found ((and_rect1 ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx00) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found ((and_rect1 ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx00) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx00) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found ((and_rect1 ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found x7:(Xx00 Xx000)
% Found x7 as proof of (Xx0 Xx000)
% Found (fun (x7:(Xx00 Xx000))=> x7) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found x7:(Xx00 Xx000)
% Found x7 as proof of (Xx0 Xx000)
% Found (fun (x7:(Xx00 Xx000))=> x7) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx00) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found ((and_rect1 ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx00) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found ((and_rect1 ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx00) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx00) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found ((and_rect1 ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx00) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx00) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found ((and_rect1 ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx00) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found ((and_rect1 ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx00) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx00) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found ((and_rect1 ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx00) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found ((and_rect1 ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx00) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found ((and_rect1 ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx00) Xx)
% Found x00:(x3 Xx0)
% Instantiate: x3:=(K Xx00):(fofType->Prop)
% Found x00 as proof of ((K Xx00) Xx0)
% Found x00:(x3 Xx0)
% Instantiate: x3:=(K Xx00):(fofType->Prop)
% Found x00 as proof of ((K Xx00) Xx0)
% Found x50:=(x5 Xx):((x1 Xx)->((K x1) Xx))
% Found (x5 Xx) as proof of ((x1 Xx)->((K Xx00) Xx))
% Found (x5 Xx) as proof of ((x1 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x5 Xx)) as proof of ((x1 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->((K Xx00) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found ((and_rect1 ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x5) x2)) ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x5) x2)) ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found x50:=(x5 Xx):((x1 Xx)->((K x1) Xx))
% Found (x5 Xx) as proof of ((x1 Xx)->((K Xx00) Xx))
% Found (x5 Xx) as proof of ((x1 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x5 Xx)) as proof of ((x1 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->((K Xx00) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found ((and_rect1 ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x5) x2)) ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x5) x2)) ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found x5:(Xx00 Xx000)
% Found x5 as proof of (Xx0 Xx000)
% Found (fun (x5:(Xx00 Xx000))=> x5) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x5:(Xx00 Xx000)
% Found x5 as proof of (Xx0 Xx000)
% Found (fun (x5:(Xx00 Xx000))=> x5) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx)) as proof of ((forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000)))->((x3 Xx)->((K Xx00) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found ((and_rect1 ((K Xx00) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found x5:(Xx00 Xx000)
% Instantiate: Xx0:=Xx00:(fofType->Prop)
% Found (fun (x5:(Xx00 Xx000))=> x5) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found ((x1010 (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx)))) as proof of ((K Xx0) Xx)
% Found (((x101 Xx0) (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx)))) as proof of ((K Xx0) Xx)
% Found ((((x10 x3) Xx0) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx)))) as proof of ((K Xx0) Xx)
% Found (fun (x4:((and (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)))=> ((((x10 x3) Xx0) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))))) as proof of ((K Xx0) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx)) as proof of ((forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000)))->((x3 Xx)->((K Xx00) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found ((and_rect1 ((K Xx00) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found x5:(Xx00 Xx000)
% Instantiate: Xx0:=Xx00:(fofType->Prop)
% Found (fun (x5:(Xx00 Xx000))=> x5) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found ((x0010 (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx)))) as proof of ((K Xx0) Xx)
% Found (((x001 Xx0) (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx)))) as proof of ((K Xx0) Xx)
% Found ((((x00 x3) Xx0) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx)))) as proof of ((K Xx0) Xx)
% Found (fun (x4:((and (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)))=> ((((x00 x3) Xx0) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))))) as proof of ((K Xx0) Xx)
% Found x00:(x1 Xx0)
% Instantiate: x1:=(K Xx1):(fofType->Prop)
% Found x00 as proof of ((K Xx1) Xx0)
% Found x00:(x1 Xx0)
% Instantiate: x1:=(K Xx1):(fofType->Prop)
% Found x00 as proof of ((K Xx1) Xx0)
% Found x00:(x1 Xx0)
% Instantiate: x1:=(K Xx00):(fofType->Prop)
% Found x00 as proof of ((K Xx00) Xx0)
% Found x00:(x1 Xx0)
% Instantiate: x1:=(K Xx00):(fofType->Prop)
% Found x00 as proof of ((K Xx00) Xx0)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx00) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found ((and_rect1 ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx00) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx00) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found ((and_rect1 ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx00) Xx)
% Found x5:(Xx00 Xx000)
% Found x5 as proof of (Xx0 Xx000)
% Found (fun (x5:(Xx00 Xx000))=> x5) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x5:(Xx00 Xx000)
% Found x5 as proof of (Xx0 Xx000)
% Found (fun (x5:(Xx00 Xx000))=> x5) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x5:(Xx00 Xx000)
% Found x5 as proof of (Xx0 Xx000)
% Found (fun (x5:(Xx00 Xx000))=> x5) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x5:(Xx00 Xx000)
% Found x5 as proof of (Xx0 Xx000)
% Found (fun (x5:(Xx00 Xx000))=> x5) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx)) as proof of ((forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000)))->((x3 Xx)->((K Xx00) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found ((and_rect1 ((K Xx00) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found x5:(Xx00 Xx000)
% Instantiate: Xx0:=Xx00:(fofType->Prop)
% Found (fun (x5:(Xx00 Xx000))=> x5) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found ((x1010 (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx)))) as proof of ((K Xx0) Xx)
% Found (((x101 Xx0) (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx)))) as proof of ((K Xx0) Xx)
% Found ((((x10 x3) Xx0) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx)))) as proof of ((K Xx0) Xx)
% Found (fun (x4:((and (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)))=> ((((x10 x3) Xx0) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))))) as proof of ((K Xx0) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx)) as proof of ((forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000)))->((x3 Xx)->((K Xx00) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found ((and_rect1 ((K Xx00) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found x5:(Xx00 Xx000)
% Instantiate: Xx0:=Xx00:(fofType->Prop)
% Found (fun (x5:(Xx00 Xx000))=> x5) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found ((x0010 (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx)))) as proof of ((K Xx0) Xx)
% Found (((x001 Xx0) (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx)))) as proof of ((K Xx0) Xx)
% Found ((((x00 x3) Xx0) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx)))) as proof of ((K Xx0) Xx)
% Found (fun (x4:((and (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)))=> ((((x00 x3) Xx0) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))))) as proof of ((K Xx0) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx)) as proof of ((forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000)))->((x3 Xx)->((K Xx00) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found ((and_rect1 ((K Xx00) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found x5:(Xx00 Xx000)
% Instantiate: Xx0:=Xx00:(fofType->Prop)
% Found (fun (x5:(Xx00 Xx000))=> x5) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found ((x1010 (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx)))) as proof of ((K Xx0) Xx)
% Found (((x101 Xx0) (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx)))) as proof of ((K Xx0) Xx)
% Found ((((x10 x3) Xx0) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx)))) as proof of ((K Xx0) Xx)
% Found (fun (x4:((and (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)))=> ((((x10 x3) Xx0) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))))) as proof of ((K Xx0) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx)) as proof of ((forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000)))->((x3 Xx)->((K Xx00) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found ((and_rect1 ((K Xx00) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found x5:(Xx00 Xx000)
% Instantiate: Xx0:=Xx00:(fofType->Prop)
% Found (fun (x5:(Xx00 Xx000))=> x5) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found ((x2010 (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx)))) as proof of ((K Xx0) Xx)
% Found (((x201 Xx0) (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx)))) as proof of ((K Xx0) Xx)
% Found ((((x20 x3) Xx0) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx)))) as proof of ((K Xx0) Xx)
% Found (fun (x4:((and (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)))=> ((((x20 x3) Xx0) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))))) as proof of ((K Xx0) Xx)
% Found x7:(Xx00 Xx000)
% Found x7 as proof of (Xx0 Xx000)
% Found (fun (x7:(Xx00 Xx000))=> x7) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found x7:(Xx00 Xx000)
% Found x7 as proof of (Xx0 Xx000)
% Found (fun (x7:(Xx00 Xx000))=> x7) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found x7:(Xx00 Xx000)
% Found x7 as proof of (Xx0 Xx000)
% Found (fun (x7:(Xx00 Xx000))=> x7) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found x7:(Xx00 Xx000)
% Found x7 as proof of (Xx0 Xx000)
% Found (fun (x7:(Xx00 Xx000))=> x7) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx)) as proof of ((forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000)))->((x3 Xx)->((K Xx00) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found ((and_rect1 ((K Xx00) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx)) as proof of ((forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000)))->((x3 Xx)->((K Xx00) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found ((and_rect1 ((K Xx00) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found x7:(Xx00 Xx000)
% Found x7 as proof of (Xx0 Xx000)
% Found (fun (x7:(Xx00 Xx000))=> x7) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found x7:(Xx00 Xx000)
% Found x7 as proof of (Xx0 Xx000)
% Found (fun (x7:(Xx00 Xx000))=> x7) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found x7:(Xx00 Xx000)
% Found x7 as proof of (Xx0 Xx000)
% Found (fun (x7:(Xx00 Xx000))=> x7) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found x7:(Xx00 Xx000)
% Found x7 as proof of (Xx0 Xx000)
% Found (fun (x7:(Xx00 Xx000))=> x7) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found x7:(Xx00 Xx000)
% Found x7 as proof of (Xx0 Xx000)
% Found (fun (x7:(Xx00 Xx000))=> x7) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found x7:(Xx00 Xx000)
% Found x7 as proof of (Xx0 Xx000)
% Found (fun (x7:(Xx00 Xx000))=> x7) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found x7:(Xx00 Xx000)
% Found x7 as proof of (Xx0 Xx000)
% Found (fun (x7:(Xx00 Xx000))=> x7) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found x7:(Xx00 Xx000)
% Found x7 as proof of (Xx0 Xx000)
% Found (fun (x7:(Xx00 Xx000))=> x7) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found x7:(Xx00 Xx000)
% Found x7 as proof of (Xx0 Xx000)
% Found (fun (x7:(Xx00 Xx000))=> x7) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found x7:(Xx00 Xx000)
% Found x7 as proof of (Xx0 Xx000)
% Found (fun (x7:(Xx00 Xx000))=> x7) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found x7:(Xx00 Xx000)
% Found x7 as proof of (Xx0 Xx000)
% Found (fun (x7:(Xx00 Xx000))=> x7) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found x7:(Xx00 Xx000)
% Found x7 as proof of (Xx0 Xx000)
% Found (fun (x7:(Xx00 Xx000))=> x7) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found x7:(Xx00 Xx000)
% Found x7 as proof of (Xx0 Xx000)
% Found (fun (x7:(Xx00 Xx000))=> x7) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found x7:(Xx00 Xx000)
% Found x7 as proof of (Xx0 Xx000)
% Found (fun (x7:(Xx00 Xx000))=> x7) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found x7:(Xx00 Xx000)
% Found x7 as proof of (Xx0 Xx000)
% Found (fun (x7:(Xx00 Xx000))=> x7) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x500:=(x50 x6):((K x1) Xx)
% Found (x50 x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found x7:(Xx00 Xx000)
% Found x7 as proof of (Xx0 Xx000)
% Found (fun (x7:(Xx00 Xx000))=> x7) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x500:=(x50 x6):((K x1) Xx)
% Found (x50 x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx00) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found ((and_rect1 ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx00) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx00) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found ((and_rect1 ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx00) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found ((and_rect1 ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx00) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found ((and_rect1 ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx00) Xx)
% Found x7:(Xx00 Xx000)
% Found x7 as proof of (Xx0 Xx000)
% Found (fun (x7:(Xx00 Xx000))=> x7) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x300:=(x30 x4):((K x1) Xx)
% Found (x30 x4) as proof of ((K Xx00) Xx)
% Found ((x3 Xx) x4) as proof of ((K Xx00) Xx)
% Found ((x3 Xx) x4) as proof of ((K Xx00) Xx)
% Found ((x3 Xx) x4) as proof of ((K Xx00) Xx)
% Found x7:(Xx00 Xx000)
% Found x7 as proof of (Xx0 Xx000)
% Found (fun (x7:(Xx00 Xx000))=> x7) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x300:=(x30 x4):((K x1) Xx)
% Found (x30 x4) as proof of ((K Xx00) Xx)
% Found ((x3 Xx) x4) as proof of ((K Xx00) Xx)
% Found ((x3 Xx) x4) as proof of ((K Xx00) Xx)
% Found ((x3 Xx) x4) as proof of ((K Xx00) Xx)
% Found x7:(Xx00 Xx000)
% Found x7 as proof of (Xx0 Xx000)
% Found (fun (x7:(Xx00 Xx000))=> x7) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x500:=(x50 x6):((K x1) Xx)
% Found (x50 x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found x7:(Xx00 Xx000)
% Found x7 as proof of (Xx0 Xx000)
% Found (fun (x7:(Xx00 Xx000))=> x7) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x500:=(x50 x6):((K x1) Xx)
% Found (x50 x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found x00:(x1 Xx0)
% Instantiate: x1:=(K Xx1):(fofType->Prop)
% Found x00 as proof of ((K Xx1) Xx0)
% Found x00:(x1 Xx0)
% Instantiate: x1:=(K Xx1):(fofType->Prop)
% Found x00 as proof of ((K Xx1) Xx0)
% Found x50:=(x5 Xx):((x1 Xx)->((K x1) Xx))
% Found (x5 Xx) as proof of ((x1 Xx)->((K Xx00) Xx))
% Found (x5 Xx) as proof of ((x1 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x5 Xx)) as proof of ((x1 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->((K Xx00) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found ((and_rect1 ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x5) x2)) ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x5) x2)) ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found x50:=(x5 Xx):((x1 Xx)->((K x1) Xx))
% Found (x5 Xx) as proof of ((x1 Xx)->((K Xx00) Xx))
% Found (x5 Xx) as proof of ((x1 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x5 Xx)) as proof of ((x1 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->((K Xx00) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found ((and_rect1 ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x5) x2)) ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x5) x2)) ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx00) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found ((and_rect1 ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx00) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx00) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found ((and_rect1 ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx00) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx00) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found ((and_rect1 ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx00) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx00) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found ((and_rect1 ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx00) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx00) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found ((and_rect1 ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx00) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx00) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found ((and_rect1 ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx00) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx)) as proof of ((forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000)))->((x3 Xx)->((K Xx00) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found ((and_rect1 ((K Xx00) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found x5:(Xx00 Xx000)
% Instantiate: Xx0:=Xx00:(fofType->Prop)
% Found (fun (x5:(Xx00 Xx000))=> x5) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found ((x1010 (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx)))) as proof of ((K Xx0) Xx)
% Found (((x101 Xx0) (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx)))) as proof of ((K Xx0) Xx)
% Found ((((x10 x3) Xx0) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx)))) as proof of ((K Xx0) Xx)
% Found (fun (x4:((and (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)))=> ((((x10 x3) Xx0) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))))) as proof of ((K Xx0) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx)) as proof of ((forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000)))->((x3 Xx)->((K Xx00) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found ((and_rect1 ((K Xx00) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found x5:(Xx00 Xx000)
% Instantiate: Xx0:=Xx00:(fofType->Prop)
% Found (fun (x5:(Xx00 Xx000))=> x5) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found ((x2010 (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx)))) as proof of ((K Xx0) Xx)
% Found (((x201 Xx0) (fun (Xx000:fofType) (x5:(Xx00 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx)))) as proof of ((K Xx0) Xx)
% Found ((((x20 x3) Xx0) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx)))) as proof of ((K Xx0) Xx)
% Found (fun (x4:((and (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)))=> ((((x20 x3) Xx0) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx000:fofType), ((x3 Xx000)->((K x3) Xx000))))=> (x5 Xx))))) as proof of ((K Xx0) Xx)
% Found x3:(Xx00 Xx000)
% Instantiate: Xx00:=(K x4):(fofType->Prop)
% Found x3 as proof of (Xx0 Xx000)
% Found (fun (x7:(x4 Xx))=> x3) as proof of (Xx0 Xx000)
% Found (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3) as proof of ((x4 Xx)->(Xx0 Xx000))
% Found (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3) as proof of ((forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))->((x4 Xx)->(Xx0 Xx000)))
% Found (and_rect10 (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3)) as proof of (Xx0 Xx000)
% Found ((and_rect1 (Xx0 Xx000)) (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3)) as proof of (Xx0 Xx000)
% Found (((fun (P:Type) (x6:((forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))->((x4 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x4 Xx)) P) x6) x5)) (Xx0 Xx000)) (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3)) as proof of (Xx0 Xx000)
% Found (fun (x5:((and (forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x4 Xx)))=> (((fun (P:Type) (x6:((forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))->((x4 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x4 Xx)) P) x6) x5)) (Xx0 Xx000)) (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3))) as proof of (Xx0 Xx000)
% Found x3:(Xx00 Xx000)
% Instantiate: Xx00:=(K x4):(fofType->Prop)
% Found x3 as proof of (Xx0 Xx000)
% Found (fun (x7:(x4 Xx))=> x3) as proof of (Xx0 Xx000)
% Found (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3) as proof of ((x4 Xx)->(Xx0 Xx000))
% Found (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3) as proof of ((forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))->((x4 Xx)->(Xx0 Xx000)))
% Found (and_rect10 (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3)) as proof of (Xx0 Xx000)
% Found ((and_rect1 (Xx0 Xx000)) (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3)) as proof of (Xx0 Xx000)
% Found (((fun (P:Type) (x6:((forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))->((x4 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x4 Xx)) P) x6) x5)) (Xx0 Xx000)) (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3)) as proof of (Xx0 Xx000)
% Found (fun (x5:((and (forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x4 Xx)))=> (((fun (P:Type) (x6:((forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))->((x4 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x4 Xx)) P) x6) x5)) (Xx0 Xx000)) (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3))) as proof of (Xx0 Xx000)
% Found x7:(Xx00 Xx000)
% Found x7 as proof of (Xx0 Xx000)
% Found (fun (x7:(Xx00 Xx000))=> x7) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found x7:(Xx00 Xx000)
% Found x7 as proof of (Xx0 Xx000)
% Found (fun (x7:(Xx00 Xx000))=> x7) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found x7:(Xx00 Xx000)
% Found x7 as proof of (Xx0 Xx000)
% Found (fun (x7:(Xx00 Xx000))=> x7) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found x7:(Xx00 Xx000)
% Found x7 as proof of (Xx0 Xx000)
% Found (fun (x7:(Xx00 Xx000))=> x7) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found x3:(Xx00 Xx000)
% Found x3 as proof of (Xx0 Xx000)
% Found (fun (x7:(x4 Xx))=> x3) as proof of (Xx0 Xx000)
% Found (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3) as proof of ((x4 Xx)->(Xx0 Xx000))
% Found (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3) as proof of ((forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))->((x4 Xx)->(Xx0 Xx000)))
% Found (and_rect10 (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3)) as proof of (Xx0 Xx000)
% Found ((and_rect1 (Xx0 Xx000)) (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3)) as proof of (Xx0 Xx000)
% Found (((fun (P:Type) (x6:((forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))->((x4 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x4 Xx)) P) x6) x5)) (Xx0 Xx000)) (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3)) as proof of (Xx0 Xx000)
% Found (fun (x5:((and (forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x4 Xx)))=> (((fun (P:Type) (x6:((forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))->((x4 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x4 Xx)) P) x6) x5)) (Xx0 Xx000)) (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3))) as proof of (Xx0 Xx000)
% Found x3:(Xx00 Xx000)
% Found x3 as proof of (Xx0 Xx000)
% Found (fun (x7:(x4 Xx))=> x3) as proof of (Xx0 Xx000)
% Found (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3) as proof of ((x4 Xx)->(Xx0 Xx000))
% Found (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3) as proof of ((forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))->((x4 Xx)->(Xx0 Xx000)))
% Found (and_rect10 (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3)) as proof of (Xx0 Xx000)
% Found ((and_rect1 (Xx0 Xx000)) (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3)) as proof of (Xx0 Xx000)
% Found (((fun (P:Type) (x6:((forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))->((x4 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x4 Xx)) P) x6) x5)) (Xx0 Xx000)) (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3)) as proof of (Xx0 Xx000)
% Found (fun (x5:((and (forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x4 Xx)))=> (((fun (P:Type) (x6:((forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))->((x4 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x4 Xx)) P) x6) x5)) (Xx0 Xx000)) (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3))) as proof of (Xx0 Xx000)
% Found x7:(Xx00 Xx000)
% Found x7 as proof of (Xx0 Xx000)
% Found (fun (x7:(Xx00 Xx000))=> x7) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found x7:(Xx00 Xx000)
% Found x7 as proof of (Xx0 Xx000)
% Found (fun (x7:(Xx00 Xx000))=> x7) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found x7:(Xx00 Xx000)
% Found x7 as proof of (Xx0 Xx000)
% Found (fun (x7:(Xx00 Xx000))=> x7) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x500:=(x50 x6):((K x1) Xx)
% Found (x50 x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found x7:(Xx00 Xx000)
% Found x7 as proof of (Xx0 Xx000)
% Found (fun (x7:(Xx00 Xx000))=> x7) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x500:=(x50 x6):((K x1) Xx)
% Found (x50 x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found x7:(Xx00 Xx000)
% Found x7 as proof of (Xx0 Xx000)
% Found (fun (x7:(Xx00 Xx000))=> x7) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x300:=(x30 x4):((K x1) Xx)
% Found (x30 x4) as proof of ((K Xx00) Xx)
% Found ((x3 Xx) x4) as proof of ((K Xx00) Xx)
% Found ((x3 Xx) x4) as proof of ((K Xx00) Xx)
% Found ((x3 Xx) x4) as proof of ((K Xx00) Xx)
% Found x7:(Xx00 Xx000)
% Found x7 as proof of (Xx0 Xx000)
% Found (fun (x7:(Xx00 Xx000))=> x7) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x300:=(x30 x4):((K x1) Xx)
% Found (x30 x4) as proof of ((K Xx00) Xx)
% Found ((x3 Xx) x4) as proof of ((K Xx00) Xx)
% Found ((x3 Xx) x4) as proof of ((K Xx00) Xx)
% Found ((x3 Xx) x4) as proof of ((K Xx00) Xx)
% Found x7:(Xx00 Xx000)
% Found x7 as proof of (Xx0 Xx000)
% Found (fun (x7:(Xx00 Xx000))=> x7) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x500:=(x50 x6):((K x1) Xx)
% Found (x50 x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found x7:(Xx00 Xx000)
% Found x7 as proof of (Xx0 Xx000)
% Found (fun (x7:(Xx00 Xx000))=> x7) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx00 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x500:=(x50 x6):((K x1) Xx)
% Found (x50 x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx00) Xx)
% Found x3:(Xx00 Xx000)
% Instantiate: Xx00:=(K x4):(fofType->Prop)
% Found x3 as proof of (Xx0 Xx000)
% Found (fun (x7:(x4 Xx))=> x3) as proof of (Xx0 Xx000)
% Found (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3) as proof of ((x4 Xx)->(Xx0 Xx000))
% Found (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3) as proof of ((forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))->((x4 Xx)->(Xx0 Xx000)))
% Found (and_rect10 (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3)) as proof of (Xx0 Xx000)
% Found ((and_rect1 (Xx0 Xx000)) (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3)) as proof of (Xx0 Xx000)
% Found (((fun (P:Type) (x6:((forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))->((x4 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x4 Xx)) P) x6) x5)) (Xx0 Xx000)) (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3)) as proof of (Xx0 Xx000)
% Found (fun (x5:((and (forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x4 Xx)))=> (((fun (P:Type) (x6:((forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))->((x4 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x4 Xx)) P) x6) x5)) (Xx0 Xx000)) (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3))) as proof of (Xx0 Xx000)
% Found x3:(Xx00 Xx000)
% Instantiate: Xx00:=(K x4):(fofType->Prop)
% Found x3 as proof of (Xx0 Xx000)
% Found (fun (x7:(x4 Xx))=> x3) as proof of (Xx0 Xx000)
% Found (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3) as proof of ((x4 Xx)->(Xx0 Xx000))
% Found (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3) as proof of ((forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))->((x4 Xx)->(Xx0 Xx000)))
% Found (and_rect10 (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3)) as proof of (Xx0 Xx000)
% Found ((and_rect1 (Xx0 Xx000)) (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3)) as proof of (Xx0 Xx000)
% Found (((fun (P:Type) (x6:((forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))->((x4 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x4 Xx)) P) x6) x5)) (Xx0 Xx000)) (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3)) as proof of (Xx0 Xx000)
% Found (fun (x5:((and (forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x4 Xx)))=> (((fun (P:Type) (x6:((forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))->((x4 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x4 Xx)) P) x6) x5)) (Xx0 Xx000)) (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3))) as proof of (Xx0 Xx000)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx00) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found ((and_rect1 ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx00) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx00) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx00) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found ((and_rect1 ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx00) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx00) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx00) Xx)
% Found x3:(Xx01 Xx000)
% Found x3 as proof of (Xx00 Xx000)
% Found (fun (x3:(Xx01 Xx000))=> x3) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx01 Xx000))=> x3) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx01 Xx000))=> x3) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x3:(Xx01 Xx000)
% Found x3 as proof of (Xx00 Xx000)
% Found (fun (x3:(Xx01 Xx000))=> x3) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx01 Xx000))=> x3) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx01 Xx000))=> x3) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x3:(Xx00 Xx000)
% Instantiate: Xx00:=(K x4):(fofType->Prop)
% Found x3 as proof of (Xx0 Xx000)
% Found (fun (x7:(x4 Xx))=> x3) as proof of (Xx0 Xx000)
% Found (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3) as proof of ((x4 Xx)->(Xx0 Xx000))
% Found (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3) as proof of ((forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))->((x4 Xx)->(Xx0 Xx000)))
% Found (and_rect10 (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3)) as proof of (Xx0 Xx000)
% Found ((and_rect1 (Xx0 Xx000)) (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3)) as proof of (Xx0 Xx000)
% Found (((fun (P:Type) (x6:((forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))->((x4 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x4 Xx)) P) x6) x5)) (Xx0 Xx000)) (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3)) as proof of (Xx0 Xx000)
% Found (fun (x5:((and (forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x4 Xx)))=> (((fun (P:Type) (x6:((forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))->((x4 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x4 Xx)) P) x6) x5)) (Xx0 Xx000)) (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3))) as proof of (Xx0 Xx000)
% Found x3:(Xx00 Xx000)
% Instantiate: Xx00:=(K x4):(fofType->Prop)
% Found x3 as proof of (Xx0 Xx000)
% Found (fun (x7:(x4 Xx))=> x3) as proof of (Xx0 Xx000)
% Found (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3) as proof of ((x4 Xx)->(Xx0 Xx000))
% Found (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3) as proof of ((forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))->((x4 Xx)->(Xx0 Xx000)))
% Found (and_rect10 (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3)) as proof of (Xx0 Xx000)
% Found ((and_rect1 (Xx0 Xx000)) (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3)) as proof of (Xx0 Xx000)
% Found (((fun (P:Type) (x6:((forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))->((x4 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x4 Xx)) P) x6) x5)) (Xx0 Xx000)) (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3)) as proof of (Xx0 Xx000)
% Found (fun (x5:((and (forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x4 Xx)))=> (((fun (P:Type) (x6:((forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))->((x4 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x4 Xx)) P) x6) x5)) (Xx0 Xx000)) (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3))) as proof of (Xx0 Xx000)
% Found x3:(Xx00 Xx000)
% Instantiate: Xx00:=(K x4):(fofType->Prop)
% Found x3 as proof of (Xx0 Xx000)
% Found (fun (x7:(x4 Xx))=> x3) as proof of (Xx0 Xx000)
% Found (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3) as proof of ((x4 Xx)->(Xx0 Xx000))
% Found (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3) as proof of ((forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))->((x4 Xx)->(Xx0 Xx000)))
% Found (and_rect10 (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3)) as proof of (Xx0 Xx000)
% Found ((and_rect1 (Xx0 Xx000)) (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3)) as proof of (Xx0 Xx000)
% Found (((fun (P:Type) (x6:((forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))->((x4 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x4 Xx)) P) x6) x5)) (Xx0 Xx000)) (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3)) as proof of (Xx0 Xx000)
% Found (fun (x5:((and (forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x4 Xx)))=> (((fun (P:Type) (x6:((forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))->((x4 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x4 Xx)) P) x6) x5)) (Xx0 Xx000)) (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3))) as proof of (Xx0 Xx000)
% Found x3:(Xx00 Xx000)
% Instantiate: Xx00:=(K x4):(fofType->Prop)
% Found x3 as proof of (Xx0 Xx000)
% Found (fun (x7:(x4 Xx))=> x3) as proof of (Xx0 Xx000)
% Found (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3) as proof of ((x4 Xx)->(Xx0 Xx000))
% Found (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3) as proof of ((forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))->((x4 Xx)->(Xx0 Xx000)))
% Found (and_rect10 (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3)) as proof of (Xx0 Xx000)
% Found ((and_rect1 (Xx0 Xx000)) (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3)) as proof of (Xx0 Xx000)
% Found (((fun (P:Type) (x6:((forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))->((x4 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x4 Xx)) P) x6) x5)) (Xx0 Xx000)) (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3)) as proof of (Xx0 Xx000)
% Found (fun (x5:((and (forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x4 Xx)))=> (((fun (P:Type) (x6:((forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))->((x4 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x4 Xx)) P) x6) x5)) (Xx0 Xx000)) (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3))) as proof of (Xx0 Xx000)
% Found x3:(Xx00 Xx000)
% Found x3 as proof of (Xx0 Xx000)
% Found (fun (x7:(x4 Xx))=> x3) as proof of (Xx0 Xx000)
% Found (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3) as proof of ((x4 Xx)->(Xx0 Xx000))
% Found (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3) as proof of ((forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))->((x4 Xx)->(Xx0 Xx000)))
% Found (and_rect10 (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3)) as proof of (Xx0 Xx000)
% Found ((and_rect1 (Xx0 Xx000)) (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3)) as proof of (Xx0 Xx000)
% Found (((fun (P:Type) (x6:((forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))->((x4 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x4 Xx)) P) x6) x5)) (Xx0 Xx000)) (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3)) as proof of (Xx0 Xx000)
% Found (fun (x5:((and (forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x4 Xx)))=> (((fun (P:Type) (x6:((forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))->((x4 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x4 Xx)) P) x6) x5)) (Xx0 Xx000)) (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3))) as proof of (Xx0 Xx000)
% Found x3:(Xx00 Xx000)
% Found x3 as proof of (Xx0 Xx000)
% Found (fun (x7:(x4 Xx))=> x3) as proof of (Xx0 Xx000)
% Found (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3) as proof of ((x4 Xx)->(Xx0 Xx000))
% Found (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3) as proof of ((forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))->((x4 Xx)->(Xx0 Xx000)))
% Found (and_rect10 (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3)) as proof of (Xx0 Xx000)
% Found ((and_rect1 (Xx0 Xx000)) (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3)) as proof of (Xx0 Xx000)
% Found (((fun (P:Type) (x6:((forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))->((x4 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x4 Xx)) P) x6) x5)) (Xx0 Xx000)) (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3)) as proof of (Xx0 Xx000)
% Found (fun (x5:((and (forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x4 Xx)))=> (((fun (P:Type) (x6:((forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))->((x4 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x4 Xx)) P) x6) x5)) (Xx0 Xx000)) (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3))) as proof of (Xx0 Xx000)
% Found x3:(Xx00 Xx000)
% Found x3 as proof of (Xx0 Xx000)
% Found (fun (x7:(x4 Xx))=> x3) as proof of (Xx0 Xx000)
% Found (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3) as proof of ((x4 Xx)->(Xx0 Xx000))
% Found (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3) as proof of ((forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))->((x4 Xx)->(Xx0 Xx000)))
% Found (and_rect10 (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3)) as proof of (Xx0 Xx000)
% Found ((and_rect1 (Xx0 Xx000)) (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3)) as proof of (Xx0 Xx000)
% Found (((fun (P:Type) (x6:((forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))->((x4 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x4 Xx)) P) x6) x5)) (Xx0 Xx000)) (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3)) as proof of (Xx0 Xx000)
% Found (fun (x5:((and (forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x4 Xx)))=> (((fun (P:Type) (x6:((forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))->((x4 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x4 Xx)) P) x6) x5)) (Xx0 Xx000)) (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3))) as proof of (Xx0 Xx000)
% Found x3:(Xx00 Xx000)
% Found x3 as proof of (Xx0 Xx000)
% Found (fun (x7:(x4 Xx))=> x3) as proof of (Xx0 Xx000)
% Found (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3) as proof of ((x4 Xx)->(Xx0 Xx000))
% Found (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3) as proof of ((forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))->((x4 Xx)->(Xx0 Xx000)))
% Found (and_rect10 (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3)) as proof of (Xx0 Xx000)
% Found ((and_rect1 (Xx0 Xx000)) (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3)) as proof of (Xx0 Xx000)
% Found (((fun (P:Type) (x6:((forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))->((x4 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x4 Xx)) P) x6) x5)) (Xx0 Xx000)) (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3)) as proof of (Xx0 Xx000)
% Found (fun (x5:((and (forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x4 Xx)))=> (((fun (P:Type) (x6:((forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))->((x4 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x4 Xx)) P) x6) x5)) (Xx0 Xx000)) (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3))) as proof of (Xx0 Xx000)
% Found x3:(Xx00 Xx000)
% Found x3 as proof of (Xx0 Xx000)
% Found (fun (x7:(x4 Xx))=> x3) as proof of (Xx0 Xx000)
% Found (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3) as proof of ((x4 Xx)->(Xx0 Xx000))
% Found (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3) as proof of ((forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))->((x4 Xx)->(Xx0 Xx000)))
% Found (and_rect10 (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3)) as proof of (Xx0 Xx000)
% Found ((and_rect1 (Xx0 Xx000)) (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3)) as proof of (Xx0 Xx000)
% Found (((fun (P:Type) (x6:((forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))->((x4 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x4 Xx)) P) x6) x5)) (Xx0 Xx000)) (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3)) as proof of (Xx0 Xx000)
% Found (fun (x5:((and (forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x4 Xx)))=> (((fun (P:Type) (x6:((forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))->((x4 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x4 Xx)) P) x6) x5)) (Xx0 Xx000)) (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3))) as proof of (Xx0 Xx000)
% Found x3:(Xx00 Xx000)
% Found x3 as proof of (Xx0 Xx000)
% Found (fun (x7:(x4 Xx))=> x3) as proof of (Xx0 Xx000)
% Found (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3) as proof of ((x4 Xx)->(Xx0 Xx000))
% Found (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3) as proof of ((forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))->((x4 Xx)->(Xx0 Xx000)))
% Found (and_rect10 (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3)) as proof of (Xx0 Xx000)
% Found ((and_rect1 (Xx0 Xx000)) (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3)) as proof of (Xx0 Xx000)
% Found (((fun (P:Type) (x6:((forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))->((x4 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x4 Xx)) P) x6) x5)) (Xx0 Xx000)) (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3)) as proof of (Xx0 Xx000)
% Found (fun (x5:((and (forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x4 Xx)))=> (((fun (P:Type) (x6:((forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))->((x4 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x4 Xx)) P) x6) x5)) (Xx0 Xx000)) (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3))) as proof of (Xx0 Xx000)
% Found x3:(Xx01 Xx000)
% Found x3 as proof of (Xx00 Xx000)
% Found (fun (x3:(Xx01 Xx000))=> x3) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx01 Xx000))=> x3) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx01 Xx000))=> x3) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x3:(Xx01 Xx000)
% Found x3 as proof of (Xx00 Xx000)
% Found (fun (x3:(Xx01 Xx000))=> x3) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx01 Xx000))=> x3) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx01 Xx000))=> x3) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x3:(Xx01 Xx000)
% Found x3 as proof of (Xx00 Xx000)
% Found (fun (x3:(Xx01 Xx000))=> x3) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx01 Xx000))=> x3) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx01 Xx000))=> x3) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x3:(Xx01 Xx000)
% Found x3 as proof of (Xx00 Xx000)
% Found (fun (x3:(Xx01 Xx000))=> x3) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx01 Xx000))=> x3) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx01 Xx000))=> x3) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x3:(Xx01 Xx000)
% Found x3 as proof of (Xx00 Xx000)
% Found (fun (x3:(Xx01 Xx000))=> x3) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx01 Xx000))=> x3) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx01 Xx000))=> x3) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x3:(Xx01 Xx000)
% Found x3 as proof of (Xx00 Xx000)
% Found (fun (x3:(Xx01 Xx000))=> x3) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx01 Xx000))=> x3) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx01 Xx000))=> x3) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x3:(Xx00 Xx000)
% Instantiate: Xx00:=(K x4):(fofType->Prop)
% Found x3 as proof of (Xx0 Xx000)
% Found (fun (x7:(x4 Xx))=> x3) as proof of (Xx0 Xx000)
% Found (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3) as proof of ((x4 Xx)->(Xx0 Xx000))
% Found (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3) as proof of ((forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))->((x4 Xx)->(Xx0 Xx000)))
% Found (and_rect10 (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3)) as proof of (Xx0 Xx000)
% Found ((and_rect1 (Xx0 Xx000)) (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3)) as proof of (Xx0 Xx000)
% Found (((fun (P:Type) (x6:((forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))->((x4 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x4 Xx)) P) x6) x5)) (Xx0 Xx000)) (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3)) as proof of (Xx0 Xx000)
% Found (fun (x5:((and (forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x4 Xx)))=> (((fun (P:Type) (x6:((forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))->((x4 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x4 Xx)) P) x6) x5)) (Xx0 Xx000)) (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3))) as proof of (Xx0 Xx000)
% Found x3:(Xx00 Xx000)
% Instantiate: Xx00:=(K x4):(fofType->Prop)
% Found x3 as proof of (Xx0 Xx000)
% Found (fun (x7:(x4 Xx))=> x3) as proof of (Xx0 Xx000)
% Found (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3) as proof of ((x4 Xx)->(Xx0 Xx000))
% Found (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3) as proof of ((forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))->((x4 Xx)->(Xx0 Xx000)))
% Found (and_rect10 (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3)) as proof of (Xx0 Xx000)
% Found ((and_rect1 (Xx0 Xx000)) (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3)) as proof of (Xx0 Xx000)
% Found (((fun (P:Type) (x6:((forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))->((x4 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x4 Xx)) P) x6) x5)) (Xx0 Xx000)) (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3)) as proof of (Xx0 Xx000)
% Found (fun (x5:((and (forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x4 Xx)))=> (((fun (P:Type) (x6:((forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))->((x4 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x4 Xx)) P) x6) x5)) (Xx0 Xx000)) (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3))) as proof of (Xx0 Xx000)
% Found x5:(Xx01 Xx000)
% Found x5 as proof of (Xx00 Xx000)
% Found (fun (x5:(Xx01 Xx000))=> x5) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x5:(Xx01 Xx000)
% Found x5 as proof of (Xx00 Xx000)
% Found (fun (x5:(Xx01 Xx000))=> x5) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x5:(Xx01 Xx000)
% Found x5 as proof of (Xx00 Xx000)
% Found (fun (x5:(Xx01 Xx000))=> x5) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x5:(Xx01 Xx000)
% Found x5 as proof of (Xx00 Xx000)
% Found (fun (x5:(Xx01 Xx000))=> x5) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x5:(Xx01 Xx000)
% Found x5 as proof of (Xx00 Xx000)
% Found (fun (x5:(Xx01 Xx000))=> x5) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x5:(Xx01 Xx000)
% Found x5 as proof of (Xx00 Xx000)
% Found (fun (x5:(Xx01 Xx000))=> x5) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x3:(Xx00 Xx000)
% Found x3 as proof of (Xx0 Xx000)
% Found (fun (x7:(x4 Xx))=> x3) as proof of (Xx0 Xx000)
% Found (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3) as proof of ((x4 Xx)->(Xx0 Xx000))
% Found (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3) as proof of ((forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))->((x4 Xx)->(Xx0 Xx000)))
% Found (and_rect10 (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3)) as proof of (Xx0 Xx000)
% Found ((and_rect1 (Xx0 Xx000)) (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3)) as proof of (Xx0 Xx000)
% Found (((fun (P:Type) (x6:((forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))->((x4 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x4 Xx)) P) x6) x5)) (Xx0 Xx000)) (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3)) as proof of (Xx0 Xx000)
% Found (fun (x5:((and (forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x4 Xx)))=> (((fun (P:Type) (x6:((forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))->((x4 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x4 Xx)) P) x6) x5)) (Xx0 Xx000)) (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3))) as proof of (Xx0 Xx000)
% Found x3:(Xx00 Xx000)
% Found x3 as proof of (Xx0 Xx000)
% Found (fun (x7:(x4 Xx))=> x3) as proof of (Xx0 Xx000)
% Found (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3) as proof of ((x4 Xx)->(Xx0 Xx000))
% Found (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3) as proof of ((forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))->((x4 Xx)->(Xx0 Xx000)))
% Found (and_rect10 (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3)) as proof of (Xx0 Xx000)
% Found ((and_rect1 (Xx0 Xx000)) (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3)) as proof of (Xx0 Xx000)
% Found (((fun (P:Type) (x6:((forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))->((x4 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x4 Xx)) P) x6) x5)) (Xx0 Xx000)) (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3)) as proof of (Xx0 Xx000)
% Found (fun (x5:((and (forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x4 Xx)))=> (((fun (P:Type) (x6:((forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))->((x4 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x4 Xx)) P) x6) x5)) (Xx0 Xx000)) (fun (x6:(forall (Xx00:fofType), ((x4 Xx00)->((K x4) Xx00)))) (x7:(x4 Xx))=> x3))) as proof of (Xx0 Xx000)
% Found x3:(Xx01 Xx000)
% Found x3 as proof of (Xx00 Xx000)
% Found (fun (x3:(Xx01 Xx000))=> x3) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx01 Xx000))=> x3) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx01 Xx000))=> x3) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x3:(Xx01 Xx000)
% Found x3 as proof of (Xx00 Xx000)
% Found (fun (x3:(Xx01 Xx000))=> x3) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx01 Xx000))=> x3) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx01 Xx000))=> x3) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)) as proof of ((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)) as proof of ((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found x5:(Xx01 Xx000)
% Found x5 as proof of (Xx00 Xx000)
% Found (fun (x5:(Xx01 Xx000))=> x5) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x5:(Xx01 Xx000)
% Found x5 as proof of (Xx00 Xx000)
% Found (fun (x5:(Xx01 Xx000))=> x5) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found x5:(Xx01 Xx000)
% Found x5 as proof of (Xx00 Xx000)
% Found (fun (x5:(Xx01 Xx000))=> x5) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x5:(Xx01 Xx000)
% Found x5 as proof of (Xx00 Xx000)
% Found (fun (x5:(Xx01 Xx000))=> x5) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x5:(Xx01 Xx000)
% Found x5 as proof of (Xx00 Xx000)
% Found (fun (x5:(Xx01 Xx000))=> x5) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x5:(Xx01 Xx000)
% Found x5 as proof of (Xx00 Xx000)
% Found (fun (x5:(Xx01 Xx000))=> x5) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x5:(Xx01 Xx000)
% Found x5 as proof of (Xx00 Xx000)
% Found (fun (x5:(Xx01 Xx000))=> x5) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x5:(Xx01 Xx000)
% Found x5 as proof of (Xx00 Xx000)
% Found (fun (x5:(Xx01 Xx000))=> x5) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x5:(Xx01 Xx000)
% Found x5 as proof of (Xx00 Xx000)
% Found (fun (x5:(Xx01 Xx000))=> x5) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x5:(Xx01 Xx000)
% Found x5 as proof of (Xx00 Xx000)
% Found (fun (x5:(Xx01 Xx000))=> x5) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x5:(Xx01 Xx000)
% Found x5 as proof of (Xx00 Xx000)
% Found (fun (x5:(Xx01 Xx000))=> x5) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x5:(Xx01 Xx000)
% Found x5 as proof of (Xx00 Xx000)
% Found (fun (x5:(Xx01 Xx000))=> x5) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x5:(Xx01 Xx000)
% Found x5 as proof of (Xx00 Xx000)
% Found (fun (x5:(Xx01 Xx000))=> x5) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x5:(Xx01 Xx000)
% Found x5 as proof of (Xx00 Xx000)
% Found (fun (x5:(Xx01 Xx000))=> x5) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x5:(Xx01 Xx000)
% Found x5 as proof of (Xx00 Xx000)
% Found (fun (x5:(Xx01 Xx000))=> x5) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x5:(Xx01 Xx000)
% Found x5 as proof of (Xx00 Xx000)
% Found (fun (x5:(Xx01 Xx000))=> x5) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x5:(Xx01 Xx000)
% Found x5 as proof of (Xx00 Xx000)
% Found (fun (x5:(Xx01 Xx000))=> x5) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x5:(Xx01 Xx000)
% Found x5 as proof of (Xx00 Xx000)
% Found (fun (x5:(Xx01 Xx000))=> x5) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x5:(Xx01 Xx000)
% Found x5 as proof of (Xx00 Xx000)
% Found (fun (x5:(Xx01 Xx000))=> x5) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x5:(Xx01 Xx000)
% Found x5 as proof of (Xx00 Xx000)
% Found (fun (x5:(Xx01 Xx000))=> x5) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found x5:(Xx01 Xx000)
% Instantiate: Xx00:=Xx01:(fofType->Prop)
% Found (fun (x5:(Xx01 Xx000))=> x5) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found ((x0020 (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx00) Xx)
% Found (((x002 Xx00) (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx00) Xx)
% Found ((((x00 x3) Xx00) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx00) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> ((((x00 x3) Xx00) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))))) as proof of ((K Xx00) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found x5:(Xx01 Xx000)
% Instantiate: Xx00:=Xx01:(fofType->Prop)
% Found (fun (x5:(Xx01 Xx000))=> x5) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found ((x1020 (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx00) Xx)
% Found (((x102 Xx00) (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx00) Xx)
% Found ((((x10 x3) Xx00) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx00) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> ((((x10 x3) Xx00) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))))) as proof of ((K Xx00) Xx)
% Found x4:(Xx00 Xx000)
% Instantiate: Xx00:=(K Xx01):(fofType->Prop)
% Found x4 as proof of ((K Xx01) Xx000)
% Found x7:(Xx01 Xx000)
% Found x7 as proof of (Xx00 Xx000)
% Found (fun (x7:(Xx01 Xx000))=> x7) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found x4:(Xx00 Xx000)
% Instantiate: Xx00:=(K Xx01):(fofType->Prop)
% Found x4 as proof of ((K Xx01) Xx000)
% Found x4:(Xx00 Xx000)
% Instantiate: Xx00:=(K Xx01):(fofType->Prop)
% Found x4 as proof of ((K Xx01) Xx000)
% Found x4:(Xx00 Xx000)
% Instantiate: Xx00:=(K Xx01):(fofType->Prop)
% Found x4 as proof of ((K Xx01) Xx000)
% Found x7:(Xx01 Xx000)
% Found x7 as proof of (Xx00 Xx000)
% Found (fun (x7:(Xx01 Xx000))=> x7) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)) as proof of ((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)) as proof of ((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found x7:(Xx01 Xx000)
% Found x7 as proof of (Xx00 Xx000)
% Found (fun (x7:(Xx01 Xx000))=> x7) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found x7:(Xx01 Xx000)
% Found x7 as proof of (Xx00 Xx000)
% Found (fun (x7:(Xx01 Xx000))=> x7) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found x7:(Xx01 Xx000)
% Found x7 as proof of (Xx00 Xx000)
% Found (fun (x7:(Xx01 Xx000))=> x7) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found x7:(Xx01 Xx000)
% Found x7 as proof of (Xx00 Xx000)
% Found (fun (x7:(Xx01 Xx000))=> x7) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)) as proof of ((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)) as proof of ((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)) as proof of ((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)) as proof of ((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found x3:(Xx01 Xx000)
% Instantiate: Xx00:=Xx01:(fofType->Prop)
% Found x3 as proof of (Xx00 Xx000)
% Found x3 as proof of (Xx00 Xx000)
% Found (fun (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (Xx00 Xx000)
% Found (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx))->(Xx00 Xx000))
% Found (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->(Xx00 Xx000)))
% Found (ex_ind00 (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx00 Xx000)
% Found ((ex_ind0 (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx00 Xx000)
% Found (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx00 Xx000)
% Found (fun (x3:(Xx01 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx01 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx01 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found x3:(Xx01 Xx000)
% Instantiate: Xx00:=Xx01:(fofType->Prop)
% Found x3 as proof of (Xx00 Xx000)
% Found x3 as proof of (Xx00 Xx000)
% Found (fun (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (Xx00 Xx000)
% Found (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx))->(Xx00 Xx000))
% Found (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->(Xx00 Xx000)))
% Found (ex_ind00 (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx00 Xx000)
% Found ((ex_ind0 (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx00 Xx000)
% Found (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx00 Xx000)
% Found (fun (x3:(Xx01 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx01 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx01 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found x7:(Xx01 Xx000)
% Found x7 as proof of (Xx00 Xx000)
% Found (fun (x7:(Xx01 Xx000))=> x7) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found x7:(Xx01 Xx000)
% Found x7 as proof of (Xx00 Xx000)
% Found (fun (x7:(Xx01 Xx000))=> x7) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found x7:(Xx01 Xx000)
% Found x7 as proof of (Xx00 Xx000)
% Found (fun (x7:(Xx01 Xx000))=> x7) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found x7:(Xx01 Xx000)
% Found x7 as proof of (Xx00 Xx000)
% Found (fun (x7:(Xx01 Xx000))=> x7) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found x7:(Xx01 Xx000)
% Found x7 as proof of (Xx00 Xx000)
% Found (fun (x7:(Xx01 Xx000))=> x7) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found x7:(Xx01 Xx000)
% Found x7 as proof of (Xx00 Xx000)
% Found (fun (x7:(Xx01 Xx000))=> x7) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found x5:(Xx01 Xx000)
% Found x5 as proof of (Xx00 Xx000)
% Found (fun (x5:(Xx01 Xx000))=> x5) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x5:(Xx01 Xx000)
% Found x5 as proof of (Xx00 Xx000)
% Found (fun (x5:(Xx01 Xx000))=> x5) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x50:=(x5 Xx):((x1 Xx)->((K x1) Xx))
% Found (x5 Xx) as proof of ((x1 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x1 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x5 Xx)) as proof of ((x1 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x5) x2)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x5) x2)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x1 Xx)->((K x1) Xx))
% Found (x5 Xx) as proof of ((x1 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x1 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x5 Xx)) as proof of ((x1 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x5) x2)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x5) x2)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found x4:(Xx00 Xx000)
% Instantiate: Xx00:=(K Xx01):(fofType->Prop)
% Found x4 as proof of ((K Xx01) Xx000)
% Found x4:(Xx00 Xx000)
% Instantiate: Xx00:=(K Xx01):(fofType->Prop)
% Found x4 as proof of ((K Xx01) Xx000)
% Found x4:(Xx00 Xx000)
% Instantiate: Xx00:=(K Xx01):(fofType->Prop)
% Found x4 as proof of ((K Xx01) Xx000)
% Found x4:(Xx00 Xx000)
% Instantiate: Xx00:=(K Xx01):(fofType->Prop)
% Found x4 as proof of ((K Xx01) Xx000)
% Found x5:(Xx01 Xx000)
% Found x5 as proof of (Xx00 Xx000)
% Found (fun (x5:(Xx01 Xx000))=> x5) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x5:(Xx01 Xx000)
% Found x5 as proof of (Xx00 Xx000)
% Found (fun (x5:(Xx01 Xx000))=> x5) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x5:(Xx01 Xx000)
% Found x5 as proof of (Xx00 Xx000)
% Found (fun (x5:(Xx01 Xx000))=> x5) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x5:(Xx01 Xx000)
% Found x5 as proof of (Xx00 Xx000)
% Found (fun (x5:(Xx01 Xx000))=> x5) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x5:(Xx01 Xx000)
% Found x5 as proof of (Xx00 Xx000)
% Found (fun (x5:(Xx01 Xx000))=> x5) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x5:(Xx01 Xx000)
% Found x5 as proof of (Xx00 Xx000)
% Found (fun (x5:(Xx01 Xx000))=> x5) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x4:(Xx00 Xx000)
% Instantiate: Xx00:=(K Xx01):(fofType->Prop)
% Found x4 as proof of ((K Xx01) Xx000)
% Found x4:(Xx00 Xx000)
% Instantiate: Xx00:=(K Xx01):(fofType->Prop)
% Found x4 as proof of ((K Xx01) Xx000)
% Found x4:(Xx00 Xx000)
% Instantiate: Xx00:=(K Xx01):(fofType->Prop)
% Found x4 as proof of ((K Xx01) Xx000)
% Found x4:(Xx00 Xx000)
% Instantiate: Xx00:=(K Xx01):(fofType->Prop)
% Found x4 as proof of ((K Xx01) Xx000)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found x5:(Xx01 Xx000)
% Instantiate: Xx00:=Xx01:(fofType->Prop)
% Found (fun (x5:(Xx01 Xx000))=> x5) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found ((x0020 (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx00) Xx)
% Found (((x002 Xx00) (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx00) Xx)
% Found ((((x00 x3) Xx00) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx00) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> ((((x00 x3) Xx00) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))))) as proof of ((K Xx00) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found x5:(Xx01 Xx000)
% Instantiate: Xx00:=Xx01:(fofType->Prop)
% Found (fun (x5:(Xx01 Xx000))=> x5) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found ((x1020 (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx00) Xx)
% Found (((x102 Xx00) (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx00) Xx)
% Found ((((x10 x3) Xx00) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx00) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> ((((x10 x3) Xx00) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))))) as proof of ((K Xx00) Xx)
% Found x7:(Xx01 Xx000)
% Found x7 as proof of (Xx00 Xx000)
% Found (fun (x7:(Xx01 Xx000))=> x7) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found x7:(Xx01 Xx000)
% Found x7 as proof of (Xx00 Xx000)
% Found (fun (x7:(Xx01 Xx000))=> x7) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found x4:(Xx00 Xx000)
% Instantiate: Xx00:=(K Xx01):(fofType->Prop)
% Found x4 as proof of ((K Xx01) Xx000)
% Found x4:(Xx00 Xx000)
% Instantiate: Xx00:=(K Xx01):(fofType->Prop)
% Found x4 as proof of ((K Xx01) Xx000)
% Found x4:(Xx00 Xx000)
% Instantiate: Xx00:=(K Xx01):(fofType->Prop)
% Found x4 as proof of ((K Xx01) Xx000)
% Found x4:(Xx00 Xx000)
% Instantiate: Xx00:=(K Xx01):(fofType->Prop)
% Found x4 as proof of ((K Xx01) Xx000)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found x5:(Xx01 Xx000)
% Instantiate: Xx00:=Xx01:(fofType->Prop)
% Found (fun (x5:(Xx01 Xx000))=> x5) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found ((x1020 (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx00) Xx)
% Found (((x102 Xx00) (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx00) Xx)
% Found ((((x10 x3) Xx00) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx00) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> ((((x10 x3) Xx00) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))))) as proof of ((K Xx00) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found x5:(Xx01 Xx000)
% Instantiate: Xx00:=Xx01:(fofType->Prop)
% Found (fun (x5:(Xx01 Xx000))=> x5) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found ((x2020 (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx00) Xx)
% Found (((x202 Xx00) (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx00) Xx)
% Found ((((x20 x3) Xx00) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx00) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> ((((x20 x3) Xx00) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))))) as proof of ((K Xx00) Xx)
% Found x4:(Xx00 Xx000)
% Instantiate: Xx00:=(K Xx01):(fofType->Prop)
% Found x4 as proof of ((K Xx01) Xx000)
% Found x4:(Xx00 Xx000)
% Instantiate: Xx00:=(K Xx01):(fofType->Prop)
% Found x4 as proof of ((K Xx01) Xx000)
% Found x4:(Xx00 Xx000)
% Instantiate: Xx00:=(K Xx01):(fofType->Prop)
% Found x4 as proof of ((K Xx01) Xx000)
% Found x4:(Xx00 Xx000)
% Instantiate: Xx00:=(K Xx01):(fofType->Prop)
% Found x4 as proof of ((K Xx01) Xx000)
% Found x7:(Xx01 Xx000)
% Found x7 as proof of (Xx00 Xx000)
% Found (fun (x7:(Xx01 Xx000))=> x7) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found x7:(Xx01 Xx000)
% Found x7 as proof of (Xx00 Xx000)
% Found (fun (x7:(Xx01 Xx000))=> x7) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found x5:(Xx01 Xx000)
% Instantiate: Xx00:=Xx01:(fofType->Prop)
% Found (fun (x5:(Xx01 Xx000))=> x5) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found ((x1020 (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx00) Xx)
% Found (((x102 Xx00) (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx00) Xx)
% Found ((((x10 x3) Xx00) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx00) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> ((((x10 x3) Xx00) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))))) as proof of ((K Xx00) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found x5:(Xx01 Xx000)
% Instantiate: Xx00:=Xx01:(fofType->Prop)
% Found (fun (x5:(Xx01 Xx000))=> x5) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found ((x0020 (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx00) Xx)
% Found (((x002 Xx00) (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx00) Xx)
% Found ((((x00 x3) Xx00) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx00) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> ((((x00 x3) Xx00) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))))) as proof of ((K Xx00) Xx)
% Found x7:(Xx01 Xx000)
% Found x7 as proof of (Xx00 Xx000)
% Found (fun (x7:(Xx01 Xx000))=> x7) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found x7:(Xx01 Xx000)
% Found x7 as proof of (Xx00 Xx000)
% Found (fun (x7:(Xx01 Xx000))=> x7) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found x7:(Xx01 Xx000)
% Found x7 as proof of (Xx00 Xx000)
% Found (fun (x7:(Xx01 Xx000))=> x7) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found x7:(Xx01 Xx000)
% Found x7 as proof of (Xx00 Xx000)
% Found (fun (x7:(Xx01 Xx000))=> x7) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found x7:(Xx01 Xx000)
% Found x7 as proof of (Xx00 Xx000)
% Found (fun (x7:(Xx01 Xx000))=> x7) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found x7:(Xx01 Xx000)
% Found x7 as proof of (Xx00 Xx000)
% Found (fun (x7:(Xx01 Xx000))=> x7) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found x3:(Xx01 Xx000)
% Instantiate: Xx00:=Xx01:(fofType->Prop)
% Found x3 as proof of (Xx00 Xx000)
% Found x3 as proof of (Xx00 Xx000)
% Found (fun (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (Xx00 Xx000)
% Found (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx))->(Xx00 Xx000))
% Found (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->(Xx00 Xx000)))
% Found (ex_ind00 (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx00 Xx000)
% Found ((ex_ind0 (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx00 Xx000)
% Found (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx00 Xx000)
% Found (fun (x3:(Xx01 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx01 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx01 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found x3:(Xx01 Xx000)
% Instantiate: Xx00:=Xx01:(fofType->Prop)
% Found x3 as proof of (Xx00 Xx000)
% Found x3 as proof of (Xx00 Xx000)
% Found (fun (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (Xx00 Xx000)
% Found (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx))->(Xx00 Xx000))
% Found (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->(Xx00 Xx000)))
% Found (ex_ind00 (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx00 Xx000)
% Found ((ex_ind0 (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx00 Xx000)
% Found (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx00 Xx000)
% Found (fun (x3:(Xx01 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx01 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx01 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found x7:(Xx01 Xx000)
% Found x7 as proof of (Xx00 Xx000)
% Found (fun (x7:(Xx01 Xx000))=> x7) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found x7:(Xx01 Xx000)
% Found x7 as proof of (Xx00 Xx000)
% Found (fun (x7:(Xx01 Xx000))=> x7) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found x7:(Xx01 Xx000)
% Found x7 as proof of (Xx00 Xx000)
% Found (fun (x7:(Xx01 Xx000))=> x7) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found x7:(Xx01 Xx000)
% Found x7 as proof of (Xx00 Xx000)
% Found (fun (x7:(Xx01 Xx000))=> x7) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)) as proof of ((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)) as proof of ((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found x7:(Xx01 Xx000)
% Found x7 as proof of (Xx00 Xx000)
% Found (fun (x7:(Xx01 Xx000))=> x7) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found x7:(Xx01 Xx000)
% Found x7 as proof of (Xx00 Xx000)
% Found (fun (x7:(Xx01 Xx000))=> x7) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found x7:(Xx01 Xx000)
% Found x7 as proof of (Xx00 Xx000)
% Found (fun (x7:(Xx01 Xx000))=> x7) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found x7:(Xx01 Xx000)
% Found x7 as proof of (Xx00 Xx000)
% Found (fun (x7:(Xx01 Xx000))=> x7) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found x7:(Xx01 Xx000)
% Found x7 as proof of (Xx00 Xx000)
% Found (fun (x7:(Xx01 Xx000))=> x7) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found x7:(Xx01 Xx000)
% Found x7 as proof of (Xx00 Xx000)
% Found (fun (x7:(Xx01 Xx000))=> x7) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found x7:(Xx01 Xx000)
% Found x7 as proof of (Xx00 Xx000)
% Found (fun (x7:(Xx01 Xx000))=> x7) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found x7:(Xx01 Xx000)
% Found x7 as proof of (Xx00 Xx000)
% Found (fun (x7:(Xx01 Xx000))=> x7) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found x7:(Xx01 Xx000)
% Found x7 as proof of (Xx00 Xx000)
% Found (fun (x7:(Xx01 Xx000))=> x7) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found x7:(Xx01 Xx000)
% Found x7 as proof of (Xx00 Xx000)
% Found (fun (x7:(Xx01 Xx000))=> x7) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found x3:(Xx01 Xx000)
% Instantiate: Xx00:=Xx01:(fofType->Prop)
% Found x3 as proof of (Xx00 Xx000)
% Found x3 as proof of (Xx00 Xx000)
% Found (fun (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (Xx00 Xx000)
% Found (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx))->(Xx00 Xx000))
% Found (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->(Xx00 Xx000)))
% Found (ex_ind00 (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx00 Xx000)
% Found ((ex_ind0 (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx00 Xx000)
% Found (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx00 Xx000)
% Found (fun (x3:(Xx01 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx01 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx01 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found x3:(Xx01 Xx000)
% Instantiate: Xx00:=Xx01:(fofType->Prop)
% Found x3 as proof of (Xx00 Xx000)
% Found x3 as proof of (Xx00 Xx000)
% Found (fun (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (Xx00 Xx000)
% Found (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx))->(Xx00 Xx000))
% Found (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->(Xx00 Xx000)))
% Found (ex_ind00 (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx00 Xx000)
% Found ((ex_ind0 (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx00 Xx000)
% Found (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x0)) (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx00 Xx000)
% Found (fun (x3:(Xx01 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x0)) (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx01 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x0)) (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx01 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x0)) (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found x3:(Xx01 Xx000)
% Instantiate: Xx00:=Xx01:(fofType->Prop)
% Found x3 as proof of (Xx00 Xx000)
% Found x3 as proof of (Xx00 Xx000)
% Found (fun (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (Xx00 Xx000)
% Found (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx))->(Xx00 Xx000))
% Found (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->(Xx00 Xx000)))
% Found (ex_ind00 (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx00 Xx000)
% Found ((ex_ind0 (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx00 Xx000)
% Found (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x0)) (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx00 Xx000)
% Found (fun (x3:(Xx01 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x0)) (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx01 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x0)) (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx01 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x0)) (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found x3:(Xx01 Xx000)
% Instantiate: Xx00:=Xx01:(fofType->Prop)
% Found x3 as proof of (Xx00 Xx000)
% Found x3 as proof of (Xx00 Xx000)
% Found (fun (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (Xx00 Xx000)
% Found (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx))->(Xx00 Xx000))
% Found (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->(Xx00 Xx000)))
% Found (ex_ind00 (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx00 Xx000)
% Found ((ex_ind0 (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx00 Xx000)
% Found (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx00 Xx000)
% Found (fun (x3:(Xx01 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx01 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx01 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found x7:(Xx01 Xx000)
% Found x7 as proof of (Xx00 Xx000)
% Found (fun (x7:(Xx01 Xx000))=> x7) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found x7:(Xx01 Xx000)
% Found x7 as proof of (Xx00 Xx000)
% Found (fun (x7:(Xx01 Xx000))=> x7) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found x7:(Xx01 Xx000)
% Found x7 as proof of (Xx00 Xx000)
% Found (fun (x7:(Xx01 Xx000))=> x7) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found x7:(Xx01 Xx000)
% Found x7 as proof of (Xx00 Xx000)
% Found (fun (x7:(Xx01 Xx000))=> x7) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found x7:(Xx01 Xx000)
% Found x7 as proof of (Xx00 Xx000)
% Found (fun (x7:(Xx01 Xx000))=> x7) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found x7:(Xx01 Xx000)
% Found x7 as proof of (Xx00 Xx000)
% Found (fun (x7:(Xx01 Xx000))=> x7) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found x7:(Xx01 Xx000)
% Found x7 as proof of (Xx00 Xx000)
% Found (fun (x7:(Xx01 Xx000))=> x7) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x500:=(x50 x6):((K x1) Xx)
% Found (x50 x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found x7:(Xx01 Xx000)
% Found x7 as proof of (Xx00 Xx000)
% Found (fun (x7:(Xx01 Xx000))=> x7) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x500:=(x50 x6):((K x1) Xx)
% Found (x50 x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found x7:(Xx01 Xx000)
% Found x7 as proof of (Xx00 Xx000)
% Found (fun (x7:(Xx01 Xx000))=> x7) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found x7:(Xx01 Xx000)
% Found x7 as proof of (Xx00 Xx000)
% Found (fun (x7:(Xx01 Xx000))=> x7) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found x7:(Xx01 Xx000)
% Found x7 as proof of (Xx00 Xx000)
% Found (fun (x7:(Xx01 Xx000))=> x7) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found x7:(Xx01 Xx000)
% Found x7 as proof of (Xx00 Xx000)
% Found (fun (x7:(Xx01 Xx000))=> x7) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found x7:(Xx01 Xx000)
% Found x7 as proof of (Xx00 Xx000)
% Found (fun (x7:(Xx01 Xx000))=> x7) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found x7:(Xx01 Xx000)
% Found x7 as proof of (Xx00 Xx000)
% Found (fun (x7:(Xx01 Xx000))=> x7) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found x7:(Xx01 Xx000)
% Found x7 as proof of (Xx00 Xx000)
% Found (fun (x7:(Xx01 Xx000))=> x7) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x500:=(x50 x6):((K x1) Xx)
% Found (x50 x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found x7:(Xx01 Xx000)
% Found x7 as proof of (Xx00 Xx000)
% Found (fun (x7:(Xx01 Xx000))=> x7) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x500:=(x50 x6):((K x1) Xx)
% Found (x50 x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found x7:(Xx01 Xx000)
% Found x7 as proof of (Xx00 Xx000)
% Found (fun (x7:(Xx01 Xx000))=> x7) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x300:=(x30 x4):((K x1) Xx)
% Found (x30 x4) as proof of ((K Xx01) Xx)
% Found ((x3 Xx) x4) as proof of ((K Xx01) Xx)
% Found ((x3 Xx) x4) as proof of ((K Xx01) Xx)
% Found ((x3 Xx) x4) as proof of ((K Xx01) Xx)
% Found x7:(Xx01 Xx000)
% Found x7 as proof of (Xx00 Xx000)
% Found (fun (x7:(Xx01 Xx000))=> x7) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x300:=(x30 x4):((K x1) Xx)
% Found (x30 x4) as proof of ((K Xx01) Xx)
% Found ((x3 Xx) x4) as proof of ((K Xx01) Xx)
% Found ((x3 Xx) x4) as proof of ((K Xx01) Xx)
% Found ((x3 Xx) x4) as proof of ((K Xx01) Xx)
% Found x7:(Xx01 Xx000)
% Found x7 as proof of (Xx00 Xx000)
% Found (fun (x7:(Xx01 Xx000))=> x7) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x500:=(x50 x6):((K x1) Xx)
% Found (x50 x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found x7:(Xx01 Xx000)
% Found x7 as proof of (Xx00 Xx000)
% Found (fun (x7:(Xx01 Xx000))=> x7) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x500:=(x50 x6):((K x1) Xx)
% Found (x50 x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found x4:(Xx00 Xx000)
% Instantiate: Xx00:=(K Xx01):(fofType->Prop)
% Found x4 as proof of ((K Xx01) Xx000)
% Found x4:(Xx00 Xx000)
% Instantiate: Xx00:=(K Xx01):(fofType->Prop)
% Found x4 as proof of ((K Xx01) Xx000)
% Found x4:(Xx00 Xx000)
% Instantiate: Xx00:=(K Xx01):(fofType->Prop)
% Found x4 as proof of ((K Xx01) Xx000)
% Found x4:(Xx00 Xx000)
% Instantiate: Xx00:=(K Xx01):(fofType->Prop)
% Found x4 as proof of ((K Xx01) Xx000)
% Found x50:=(x5 Xx):((x1 Xx)->((K x1) Xx))
% Found (x5 Xx) as proof of ((x1 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x1 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x5 Xx)) as proof of ((x1 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x5) x2)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x5) x2)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found x4:(Xx1 Xx00)
% Instantiate: Xx1:=(K Xx2):(fofType->Prop)
% Found x4 as proof of ((K Xx2) Xx00)
% Found x50:=(x5 Xx):((x1 Xx)->((K x1) Xx))
% Found (x5 Xx) as proof of ((x1 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x1 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x5 Xx)) as proof of ((x1 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x5) x2)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x5) x2)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found x4:(Xx1 Xx00)
% Instantiate: Xx1:=(K Xx2):(fofType->Prop)
% Found x4 as proof of ((K Xx2) Xx00)
% Found x4:(Xx1 Xx00)
% Instantiate: Xx1:=(K Xx2):(fofType->Prop)
% Found x4 as proof of ((K Xx2) Xx00)
% Found x4:(Xx1 Xx00)
% Instantiate: Xx1:=(K Xx2):(fofType->Prop)
% Found x4 as proof of ((K Xx2) Xx00)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found x5:(Xx01 Xx000)
% Instantiate: Xx00:=Xx01:(fofType->Prop)
% Found (fun (x5:(Xx01 Xx000))=> x5) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found ((x1020 (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx00) Xx)
% Found (((x102 Xx00) (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx00) Xx)
% Found ((((x10 x3) Xx00) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx00) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> ((((x10 x3) Xx00) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))))) as proof of ((K Xx00) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found x5:(Xx01 Xx000)
% Instantiate: Xx00:=Xx01:(fofType->Prop)
% Found (fun (x5:(Xx01 Xx000))=> x5) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found ((x0020 (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx00) Xx)
% Found (((x002 Xx00) (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx00) Xx)
% Found ((((x00 x3) Xx00) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx00) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> ((((x00 x3) Xx00) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))))) as proof of ((K Xx00) Xx)
% Found x3:(Xx01 Xx000)
% Instantiate: Xx00:=Xx01:(fofType->Prop)
% Found x3 as proof of (Xx00 Xx000)
% Found x3 as proof of (Xx00 Xx000)
% Found (fun (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (Xx00 Xx000)
% Found (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx))->(Xx00 Xx000))
% Found (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->(Xx00 Xx000)))
% Found (ex_ind00 (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx00 Xx000)
% Found ((ex_ind0 (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx00 Xx000)
% Found (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx00 Xx000)
% Found (fun (x3:(Xx01 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx01 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx01 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found x3:(Xx01 Xx000)
% Instantiate: Xx00:=Xx01:(fofType->Prop)
% Found x3 as proof of (Xx00 Xx000)
% Found x3 as proof of (Xx00 Xx000)
% Found (fun (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (Xx00 Xx000)
% Found (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx))->(Xx00 Xx000))
% Found (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->(Xx00 Xx000)))
% Found (ex_ind00 (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx00 Xx000)
% Found ((ex_ind0 (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx00 Xx000)
% Found (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx00 Xx000)
% Found (fun (x3:(Xx01 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx01 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx01 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found x4:(Xx00 Xx000)
% Instantiate: Xx00:=(K Xx01):(fofType->Prop)
% Found x4 as proof of ((K Xx01) Xx000)
% Found x4:(Xx00 Xx000)
% Instantiate: Xx00:=(K Xx01):(fofType->Prop)
% Found x4 as proof of ((K Xx01) Xx000)
% Found x4:(Xx00 Xx000)
% Instantiate: Xx00:=(K Xx01):(fofType->Prop)
% Found x4 as proof of ((K Xx01) Xx000)
% Found x4:(Xx00 Xx000)
% Instantiate: Xx00:=(K Xx01):(fofType->Prop)
% Found x4 as proof of ((K Xx01) Xx000)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found x5:(Xx01 Xx000)
% Instantiate: Xx00:=Xx01:(fofType->Prop)
% Found (fun (x5:(Xx01 Xx000))=> x5) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found ((x1020 (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx00) Xx)
% Found (((x102 Xx00) (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx00) Xx)
% Found ((((x10 x3) Xx00) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx00) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> ((((x10 x3) Xx00) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))))) as proof of ((K Xx00) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found x5:(Xx01 Xx000)
% Instantiate: Xx00:=Xx01:(fofType->Prop)
% Found (fun (x5:(Xx01 Xx000))=> x5) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found ((x2020 (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx00) Xx)
% Found (((x202 Xx00) (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx00) Xx)
% Found ((((x20 x3) Xx00) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx00) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> ((((x20 x3) Xx00) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))))) as proof of ((K Xx00) Xx)
% Found x7:(Xx01 Xx000)
% Found x7 as proof of (Xx00 Xx000)
% Found (fun (x7:(Xx01 Xx000))=> x7) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found x7:(Xx01 Xx000)
% Found x7 as proof of (Xx00 Xx000)
% Found (fun (x7:(Xx01 Xx000))=> x7) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found x7:(Xx01 Xx000)
% Found x7 as proof of (Xx00 Xx000)
% Found (fun (x7:(Xx01 Xx000))=> x7) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found x7:(Xx01 Xx000)
% Found x7 as proof of (Xx00 Xx000)
% Found (fun (x7:(Xx01 Xx000))=> x7) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found x7:(Xx01 Xx000)
% Found x7 as proof of (Xx00 Xx000)
% Found (fun (x7:(Xx01 Xx000))=> x7) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found x7:(Xx01 Xx000)
% Found x7 as proof of (Xx00 Xx000)
% Found (fun (x7:(Xx01 Xx000))=> x7) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found x3:(Xx01 Xx000)
% Instantiate: Xx00:=Xx01:(fofType->Prop)
% Found x3 as proof of (Xx00 Xx000)
% Found x3 as proof of (Xx00 Xx000)
% Found (fun (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (Xx00 Xx000)
% Found (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx))->(Xx00 Xx000))
% Found (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->(Xx00 Xx000)))
% Found (ex_ind00 (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx00 Xx000)
% Found ((ex_ind0 (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx00 Xx000)
% Found (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x0)) (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx00 Xx000)
% Found (fun (x3:(Xx01 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x0)) (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx01 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x0)) (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx01 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x0)) (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found x3:(Xx01 Xx000)
% Instantiate: Xx00:=Xx01:(fofType->Prop)
% Found x3 as proof of (Xx00 Xx000)
% Found x3 as proof of (Xx00 Xx000)
% Found (fun (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (Xx00 Xx000)
% Found (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx))->(Xx00 Xx000))
% Found (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->(Xx00 Xx000)))
% Found (ex_ind00 (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx00 Xx000)
% Found ((ex_ind0 (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx00 Xx000)
% Found (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x0)) (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx00 Xx000)
% Found (fun (x3:(Xx01 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x0)) (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx01 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x0)) (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx01 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x0)) (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found x7:(Xx01 Xx000)
% Found x7 as proof of (Xx00 Xx000)
% Found (fun (x7:(Xx01 Xx000))=> x7) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found x7:(Xx01 Xx000)
% Found x7 as proof of (Xx00 Xx000)
% Found (fun (x7:(Xx01 Xx000))=> x7) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found x7:(Xx01 Xx000)
% Found x7 as proof of (Xx00 Xx000)
% Found (fun (x7:(Xx01 Xx000))=> x7) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found x7:(Xx01 Xx000)
% Found x7 as proof of (Xx00 Xx000)
% Found (fun (x7:(Xx01 Xx000))=> x7) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found x7:(Xx01 Xx000)
% Found x7 as proof of (Xx00 Xx000)
% Found (fun (x7:(Xx01 Xx000))=> x7) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found x7:(Xx01 Xx000)
% Found x7 as proof of (Xx00 Xx000)
% Found (fun (x7:(Xx01 Xx000))=> x7) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found x7:(Xx01 Xx000)
% Found x7 as proof of (Xx00 Xx000)
% Found (fun (x7:(Xx01 Xx000))=> x7) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x500:=(x50 x6):((K x1) Xx)
% Found (x50 x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found x7:(Xx01 Xx000)
% Found x7 as proof of (Xx00 Xx000)
% Found (fun (x7:(Xx01 Xx000))=> x7) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x500:=(x50 x6):((K x1) Xx)
% Found (x50 x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found x7:(Xx01 Xx000)
% Found x7 as proof of (Xx00 Xx000)
% Found (fun (x7:(Xx01 Xx000))=> x7) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x500:=(x50 x6):((K x1) Xx)
% Found (x50 x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found x7:(Xx01 Xx000)
% Found x7 as proof of (Xx00 Xx000)
% Found (fun (x7:(Xx01 Xx000))=> x7) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x500:=(x50 x6):((K x1) Xx)
% Found (x50 x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found x7:(Xx01 Xx000)
% Found x7 as proof of (Xx00 Xx000)
% Found (fun (x7:(Xx01 Xx000))=> x7) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x300:=(x30 x4):((K x1) Xx)
% Found (x30 x4) as proof of ((K Xx01) Xx)
% Found ((x3 Xx) x4) as proof of ((K Xx01) Xx)
% Found ((x3 Xx) x4) as proof of ((K Xx01) Xx)
% Found ((x3 Xx) x4) as proof of ((K Xx01) Xx)
% Found x7:(Xx01 Xx000)
% Found x7 as proof of (Xx00 Xx000)
% Found (fun (x7:(Xx01 Xx000))=> x7) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x300:=(x30 x4):((K x1) Xx)
% Found (x30 x4) as proof of ((K Xx01) Xx)
% Found ((x3 Xx) x4) as proof of ((K Xx01) Xx)
% Found ((x3 Xx) x4) as proof of ((K Xx01) Xx)
% Found ((x3 Xx) x4) as proof of ((K Xx01) Xx)
% Found x7:(Xx01 Xx000)
% Found x7 as proof of (Xx00 Xx000)
% Found (fun (x7:(Xx01 Xx000))=> x7) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x500:=(x50 x6):((K x1) Xx)
% Found (x50 x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found x7:(Xx01 Xx000)
% Found x7 as proof of (Xx00 Xx000)
% Found (fun (x7:(Xx01 Xx000))=> x7) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx01 Xx000))=> x7) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x500:=(x50 x6):((K x1) Xx)
% Found (x50 x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx01) Xx)
% Found x3:(Xx01 Xx000)
% Instantiate: Xx00:=Xx01:(fofType->Prop)
% Found x3 as proof of (Xx00 Xx000)
% Found x3 as proof of (Xx00 Xx000)
% Found (fun (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (Xx00 Xx000)
% Found (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx))->(Xx00 Xx000))
% Found (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->(Xx00 Xx000)))
% Found (ex_ind00 (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx00 Xx000)
% Found ((ex_ind0 (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx00 Xx000)
% Found (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx00 Xx000)
% Found (fun (x3:(Xx01 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx01 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx01 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found x3:(Xx01 Xx000)
% Instantiate: Xx00:=Xx01:(fofType->Prop)
% Found x3 as proof of (Xx00 Xx000)
% Found x3 as proof of (Xx00 Xx000)
% Found (fun (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (Xx00 Xx000)
% Found (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx))->(Xx00 Xx000))
% Found (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->(Xx00 Xx000)))
% Found (ex_ind00 (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx00 Xx000)
% Found ((ex_ind0 (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx00 Xx000)
% Found (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx00 Xx000)
% Found (fun (x3:(Xx01 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx01 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx01 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found x5:(Xx01 Xx000)
% Instantiate: Xx00:=Xx01:(fofType->Prop)
% Found (fun (x5:(Xx01 Xx000))=> x5) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found ((x1020 (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx00) Xx)
% Found (((x102 Xx00) (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx00) Xx)
% Found ((((x10 x3) Xx00) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx00) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> ((((x10 x3) Xx00) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))))) as proof of ((K Xx00) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found x5:(Xx01 Xx000)
% Instantiate: Xx00:=Xx01:(fofType->Prop)
% Found (fun (x5:(Xx01 Xx000))=> x5) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found ((x0020 (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx00) Xx)
% Found (((x002 Xx00) (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx00) Xx)
% Found ((((x00 x3) Xx00) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx00) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> ((((x00 x3) Xx00) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))))) as proof of ((K Xx00) Xx)
% Found x4:(Xx1 Xx00)
% Instantiate: Xx1:=(K Xx2):(fofType->Prop)
% Found x4 as proof of ((K Xx2) Xx00)
% Found x4:(Xx1 Xx00)
% Instantiate: Xx1:=(K Xx2):(fofType->Prop)
% Found x4 as proof of ((K Xx2) Xx00)
% Found x4:(Xx1 Xx00)
% Instantiate: Xx1:=(K Xx2):(fofType->Prop)
% Found x4 as proof of ((K Xx2) Xx00)
% Found x4:(Xx1 Xx00)
% Instantiate: Xx1:=(K Xx2):(fofType->Prop)
% Found x4 as proof of ((K Xx2) Xx00)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found x5:(Xx01 Xx000)
% Instantiate: Xx00:=Xx01:(fofType->Prop)
% Found (fun (x5:(Xx01 Xx000))=> x5) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found ((x1020 (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx00) Xx)
% Found (((x102 Xx00) (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx00) Xx)
% Found ((((x10 x3) Xx00) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx00) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> ((((x10 x3) Xx00) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))))) as proof of ((K Xx00) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found x5:(Xx01 Xx000)
% Instantiate: Xx00:=Xx01:(fofType->Prop)
% Found (fun (x5:(Xx01 Xx000))=> x5) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found ((x2020 (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx00) Xx)
% Found (((x202 Xx00) (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx00) Xx)
% Found ((((x20 x3) Xx00) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx00) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> ((((x20 x3) Xx00) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))))) as proof of ((K Xx00) Xx)
% Found x3:(Xx01 Xx000)
% Instantiate: Xx00:=Xx01:(fofType->Prop)
% Found x3 as proof of (Xx00 Xx000)
% Found x3 as proof of (Xx00 Xx000)
% Found (fun (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (Xx00 Xx000)
% Found (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx))->(Xx00 Xx000))
% Found (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->(Xx00 Xx000)))
% Found (ex_ind00 (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx00 Xx000)
% Found ((ex_ind0 (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx00 Xx000)
% Found (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x0)) (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx00 Xx000)
% Found (fun (x3:(Xx01 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x0)) (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx01 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x0)) (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx01 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x0)) (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found x3:(Xx01 Xx000)
% Instantiate: Xx00:=Xx01:(fofType->Prop)
% Found x3 as proof of (Xx00 Xx000)
% Found x3 as proof of (Xx00 Xx000)
% Found (fun (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (Xx00 Xx000)
% Found (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx))->(Xx00 Xx000))
% Found (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->(Xx00 Xx000)))
% Found (ex_ind00 (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx00 Xx000)
% Found ((ex_ind0 (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx00 Xx000)
% Found (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x0)) (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx00 Xx000)
% Found (fun (x3:(Xx01 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x0)) (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx01 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x0)) (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx01 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x0)) (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found x3:(Xx01 Xx000)
% Instantiate: Xx00:=Xx01:(fofType->Prop)
% Found x3 as proof of (Xx00 Xx000)
% Found x3 as proof of (Xx00 Xx000)
% Found (fun (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (Xx00 Xx000)
% Found (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx))->(Xx00 Xx000))
% Found (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->(Xx00 Xx000)))
% Found (ex_ind00 (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx00 Xx000)
% Found ((ex_ind0 (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx00 Xx000)
% Found (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx00 Xx000)
% Found (fun (x3:(Xx01 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx01 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx01 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found x3:(Xx01 Xx000)
% Instantiate: Xx00:=Xx01:(fofType->Prop)
% Found x3 as proof of (Xx00 Xx000)
% Found x3 as proof of (Xx00 Xx000)
% Found (fun (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (Xx00 Xx000)
% Found (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx))->(Xx00 Xx000))
% Found (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->(Xx00 Xx000)))
% Found (ex_ind00 (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx00 Xx000)
% Found ((ex_ind0 (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx00 Xx000)
% Found (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx00 Xx000)
% Found (fun (x3:(Xx01 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx01 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx01 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found x5:(Xx01 Xx000)
% Instantiate: Xx00:=Xx01:(fofType->Prop)
% Found (fun (x5:(Xx01 Xx000))=> x5) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found ((x1020 (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx00) Xx)
% Found (((x102 Xx00) (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx00) Xx)
% Found ((((x10 x3) Xx00) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx00) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> ((((x10 x3) Xx00) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))))) as proof of ((K Xx00) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found x5:(Xx01 Xx000)
% Instantiate: Xx00:=Xx01:(fofType->Prop)
% Found (fun (x5:(Xx01 Xx000))=> x5) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found ((x0020 (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx00) Xx)
% Found (((x002 Xx00) (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx00) Xx)
% Found ((((x00 x3) Xx00) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx00) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> ((((x00 x3) Xx00) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))))) as proof of ((K Xx00) Xx)
% Found x4:(Xx00 Xx000)
% Instantiate: Xx00:=(K Xx01):(fofType->Prop)
% Found x4 as proof of ((K Xx01) Xx000)
% Found x4:(Xx00 Xx000)
% Instantiate: Xx00:=(K Xx01):(fofType->Prop)
% Found x4 as proof of ((K Xx01) Xx000)
% Found x4:(Xx00 Xx000)
% Instantiate: Xx00:=(K Xx01):(fofType->Prop)
% Found x4 as proof of ((K Xx01) Xx000)
% Found x4:(Xx00 Xx000)
% Instantiate: Xx00:=(K Xx01):(fofType->Prop)
% Found x4 as proof of ((K Xx01) Xx000)
% Found x3:(Xx01 Xx000)
% Instantiate: Xx00:=Xx01:(fofType->Prop)
% Found x3 as proof of (Xx00 Xx000)
% Found x3 as proof of (Xx00 Xx000)
% Found (fun (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (Xx00 Xx000)
% Found (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx))->(Xx00 Xx000))
% Found (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->(Xx00 Xx000)))
% Found (ex_ind00 (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx00 Xx000)
% Found ((ex_ind0 (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx00 Xx000)
% Found (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x0)) (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx00 Xx000)
% Found (fun (x3:(Xx01 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x0)) (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx01 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x0)) (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx01 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x0)) (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found x3:(Xx01 Xx000)
% Instantiate: Xx00:=Xx01:(fofType->Prop)
% Found x3 as proof of (Xx00 Xx000)
% Found x3 as proof of (Xx00 Xx000)
% Found (fun (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (Xx00 Xx000)
% Found (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx))->(Xx00 Xx000))
% Found (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->(Xx00 Xx000)))
% Found (ex_ind00 (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx00 Xx000)
% Found ((ex_ind0 (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx00 Xx000)
% Found (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x0)) (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx00 Xx000)
% Found (fun (x3:(Xx01 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x0)) (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx01 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x0)) (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx01 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x0)) (Xx00 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found x5:(Xx01 Xx000)
% Instantiate: Xx00:=Xx01:(fofType->Prop)
% Found (fun (x5:(Xx01 Xx000))=> x5) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found ((x2020 (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx00) Xx)
% Found (((x202 Xx00) (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx00) Xx)
% Found ((((x20 x3) Xx00) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx00) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> ((((x20 x3) Xx00) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))))) as proof of ((K Xx00) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx01) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx01) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect1 ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx01) Xx)
% Found x5:(Xx01 Xx000)
% Instantiate: Xx00:=Xx01:(fofType->Prop)
% Found (fun (x5:(Xx01 Xx000))=> x5) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found ((x1020 (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx00) Xx)
% Found (((x102 Xx00) (fun (Xx000:fofType) (x5:(Xx01 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx01) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx00) Xx)
% Found ((((x10 x3) Xx00) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx00) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> ((((x10 x3) Xx00) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))))) as proof of ((K Xx00) Xx)
% Found x3:(Xx02 Xx000)
% Found x3 as proof of (Xx01 Xx000)
% Found (fun (x3:(Xx02 Xx000))=> x3) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> x3) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> x3) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x3:(Xx02 Xx000)
% Found x3 as proof of (Xx01 Xx000)
% Found (fun (x3:(Xx02 Xx000))=> x3) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> x3) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> x3) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x4:(Xx00 Xx000)
% Instantiate: Xx00:=(K Xx01):(fofType->Prop)
% Found x4 as proof of ((K Xx01) Xx000)
% Found x4:(Xx00 Xx000)
% Instantiate: Xx00:=(K Xx01):(fofType->Prop)
% Found x4 as proof of ((K Xx01) Xx000)
% Found x4:(Xx00 Xx000)
% Instantiate: Xx00:=(K Xx01):(fofType->Prop)
% Found x4 as proof of ((K Xx01) Xx000)
% Found x4:(Xx00 Xx000)
% Instantiate: Xx00:=(K Xx01):(fofType->Prop)
% Found x4 as proof of ((K Xx01) Xx000)
% Found x4:(Xx00 Xx000)
% Instantiate: Xx00:=(K Xx01):(fofType->Prop)
% Found x4 as proof of ((K Xx01) Xx000)
% Found x4:(Xx00 Xx000)
% Instantiate: Xx00:=(K Xx01):(fofType->Prop)
% Found x4 as proof of ((K Xx01) Xx000)
% Found x4:(Xx00 Xx000)
% Instantiate: Xx00:=(K Xx01):(fofType->Prop)
% Found x4 as proof of ((K Xx01) Xx000)
% Found x4:(Xx00 Xx000)
% Instantiate: Xx00:=(K Xx01):(fofType->Prop)
% Found x4 as proof of ((K Xx01) Xx000)
% Found x4:(Xx00 Xx000)
% Instantiate: Xx00:=(K Xx01):(fofType->Prop)
% Found x4 as proof of ((K Xx01) Xx000)
% Found x4:(Xx00 Xx000)
% Instantiate: Xx00:=(K Xx01):(fofType->Prop)
% Found x4 as proof of ((K Xx01) Xx000)
% Found x4:(Xx00 Xx000)
% Instantiate: Xx00:=(K Xx01):(fofType->Prop)
% Found x4 as proof of ((K Xx01) Xx000)
% Found x4:(Xx00 Xx000)
% Instantiate: Xx00:=(K Xx01):(fofType->Prop)
% Found x4 as proof of ((K Xx01) Xx000)
% Found x4:(Xx00 Xx000)
% Instantiate: Xx00:=(K Xx01):(fofType->Prop)
% Found x4 as proof of ((K Xx01) Xx000)
% Found x4:(Xx00 Xx000)
% Instantiate: Xx00:=(K Xx01):(fofType->Prop)
% Found x4 as proof of ((K Xx01) Xx000)
% Found x4:(Xx00 Xx000)
% Instantiate: Xx00:=(K Xx01):(fofType->Prop)
% Found x4 as proof of ((K Xx01) Xx000)
% Found x4:(Xx00 Xx000)
% Instantiate: Xx00:=(K Xx01):(fofType->Prop)
% Found x4 as proof of ((K Xx01) Xx000)
% Found x3:(Xx02 Xx000)
% Found x3 as proof of (Xx01 Xx000)
% Found (fun (x3:(Xx02 Xx000))=> x3) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> x3) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> x3) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x3:(Xx02 Xx000)
% Found x3 as proof of (Xx01 Xx000)
% Found (fun (x3:(Xx02 Xx000))=> x3) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> x3) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> x3) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x3:(Xx02 Xx000)
% Found x3 as proof of (Xx01 Xx000)
% Found (fun (x3:(Xx02 Xx000))=> x3) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> x3) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> x3) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x3:(Xx02 Xx000)
% Found x3 as proof of (Xx01 Xx000)
% Found (fun (x3:(Xx02 Xx000))=> x3) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> x3) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> x3) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x3:(Xx02 Xx000)
% Found x3 as proof of (Xx01 Xx000)
% Found (fun (x3:(Xx02 Xx000))=> x3) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> x3) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> x3) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x3:(Xx02 Xx000)
% Found x3 as proof of (Xx01 Xx000)
% Found (fun (x3:(Xx02 Xx000))=> x3) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> x3) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> x3) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x3:(Xx02 Xx000)
% Found x3 as proof of (Xx01 Xx000)
% Found (fun (x3:(Xx02 Xx000))=> x3) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> x3) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> x3) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x3:(Xx02 Xx000)
% Found x3 as proof of (Xx01 Xx000)
% Found (fun (x3:(Xx02 Xx000))=> x3) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> x3) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> x3) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x3:(Xx02 Xx000)
% Found x3 as proof of (Xx01 Xx000)
% Found (fun (x3:(Xx02 Xx000))=> x3) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> x3) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> x3) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x3:(Xx02 Xx000)
% Found x3 as proof of (Xx01 Xx000)
% Found (fun (x3:(Xx02 Xx000))=> x3) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> x3) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> x3) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x3:(Xx02 Xx000)
% Found x3 as proof of (Xx01 Xx000)
% Found (fun (x3:(Xx02 Xx000))=> x3) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> x3) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> x3) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x3:(Xx02 Xx000)
% Found x3 as proof of (Xx01 Xx000)
% Found (fun (x3:(Xx02 Xx000))=> x3) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> x3) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> x3) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x3:(Xx02 Xx000)
% Found x3 as proof of (Xx01 Xx000)
% Found (fun (x3:(Xx02 Xx000))=> x3) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> x3) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> x3) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x3:(Xx02 Xx000)
% Found x3 as proof of (Xx01 Xx000)
% Found (fun (x3:(Xx02 Xx000))=> x3) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> x3) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> x3) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x3:(Xx02 Xx000)
% Found x3 as proof of (Xx01 Xx000)
% Found (fun (x3:(Xx02 Xx000))=> x3) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> x3) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> x3) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x3:(Xx02 Xx000)
% Found x3 as proof of (Xx01 Xx000)
% Found (fun (x3:(Xx02 Xx000))=> x3) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> x3) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> x3) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x3:(Xx02 Xx000)
% Found x3 as proof of (Xx01 Xx000)
% Found (fun (x3:(Xx02 Xx000))=> x3) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> x3) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> x3) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x3:(Xx02 Xx000)
% Found x3 as proof of (Xx01 Xx000)
% Found (fun (x3:(Xx02 Xx000))=> x3) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> x3) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> x3) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x4:(Xx1 Xx00)
% Instantiate: Xx1:=(K Xx2):(fofType->Prop)
% Found x4 as proof of ((K Xx2) Xx00)
% Found x4:(Xx1 Xx00)
% Instantiate: Xx1:=(K Xx2):(fofType->Prop)
% Found x4 as proof of ((K Xx2) Xx00)
% Found x4:(Xx1 Xx00)
% Instantiate: Xx1:=(K Xx2):(fofType->Prop)
% Found x4 as proof of ((K Xx2) Xx00)
% Found x4:(Xx1 Xx00)
% Instantiate: Xx1:=(K Xx2):(fofType->Prop)
% Found x4 as proof of ((K Xx2) Xx00)
% Found x4:(Xx00 Xx000)
% Instantiate: Xx00:=(K Xx01):(fofType->Prop)
% Found x4 as proof of ((K Xx01) Xx000)
% Found x4:(Xx00 Xx000)
% Instantiate: Xx00:=(K Xx01):(fofType->Prop)
% Found x4 as proof of ((K Xx01) Xx000)
% Found x4:(Xx00 Xx000)
% Instantiate: Xx00:=(K Xx01):(fofType->Prop)
% Found x4 as proof of ((K Xx01) Xx000)
% Found x4:(Xx00 Xx000)
% Instantiate: Xx00:=(K Xx01):(fofType->Prop)
% Found x4 as proof of ((K Xx01) Xx000)
% Found x4:(Xx00 Xx000)
% Instantiate: Xx00:=(K Xx01):(fofType->Prop)
% Found x4 as proof of ((K Xx01) Xx000)
% Found x4:(Xx00 Xx000)
% Instantiate: Xx00:=(K Xx01):(fofType->Prop)
% Found x4 as proof of ((K Xx01) Xx000)
% Found x4:(Xx00 Xx000)
% Instantiate: Xx00:=(K Xx01):(fofType->Prop)
% Found x4 as proof of ((K Xx01) Xx000)
% Found x4:(Xx00 Xx000)
% Instantiate: Xx00:=(K Xx01):(fofType->Prop)
% Found x4 as proof of ((K Xx01) Xx000)
% Found x5:(Xx02 Xx000)
% Found x5 as proof of (Xx01 Xx000)
% Found (fun (x5:(Xx02 Xx000))=> x5) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x5:(Xx02 Xx000)
% Found x5 as proof of (Xx01 Xx000)
% Found (fun (x5:(Xx02 Xx000))=> x5) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x5:(Xx02 Xx000)
% Found x5 as proof of (Xx01 Xx000)
% Found (fun (x5:(Xx02 Xx000))=> x5) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x5:(Xx02 Xx000)
% Found x5 as proof of (Xx01 Xx000)
% Found (fun (x5:(Xx02 Xx000))=> x5) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x5:(Xx02 Xx000)
% Found x5 as proof of (Xx01 Xx000)
% Found (fun (x5:(Xx02 Xx000))=> x5) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x5:(Xx02 Xx000)
% Found x5 as proof of (Xx01 Xx000)
% Found (fun (x5:(Xx02 Xx000))=> x5) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x3:(Xx02 Xx000)
% Found x3 as proof of (Xx01 Xx000)
% Found (fun (x3:(Xx02 Xx000))=> x3) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> x3) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> x3) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x3:(Xx02 Xx000)
% Found x3 as proof of (Xx01 Xx000)
% Found (fun (x3:(Xx02 Xx000))=> x3) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> x3) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> x3) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x5:(Xx02 Xx000)
% Found x5 as proof of (Xx01 Xx000)
% Found (fun (x5:(Xx02 Xx000))=> x5) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x5:(Xx02 Xx000)
% Found x5 as proof of (Xx01 Xx000)
% Found (fun (x5:(Xx02 Xx000))=> x5) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x3:(Xx02 Xx000)
% Found x3 as proof of (Xx01 Xx000)
% Found (fun (x3:(Xx02 Xx000))=> x3) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> x3) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> x3) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x3:(Xx02 Xx000)
% Found x3 as proof of (Xx01 Xx000)
% Found (fun (x3:(Xx02 Xx000))=> x3) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> x3) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> x3) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x3:(Xx02 Xx000)
% Found x3 as proof of (Xx01 Xx000)
% Found (fun (x3:(Xx02 Xx000))=> x3) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> x3) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> x3) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x3:(Xx02 Xx000)
% Found x3 as proof of (Xx01 Xx000)
% Found (fun (x3:(Xx02 Xx000))=> x3) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> x3) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> x3) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x3:(Xx02 Xx000)
% Found x3 as proof of (Xx01 Xx000)
% Found (fun (x3:(Xx02 Xx000))=> x3) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> x3) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> x3) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x3:(Xx02 Xx000)
% Found x3 as proof of (Xx01 Xx000)
% Found (fun (x3:(Xx02 Xx000))=> x3) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> x3) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> x3) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x3:(Xx02 Xx000)
% Found x3 as proof of (Xx01 Xx000)
% Found (fun (x3:(Xx02 Xx000))=> x3) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> x3) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> x3) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x3:(Xx02 Xx000)
% Found x3 as proof of (Xx01 Xx000)
% Found (fun (x3:(Xx02 Xx000))=> x3) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> x3) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> x3) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x3:(Xx02 Xx000)
% Found x3 as proof of (Xx01 Xx000)
% Found (fun (x3:(Xx02 Xx000))=> x3) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> x3) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> x3) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x3:(Xx02 Xx000)
% Found x3 as proof of (Xx01 Xx000)
% Found (fun (x3:(Xx02 Xx000))=> x3) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> x3) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> x3) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)) as proof of ((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)) as proof of ((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found x3:(Xx02 Xx000)
% Found x3 as proof of (Xx01 Xx000)
% Found (fun (x3:(Xx02 Xx000))=> x3) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> x3) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> x3) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x3:(Xx02 Xx000)
% Found x3 as proof of (Xx01 Xx000)
% Found (fun (x3:(Xx02 Xx000))=> x3) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> x3) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> x3) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x4:(Xx1 Xx00)
% Instantiate: Xx1:=(K Xx2):(fofType->Prop)
% Found x4 as proof of ((K Xx2) Xx00)
% Found x4:(Xx1 Xx00)
% Instantiate: Xx1:=(K Xx2):(fofType->Prop)
% Found x4 as proof of ((K Xx2) Xx00)
% Found x4:(Xx1 Xx00)
% Instantiate: Xx1:=(K Xx2):(fofType->Prop)
% Found x4 as proof of ((K Xx2) Xx00)
% Found x4:(Xx1 Xx00)
% Instantiate: Xx1:=(K Xx2):(fofType->Prop)
% Found x4 as proof of ((K Xx2) Xx00)
% Found x3:(Xx02 Xx000)
% Found x3 as proof of (Xx01 Xx000)
% Found (fun (x3:(Xx02 Xx000))=> x3) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> x3) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> x3) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x3:(Xx02 Xx000)
% Found x3 as proof of (Xx01 Xx000)
% Found (fun (x3:(Xx02 Xx000))=> x3) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> x3) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> x3) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x5:(Xx02 Xx000)
% Found x5 as proof of (Xx01 Xx000)
% Found (fun (x5:(Xx02 Xx000))=> x5) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x5:(Xx02 Xx000)
% Found x5 as proof of (Xx01 Xx000)
% Found (fun (x5:(Xx02 Xx000))=> x5) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x5:(Xx02 Xx000)
% Found x5 as proof of (Xx01 Xx000)
% Found (fun (x5:(Xx02 Xx000))=> x5) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x5:(Xx02 Xx000)
% Found x5 as proof of (Xx01 Xx000)
% Found (fun (x5:(Xx02 Xx000))=> x5) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x5:(Xx02 Xx000)
% Found x5 as proof of (Xx01 Xx000)
% Found (fun (x5:(Xx02 Xx000))=> x5) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x5:(Xx02 Xx000)
% Found x5 as proof of (Xx01 Xx000)
% Found (fun (x5:(Xx02 Xx000))=> x5) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x5:(Xx02 Xx000)
% Found x5 as proof of (Xx01 Xx000)
% Found (fun (x5:(Xx02 Xx000))=> x5) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x5:(Xx02 Xx000)
% Found x5 as proof of (Xx01 Xx000)
% Found (fun (x5:(Xx02 Xx000))=> x5) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x5:(Xx02 Xx000)
% Found x5 as proof of (Xx01 Xx000)
% Found (fun (x5:(Xx02 Xx000))=> x5) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x5:(Xx02 Xx000)
% Found x5 as proof of (Xx01 Xx000)
% Found (fun (x5:(Xx02 Xx000))=> x5) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx02) Xx)
% Found x5:(Xx02 Xx000)
% Found x5 as proof of (Xx01 Xx000)
% Found (fun (x5:(Xx02 Xx000))=> x5) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x5:(Xx02 Xx000)
% Found x5 as proof of (Xx01 Xx000)
% Found (fun (x5:(Xx02 Xx000))=> x5) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x5:(Xx02 Xx000)
% Found x5 as proof of (Xx01 Xx000)
% Found (fun (x5:(Xx02 Xx000))=> x5) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x5:(Xx02 Xx000)
% Found x5 as proof of (Xx01 Xx000)
% Found (fun (x5:(Xx02 Xx000))=> x5) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x5:(Xx02 Xx000)
% Found x5 as proof of (Xx01 Xx000)
% Found (fun (x5:(Xx02 Xx000))=> x5) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x5:(Xx02 Xx000)
% Found x5 as proof of (Xx01 Xx000)
% Found (fun (x5:(Xx02 Xx000))=> x5) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x5:(Xx02 Xx000)
% Found x5 as proof of (Xx01 Xx000)
% Found (fun (x5:(Xx02 Xx000))=> x5) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x5:(Xx02 Xx000)
% Found x5 as proof of (Xx01 Xx000)
% Found (fun (x5:(Xx02 Xx000))=> x5) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x5:(Xx02 Xx000)
% Found x5 as proof of (Xx01 Xx000)
% Found (fun (x5:(Xx02 Xx000))=> x5) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x5:(Xx02 Xx000)
% Found x5 as proof of (Xx01 Xx000)
% Found (fun (x5:(Xx02 Xx000))=> x5) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x5:(Xx02 Xx000)
% Found x5 as proof of (Xx01 Xx000)
% Found (fun (x5:(Xx02 Xx000))=> x5) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x5:(Xx02 Xx000)
% Found x5 as proof of (Xx01 Xx000)
% Found (fun (x5:(Xx02 Xx000))=> x5) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x5:(Xx02 Xx000)
% Found x5 as proof of (Xx01 Xx000)
% Found (fun (x5:(Xx02 Xx000))=> x5) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x5:(Xx02 Xx000)
% Found x5 as proof of (Xx01 Xx000)
% Found (fun (x5:(Xx02 Xx000))=> x5) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x5:(Xx02 Xx000)
% Found x5 as proof of (Xx01 Xx000)
% Found (fun (x5:(Xx02 Xx000))=> x5) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x5:(Xx02 Xx000)
% Found x5 as proof of (Xx01 Xx000)
% Found (fun (x5:(Xx02 Xx000))=> x5) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x3:(Xx02 Xx000)
% Instantiate: Xx01:=Xx02:(fofType->Prop)
% Found x3 as proof of (Xx01 Xx000)
% Found (fun (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (Xx01 Xx000)
% Found (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx))->(Xx01 Xx000))
% Found (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->(Xx01 Xx000)))
% Found (ex_ind00 (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx01 Xx000)
% Found ((ex_ind0 (Xx01 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx01 Xx000)
% Found (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx01 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx01 Xx000)
% Found (fun (x3:(Xx02 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx01 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx01 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx01 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx02) Xx)
% Found x3:(Xx02 Xx000)
% Instantiate: Xx01:=Xx02:(fofType->Prop)
% Found x3 as proof of (Xx01 Xx000)
% Found (fun (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (Xx01 Xx000)
% Found (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx))->(Xx01 Xx000))
% Found (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->(Xx01 Xx000)))
% Found (ex_ind00 (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx01 Xx000)
% Found ((ex_ind0 (Xx01 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx01 Xx000)
% Found (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx01 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx01 Xx000)
% Found (fun (x3:(Xx02 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx01 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx01 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx01 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx02) Xx)
% Found x3:(Xx02 Xx000)
% Instantiate: Xx01:=Xx02:(fofType->Prop)
% Found x3 as proof of (Xx01 Xx000)
% Found (fun (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (Xx01 Xx000)
% Found (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx))->(Xx01 Xx000))
% Found (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->(Xx01 Xx000)))
% Found (ex_ind00 (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx01 Xx000)
% Found ((ex_ind0 (Xx01 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx01 Xx000)
% Found (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx01 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx01 Xx000)
% Found (fun (x3:(Xx02 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx01 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx01 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx01 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx02) Xx)
% Found x3:(Xx02 Xx000)
% Instantiate: Xx01:=Xx02:(fofType->Prop)
% Found x3 as proof of (Xx01 Xx000)
% Found (fun (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (Xx01 Xx000)
% Found (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx))->(Xx01 Xx000))
% Found (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->(Xx01 Xx000)))
% Found (ex_ind00 (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx01 Xx000)
% Found ((ex_ind0 (Xx01 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx01 Xx000)
% Found (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx01 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx01 Xx000)
% Found (fun (x3:(Xx02 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx01 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx01 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx01 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x3:(Xx02 Xx000)
% Instantiate: Xx01:=Xx02:(fofType->Prop)
% Found x3 as proof of (Xx01 Xx000)
% Found (fun (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (Xx01 Xx000)
% Found (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx))->(Xx01 Xx000))
% Found (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->(Xx01 Xx000)))
% Found (ex_ind00 (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx01 Xx000)
% Found ((ex_ind0 (Xx01 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx01 Xx000)
% Found (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx01 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx01 Xx000)
% Found (fun (x3:(Xx02 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx01 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx01 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx01 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx02) Xx)
% Found x3:(Xx02 Xx000)
% Instantiate: Xx01:=Xx02:(fofType->Prop)
% Found x3 as proof of (Xx01 Xx000)
% Found (fun (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (Xx01 Xx000)
% Found (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx))->(Xx01 Xx000))
% Found (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->(Xx01 Xx000)))
% Found (ex_ind00 (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx01 Xx000)
% Found ((ex_ind0 (Xx01 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx01 Xx000)
% Found (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx01 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx01 Xx000)
% Found (fun (x3:(Xx02 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx01 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx01 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx01 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found x5:(Xx02 Xx000)
% Instantiate: Xx01:=Xx02:(fofType->Prop)
% Found (fun (x5:(Xx02 Xx000))=> x5) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found ((x0030 (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found (((x003 Xx01) (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found ((((x00 x3) Xx01) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> ((((x00 x3) Xx01) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found x5:(Xx02 Xx000)
% Instantiate: Xx01:=Xx02:(fofType->Prop)
% Found (fun (x5:(Xx02 Xx000))=> x5) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found ((x1030 (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found (((x103 Xx01) (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found ((((x10 x3) Xx01) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> ((((x10 x3) Xx01) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found x5:(Xx02 Xx000)
% Instantiate: Xx01:=Xx02:(fofType->Prop)
% Found (fun (x5:(Xx02 Xx000))=> x5) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found ((x1030 (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found (((x103 Xx01) (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found ((((x10 x3) Xx01) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> ((((x10 x3) Xx01) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found x5:(Xx02 Xx000)
% Instantiate: Xx01:=Xx02:(fofType->Prop)
% Found (fun (x5:(Xx02 Xx000))=> x5) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found ((x0030 (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found (((x003 Xx01) (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found ((((x00 x3) Xx01) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> ((((x00 x3) Xx01) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found x5:(Xx02 Xx000)
% Instantiate: Xx01:=Xx02:(fofType->Prop)
% Found (fun (x5:(Xx02 Xx000))=> x5) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found ((x1030 (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found (((x103 Xx01) (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found ((((x10 x3) Xx01) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> ((((x10 x3) Xx01) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found x5:(Xx02 Xx000)
% Instantiate: Xx01:=Xx02:(fofType->Prop)
% Found (fun (x5:(Xx02 Xx000))=> x5) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found ((x0030 (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found (((x003 Xx01) (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found ((((x00 x3) Xx01) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> ((((x00 x3) Xx01) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))))) as proof of ((K Xx01) Xx)
% Found x3:(Xx02 Xx000)
% Found x3 as proof of (Xx01 Xx000)
% Found (fun (x3:(Xx02 Xx000))=> x3) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> x3) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> x3) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x3:(Xx02 Xx000)
% Found x3 as proof of (Xx01 Xx000)
% Found (fun (x3:(Xx02 Xx000))=> x3) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> x3) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> x3) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x3:(Xx02 Xx000)
% Found x3 as proof of (Xx01 Xx000)
% Found (fun (x3:(Xx02 Xx000))=> x3) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> x3) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> x3) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x3:(Xx02 Xx000)
% Found x3 as proof of (Xx01 Xx000)
% Found (fun (x3:(Xx02 Xx000))=> x3) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> x3) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> x3) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)) as proof of ((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)) as proof of ((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)) as proof of ((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)) as proof of ((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)) as proof of ((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)) as proof of ((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx02) Xx)
% Found x5:(Xx02 Xx000)
% Found x5 as proof of (Xx01 Xx000)
% Found (fun (x5:(Xx02 Xx000))=> x5) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x5:(Xx02 Xx000)
% Found x5 as proof of (Xx01 Xx000)
% Found (fun (x5:(Xx02 Xx000))=> x5) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx02) Xx)
% Found x5:(Xx02 Xx000)
% Found x5 as proof of (Xx01 Xx000)
% Found (fun (x5:(Xx02 Xx000))=> x5) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x5:(Xx02 Xx000)
% Found x5 as proof of (Xx01 Xx000)
% Found (fun (x5:(Xx02 Xx000))=> x5) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x5:(Xx02 Xx000)
% Found x5 as proof of (Xx01 Xx000)
% Found (fun (x5:(Xx02 Xx000))=> x5) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x5:(Xx02 Xx000)
% Found x5 as proof of (Xx01 Xx000)
% Found (fun (x5:(Xx02 Xx000))=> x5) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x5:(Xx02 Xx000)
% Found x5 as proof of (Xx01 Xx000)
% Found (fun (x5:(Xx02 Xx000))=> x5) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x5:(Xx02 Xx000)
% Found x5 as proof of (Xx01 Xx000)
% Found (fun (x5:(Xx02 Xx000))=> x5) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x50:=(x5 Xx):((x1 Xx)->((K x1) Xx))
% Found (x5 Xx) as proof of ((x1 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x1 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x5 Xx)) as proof of ((x1 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x5) x2)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x5) x2)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x1 Xx)->((K x1) Xx))
% Found (x5 Xx) as proof of ((x1 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x1 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x5 Xx)) as proof of ((x1 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x5) x2)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x5) x2)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found x5:(Xx02 Xx000)
% Found x5 as proof of (Xx01 Xx000)
% Found (fun (x5:(Xx02 Xx000))=> x5) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x5:(Xx02 Xx000)
% Found x5 as proof of (Xx01 Xx000)
% Found (fun (x5:(Xx02 Xx000))=> x5) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x3:(Xx02 Xx000)
% Instantiate: Xx01:=Xx02:(fofType->Prop)
% Found x3 as proof of (Xx01 Xx000)
% Found (fun (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (Xx01 Xx000)
% Found (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx))->(Xx01 Xx000))
% Found (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->(Xx01 Xx000)))
% Found (ex_ind00 (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx01 Xx000)
% Found ((ex_ind0 (Xx01 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx01 Xx000)
% Found (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x0)) (Xx01 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx01 Xx000)
% Found (fun (x3:(Xx02 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x0)) (Xx01 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x0)) (Xx01 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x0)) (Xx01 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx02) Xx)
% Found x3:(Xx02 Xx000)
% Instantiate: Xx01:=Xx02:(fofType->Prop)
% Found x3 as proof of (Xx01 Xx000)
% Found (fun (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (Xx01 Xx000)
% Found (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx))->(Xx01 Xx000))
% Found (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->(Xx01 Xx000)))
% Found (ex_ind00 (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx01 Xx000)
% Found ((ex_ind0 (Xx01 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx01 Xx000)
% Found (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x0)) (Xx01 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx01 Xx000)
% Found (fun (x3:(Xx02 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x0)) (Xx01 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x0)) (Xx01 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x0)) (Xx01 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found x5:(Xx02 Xx000)
% Instantiate: Xx01:=Xx02:(fofType->Prop)
% Found (fun (x5:(Xx02 Xx000))=> x5) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found ((x0030 (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found (((x003 Xx01) (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found ((((x00 x3) Xx01) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> ((((x00 x3) Xx01) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found x5:(Xx02 Xx000)
% Instantiate: Xx01:=Xx02:(fofType->Prop)
% Found (fun (x5:(Xx02 Xx000))=> x5) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found ((x1030 (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found (((x103 Xx01) (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found ((((x10 x3) Xx01) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> ((((x10 x3) Xx01) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))))) as proof of ((K Xx01) Xx)
% Found x3:(Xx02 Xx000)
% Instantiate: Xx01:=Xx02:(fofType->Prop)
% Found x3 as proof of (Xx01 Xx000)
% Found (fun (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (Xx01 Xx000)
% Found (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx))->(Xx01 Xx000))
% Found (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->(Xx01 Xx000)))
% Found (ex_ind00 (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx01 Xx000)
% Found ((ex_ind0 (Xx01 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx01 Xx000)
% Found (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x0)) (Xx01 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx01 Xx000)
% Found (fun (x3:(Xx02 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x0)) (Xx01 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x0)) (Xx01 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x0)) (Xx01 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx02) Xx)
% Found x3:(Xx02 Xx000)
% Instantiate: Xx01:=Xx02:(fofType->Prop)
% Found x3 as proof of (Xx01 Xx000)
% Found (fun (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (Xx01 Xx000)
% Found (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx))->(Xx01 Xx000))
% Found (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->(Xx01 Xx000)))
% Found (ex_ind00 (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx01 Xx000)
% Found ((ex_ind0 (Xx01 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx01 Xx000)
% Found (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x0)) (Xx01 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx01 Xx000)
% Found (fun (x3:(Xx02 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x0)) (Xx01 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x0)) (Xx01 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x0)) (Xx01 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x3:(Xx02 Xx000)
% Instantiate: Xx01:=Xx02:(fofType->Prop)
% Found x3 as proof of (Xx01 Xx000)
% Found (fun (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (Xx01 Xx000)
% Found (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx))->(Xx01 Xx000))
% Found (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->(Xx01 Xx000)))
% Found (ex_ind00 (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx01 Xx000)
% Found ((ex_ind0 (Xx01 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx01 Xx000)
% Found (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x0)) (Xx01 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx01 Xx000)
% Found (fun (x3:(Xx02 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x0)) (Xx01 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x0)) (Xx01 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x0)) (Xx01 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx02) Xx)
% Found x3:(Xx02 Xx000)
% Instantiate: Xx01:=Xx02:(fofType->Prop)
% Found x3 as proof of (Xx01 Xx000)
% Found (fun (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (Xx01 Xx000)
% Found (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx))->(Xx01 Xx000))
% Found (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->(Xx01 Xx000)))
% Found (ex_ind00 (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx01 Xx000)
% Found ((ex_ind0 (Xx01 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx01 Xx000)
% Found (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x0)) (Xx01 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx01 Xx000)
% Found (fun (x3:(Xx02 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x0)) (Xx01 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x0)) (Xx01 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x0)) (Xx01 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found x5:(Xx02 Xx000)
% Instantiate: Xx01:=Xx02:(fofType->Prop)
% Found (fun (x5:(Xx02 Xx000))=> x5) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found ((x1030 (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found (((x103 Xx01) (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found ((((x10 x3) Xx01) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> ((((x10 x3) Xx01) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found x5:(Xx02 Xx000)
% Instantiate: Xx01:=Xx02:(fofType->Prop)
% Found (fun (x5:(Xx02 Xx000))=> x5) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found ((x2030 (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found (((x203 Xx01) (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found ((((x20 x3) Xx01) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> ((((x20 x3) Xx01) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found x5:(Xx02 Xx000)
% Instantiate: Xx01:=Xx02:(fofType->Prop)
% Found (fun (x5:(Xx02 Xx000))=> x5) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found ((x1030 (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found (((x103 Xx01) (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found ((((x10 x3) Xx01) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> ((((x10 x3) Xx01) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found x5:(Xx02 Xx000)
% Instantiate: Xx01:=Xx02:(fofType->Prop)
% Found (fun (x5:(Xx02 Xx000))=> x5) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found ((x0030 (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found (((x003 Xx01) (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found ((((x00 x3) Xx01) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> ((((x00 x3) Xx01) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found x5:(Xx02 Xx000)
% Instantiate: Xx01:=Xx02:(fofType->Prop)
% Found (fun (x5:(Xx02 Xx000))=> x5) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found ((x0030 (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found (((x003 Xx01) (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found ((((x00 x3) Xx01) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> ((((x00 x3) Xx01) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found x5:(Xx02 Xx000)
% Instantiate: Xx01:=Xx02:(fofType->Prop)
% Found (fun (x5:(Xx02 Xx000))=> x5) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found ((x1030 (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found (((x103 Xx01) (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found ((((x10 x3) Xx01) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> ((((x10 x3) Xx01) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found x5:(Xx02 Xx000)
% Instantiate: Xx01:=Xx02:(fofType->Prop)
% Found (fun (x5:(Xx02 Xx000))=> x5) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found ((x1030 (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found (((x103 Xx01) (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found ((((x10 x3) Xx01) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> ((((x10 x3) Xx01) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found x5:(Xx02 Xx000)
% Instantiate: Xx01:=Xx02:(fofType->Prop)
% Found (fun (x5:(Xx02 Xx000))=> x5) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found ((x2030 (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found (((x203 Xx01) (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found ((((x20 x3) Xx01) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> ((((x20 x3) Xx01) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found x5:(Xx02 Xx000)
% Instantiate: Xx01:=Xx02:(fofType->Prop)
% Found (fun (x5:(Xx02 Xx000))=> x5) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found ((x1030 (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found (((x103 Xx01) (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found ((((x10 x3) Xx01) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> ((((x10 x3) Xx01) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found x5:(Xx02 Xx000)
% Instantiate: Xx01:=Xx02:(fofType->Prop)
% Found (fun (x5:(Xx02 Xx000))=> x5) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found ((x2030 (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found (((x203 Xx01) (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found ((((x20 x3) Xx01) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> ((((x20 x3) Xx01) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))))) as proof of ((K Xx01) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found x5:(Xx02 Xx000)
% Instantiate: Xx01:=Xx02:(fofType->Prop)
% Found (fun (x5:(Xx02 Xx000))=> x5) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found ((x0030 (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found (((x003 Xx01) (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found ((((x00 x3) Xx01) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> ((((x00 x3) Xx01) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))))) as proof of ((K Xx01) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found x5:(Xx02 Xx000)
% Instantiate: Xx01:=Xx02:(fofType->Prop)
% Found (fun (x5:(Xx02 Xx000))=> x5) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found ((x1030 (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found (((x103 Xx01) (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found ((((x10 x3) Xx01) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> ((((x10 x3) Xx01) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))))) as proof of ((K Xx01) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x5:(Xx01 Xx0000)
% Instantiate: Xx01:=(K Xx02):(fofType->Prop)
% Found x5 as proof of ((K Xx02) Xx0000)
% Found x5:(Xx01 Xx0000)
% Instantiate: Xx01:=(K Xx02):(fofType->Prop)
% Found x5 as proof of ((K Xx02) Xx0000)
% Found x5:(Xx01 Xx0000)
% Instantiate: Xx01:=(K Xx02):(fofType->Prop)
% Found x5 as proof of ((K Xx02) Xx0000)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x5:(Xx01 Xx0000)
% Instantiate: Xx01:=(K Xx02):(fofType->Prop)
% Found x5 as proof of ((K Xx02) Xx0000)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x5:(Xx01 Xx0000)
% Instantiate: Xx01:=(K Xx02):(fofType->Prop)
% Found x5 as proof of ((K Xx02) Xx0000)
% Found x5:(Xx01 Xx0000)
% Instantiate: Xx01:=(K Xx02):(fofType->Prop)
% Found x5 as proof of ((K Xx02) Xx0000)
% Found x5:(Xx01 Xx0000)
% Instantiate: Xx01:=(K Xx02):(fofType->Prop)
% Found x5 as proof of ((K Xx02) Xx0000)
% Found x5:(Xx01 Xx0000)
% Instantiate: Xx01:=(K Xx02):(fofType->Prop)
% Found x5 as proof of ((K Xx02) Xx0000)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found x5:(Xx02 Xx000)
% Instantiate: Xx01:=Xx02:(fofType->Prop)
% Found (fun (x5:(Xx02 Xx000))=> x5) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found ((x1030 (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found (((x103 Xx01) (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found ((((x10 x3) Xx01) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> ((((x10 x3) Xx01) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found x5:(Xx02 Xx000)
% Instantiate: Xx01:=Xx02:(fofType->Prop)
% Found (fun (x5:(Xx02 Xx000))=> x5) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found ((x0030 (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found (((x003 Xx01) (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found ((((x00 x3) Xx01) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> ((((x00 x3) Xx01) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found x5:(Xx02 Xx000)
% Instantiate: Xx01:=Xx02:(fofType->Prop)
% Found (fun (x5:(Xx02 Xx000))=> x5) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found ((x0030 (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found (((x003 Xx01) (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found ((((x00 x3) Xx01) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> ((((x00 x3) Xx01) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found x5:(Xx02 Xx000)
% Instantiate: Xx01:=Xx02:(fofType->Prop)
% Found (fun (x5:(Xx02 Xx000))=> x5) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found ((x1030 (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found (((x103 Xx01) (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found ((((x10 x3) Xx01) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> ((((x10 x3) Xx01) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))))) as proof of ((K Xx01) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)) as proof of ((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx)) as proof of ((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x1) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x1) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x1) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x1) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x300:=(x30 x4):((K x1) Xx)
% Found (x30 x4) as proof of ((K Xx02) Xx)
% Found ((x3 Xx) x4) as proof of ((K Xx02) Xx)
% Found ((x3 Xx) x4) as proof of ((K Xx02) Xx)
% Found ((x3 Xx) x4) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x300:=(x30 x4):((K x1) Xx)
% Found (x30 x4) as proof of ((K Xx02) Xx)
% Found ((x3 Xx) x4) as proof of ((K Xx02) Xx)
% Found ((x3 Xx) x4) as proof of ((K Xx02) Xx)
% Found ((x3 Xx) x4) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x1) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x1) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x1) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x1) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx02) Xx)
% Found x3:(Xx02 Xx000)
% Instantiate: Xx01:=Xx02:(fofType->Prop)
% Found x3 as proof of (Xx01 Xx000)
% Found (fun (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (Xx01 Xx000)
% Found (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx))->(Xx01 Xx000))
% Found (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->(Xx01 Xx000)))
% Found (ex_ind00 (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx01 Xx000)
% Found ((ex_ind0 (Xx01 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx01 Xx000)
% Found (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx01 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx01 Xx000)
% Found (fun (x3:(Xx02 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx01 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx01 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx01 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx02) Xx)
% Found x3:(Xx02 Xx000)
% Instantiate: Xx01:=Xx02:(fofType->Prop)
% Found x3 as proof of (Xx01 Xx000)
% Found (fun (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (Xx01 Xx000)
% Found (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx))->(Xx01 Xx000))
% Found (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->(Xx01 Xx000)))
% Found (ex_ind00 (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx01 Xx000)
% Found ((ex_ind0 (Xx01 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx01 Xx000)
% Found (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx01 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx01 Xx000)
% Found (fun (x3:(Xx02 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx01 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx01 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx01 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx02) Xx)
% Found x3:(Xx02 Xx000)
% Instantiate: Xx01:=Xx02:(fofType->Prop)
% Found x3 as proof of (Xx01 Xx000)
% Found (fun (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (Xx01 Xx000)
% Found (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx))->(Xx01 Xx000))
% Found (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->(Xx01 Xx000)))
% Found (ex_ind00 (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx01 Xx000)
% Found ((ex_ind0 (Xx01 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx01 Xx000)
% Found (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx01 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx01 Xx000)
% Found (fun (x3:(Xx02 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx01 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx01 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx01 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx02) Xx)
% Found x3:(Xx02 Xx000)
% Instantiate: Xx01:=Xx02:(fofType->Prop)
% Found x3 as proof of (Xx01 Xx000)
% Found (fun (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (Xx01 Xx000)
% Found (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx))->(Xx01 Xx000))
% Found (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3) as proof of (forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->(Xx01 Xx000)))
% Found (ex_ind00 (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx01 Xx000)
% Found ((ex_ind0 (Xx01 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx01 Xx000)
% Found (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx01 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3)) as proof of (Xx01 Xx000)
% Found (fun (x3:(Xx02 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx01 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx01 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x3:(Xx02 Xx000))=> (((fun (P:Prop) (x4:(forall (x:(fofType->Prop)), (((and (forall (Xx0:fofType), ((x Xx0)->((K x) Xx0)))) (x Xx))->P)))=> (((((ex_ind (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx0:fofType), ((S Xx0)->((K S) Xx0)))) (S Xx)))) P) x4) x2)) (Xx01 Xx000)) (fun (x4:(fofType->Prop)) (x5:((and (forall (Xx0:fofType), ((x4 Xx0)->((K x4) Xx0)))) (x4 Xx)))=> x3))) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x1 Xx)->((K x1) Xx))
% Found (x5 Xx) as proof of ((x1 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x1 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x5 Xx)) as proof of ((x1 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x5) x2)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x5) x2)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x1 Xx)->((K x1) Xx))
% Found (x5 Xx) as proof of ((x1 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x1 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x5 Xx)) as proof of ((x1 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x5) x2)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x5) x2)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found x5:(Xx01 Xx0000)
% Instantiate: Xx01:=(K Xx02):(fofType->Prop)
% Found x5 as proof of ((K Xx02) Xx0000)
% Found x5:(Xx01 Xx0000)
% Instantiate: Xx01:=(K Xx02):(fofType->Prop)
% Found x5 as proof of ((K Xx02) Xx0000)
% Found x5:(Xx01 Xx0000)
% Instantiate: Xx01:=(K Xx02):(fofType->Prop)
% Found x5 as proof of ((K Xx02) Xx0000)
% Found x5:(Xx01 Xx0000)
% Instantiate: Xx01:=(K Xx02):(fofType->Prop)
% Found x5 as proof of ((K Xx02) Xx0000)
% Found x5:(Xx01 Xx0000)
% Instantiate: Xx01:=(K Xx02):(fofType->Prop)
% Found x5 as proof of ((K Xx02) Xx0000)
% Found x5:(Xx01 Xx0000)
% Instantiate: Xx01:=(K Xx02):(fofType->Prop)
% Found x5 as proof of ((K Xx02) Xx0000)
% Found x5:(Xx01 Xx0000)
% Instantiate: Xx01:=(K Xx02):(fofType->Prop)
% Found x5 as proof of ((K Xx02) Xx0000)
% Found x5:(Xx01 Xx0000)
% Instantiate: Xx01:=(K Xx02):(fofType->Prop)
% Found x5 as proof of ((K Xx02) Xx0000)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found x5:(Xx02 Xx000)
% Instantiate: Xx01:=Xx02:(fofType->Prop)
% Found (fun (x5:(Xx02 Xx000))=> x5) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found ((x2030 (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found (((x203 Xx01) (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found ((((x20 x3) Xx01) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> ((((x20 x3) Xx01) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found x5:(Xx02 Xx000)
% Instantiate: Xx01:=Xx02:(fofType->Prop)
% Found (fun (x5:(Xx02 Xx000))=> x5) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found ((x1030 (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found (((x103 Xx01) (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found ((((x10 x3) Xx01) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> ((((x10 x3) Xx01) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))))) as proof of ((K Xx01) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x5:(Xx01 Xx0000)
% Instantiate: Xx01:=(K Xx02):(fofType->Prop)
% Found x5 as proof of ((K Xx02) Xx0000)
% Found x5:(Xx01 Xx0000)
% Instantiate: Xx01:=(K Xx02):(fofType->Prop)
% Found x5 as proof of ((K Xx02) Xx0000)
% Found x5:(Xx01 Xx0000)
% Instantiate: Xx01:=(K Xx02):(fofType->Prop)
% Found x5 as proof of ((K Xx02) Xx0000)
% Found x5:(Xx01 Xx0000)
% Instantiate: Xx01:=(K Xx02):(fofType->Prop)
% Found x5 as proof of ((K Xx02) Xx0000)
% Found x5:(Xx01 Xx0000)
% Instantiate: Xx01:=(K Xx02):(fofType->Prop)
% Found x5 as proof of ((K Xx02) Xx0000)
% Found x5:(Xx01 Xx0000)
% Instantiate: Xx01:=(K Xx02):(fofType->Prop)
% Found x5 as proof of ((K Xx02) Xx0000)
% Found x5:(Xx01 Xx0000)
% Instantiate: Xx01:=(K Xx02):(fofType->Prop)
% Found x5 as proof of ((K Xx02) Xx0000)
% Found x5:(Xx01 Xx0000)
% Instantiate: Xx01:=(K Xx02):(fofType->Prop)
% Found x5 as proof of ((K Xx02) Xx0000)
% Found x5:(Xx01 Xx0000)
% Instantiate: Xx01:=(K Xx02):(fofType->Prop)
% Found x5 as proof of ((K Xx02) Xx0000)
% Found x5:(Xx01 Xx0000)
% Instantiate: Xx01:=(K Xx02):(fofType->Prop)
% Found x5 as proof of ((K Xx02) Xx0000)
% Found x5:(Xx01 Xx0000)
% Instantiate: Xx01:=(K Xx02):(fofType->Prop)
% Found x5 as proof of ((K Xx02) Xx0000)
% Found x5:(Xx01 Xx0000)
% Instantiate: Xx01:=(K Xx02):(fofType->Prop)
% Found x5 as proof of ((K Xx02) Xx0000)
% Found x5:(Xx01 Xx0000)
% Instantiate: Xx01:=(K Xx02):(fofType->Prop)
% Found x5 as proof of ((K Xx02) Xx0000)
% Found x5:(Xx01 Xx0000)
% Instantiate: Xx01:=(K Xx02):(fofType->Prop)
% Found x5 as proof of ((K Xx02) Xx0000)
% Found x5:(Xx01 Xx0000)
% Instantiate: Xx01:=(K Xx02):(fofType->Prop)
% Found x5 as proof of ((K Xx02) Xx0000)
% Found x5:(Xx01 Xx0000)
% Instantiate: Xx01:=(K Xx02):(fofType->Prop)
% Found x5 as proof of ((K Xx02) Xx0000)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found x5:(Xx02 Xx000)
% Instantiate: Xx01:=Xx02:(fofType->Prop)
% Found (fun (x5:(Xx02 Xx000))=> x5) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found ((x2030 (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found (((x203 Xx01) (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found ((((x20 x3) Xx01) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> ((((x20 x3) Xx01) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found x5:(Xx02 Xx000)
% Instantiate: Xx01:=Xx02:(fofType->Prop)
% Found (fun (x5:(Xx02 Xx000))=> x5) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found ((x1030 (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found (((x103 Xx01) (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found ((((x10 x3) Xx01) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> ((((x10 x3) Xx01) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found x5:(Xx02 Xx000)
% Instantiate: Xx01:=Xx02:(fofType->Prop)
% Found (fun (x5:(Xx02 Xx000))=> x5) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found ((x1030 (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found (((x103 Xx01) (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found ((((x10 x3) Xx01) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> ((((x10 x3) Xx01) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found x5:(Xx02 Xx000)
% Instantiate: Xx01:=Xx02:(fofType->Prop)
% Found (fun (x5:(Xx02 Xx000))=> x5) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found ((x2030 (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found (((x203 Xx01) (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found ((((x20 x3) Xx01) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> ((((x20 x3) Xx01) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))))) as proof of ((K Xx01) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x5:(Xx01 Xx0000)
% Instantiate: Xx01:=(K Xx02):(fofType->Prop)
% Found x5 as proof of ((K Xx02) Xx0000)
% Found x5:(Xx01 Xx0000)
% Instantiate: Xx01:=(K Xx02):(fofType->Prop)
% Found x5 as proof of ((K Xx02) Xx0000)
% Found x5:(Xx01 Xx0000)
% Instantiate: Xx01:=(K Xx02):(fofType->Prop)
% Found x5 as proof of ((K Xx02) Xx0000)
% Found x5:(Xx01 Xx0000)
% Instantiate: Xx01:=(K Xx02):(fofType->Prop)
% Found x5 as proof of ((K Xx02) Xx0000)
% Found x5:(Xx01 Xx0000)
% Instantiate: Xx01:=(K Xx02):(fofType->Prop)
% Found x5 as proof of ((K Xx02) Xx0000)
% Found x5:(Xx01 Xx0000)
% Instantiate: Xx01:=(K Xx02):(fofType->Prop)
% Found x5 as proof of ((K Xx02) Xx0000)
% Found x5:(Xx01 Xx0000)
% Instantiate: Xx01:=(K Xx02):(fofType->Prop)
% Found x5 as proof of ((K Xx02) Xx0000)
% Found x5:(Xx01 Xx0000)
% Instantiate: Xx01:=(K Xx02):(fofType->Prop)
% Found x5 as proof of ((K Xx02) Xx0000)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found x5:(Xx02 Xx000)
% Instantiate: Xx01:=Xx02:(fofType->Prop)
% Found (fun (x5:(Xx02 Xx000))=> x5) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found ((x0030 (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found (((x003 Xx01) (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found ((((x00 x3) Xx01) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> ((((x00 x3) Xx01) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found x5:(Xx02 Xx000)
% Instantiate: Xx01:=Xx02:(fofType->Prop)
% Found (fun (x5:(Xx02 Xx000))=> x5) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found ((x1030 (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found (((x103 Xx01) (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found ((((x10 x3) Xx01) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> ((((x10 x3) Xx01) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found x5:(Xx02 Xx000)
% Instantiate: Xx01:=Xx02:(fofType->Prop)
% Found (fun (x5:(Xx02 Xx000))=> x5) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found ((x0030 (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found (((x003 Xx01) (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found ((((x00 x3) Xx01) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> ((((x00 x3) Xx01) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))))) as proof of ((K Xx01) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found x5:(Xx02 Xx000)
% Instantiate: Xx01:=Xx02:(fofType->Prop)
% Found (fun (x5:(Xx02 Xx000))=> x5) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found ((x1030 (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found (((x103 Xx01) (fun (Xx000:fofType) (x5:(Xx02 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found ((((x10 x3) Xx01) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx01) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> ((((x10 x3) Xx01) (fun (Xx000:fofType) (x5:(x3 Xx000))=> x5)) (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K x3) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))))) as proof of ((K Xx01) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x1) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x1) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x3) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x1) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x1) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x300:=(x30 x4):((K x1) Xx)
% Found (x30 x4) as proof of ((K Xx02) Xx)
% Found ((x3 Xx) x4) as proof of ((K Xx02) Xx)
% Found ((x3 Xx) x4) as proof of ((K Xx02) Xx)
% Found ((x3 Xx) x4) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x300:=(x30 x4):((K x1) Xx)
% Found (x30 x4) as proof of ((K Xx02) Xx)
% Found ((x3 Xx) x4) as proof of ((K Xx02) Xx)
% Found ((x3 Xx) x4) as proof of ((K Xx02) Xx)
% Found ((x3 Xx) x4) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x1) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x7:(Xx02 Xx000)
% Found x7 as proof of (Xx01 Xx000)
% Found (fun (x7:(Xx02 Xx000))=> x7) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x7:(Xx02 Xx000))=> x7) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x500:=(x50 x6):((K x1) Xx)
% Found (x50 x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found ((x5 Xx) x6) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->((K Xx02) Xx)))
% Found (and_rect10 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect1 ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx))) as proof of ((K Xx02) Xx)
% Found (fun (x4:((and (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)))=> (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) ((K Xx02) Xx)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)))) as proof of ((K Xx02) Xx)
% Found x50:=(x5 Xx):((x3 Xx)->((K x3) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (x5 Xx) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0))))=> (x5 Xx)) as proof of ((x3 Xx)->((K Xx02) Xx))
% Found (f
% EOF
%------------------------------------------------------------------------------