%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SEV244^6 : TPTP v6.1.0. Released v5.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n103.star.cs.uiowa.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory   : 32286.75MB
% OS       : Linux 2.6.32-431.20.3.el6.x86_64
% CPULimit : 300s
% DateTime : Thu Jul 17 13:33:56 EDT 2014

% Result   : Timeout 300.02s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SEV244^6 : TPTP v6.1.0. Released v5.1.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n103.star.cs.uiowa.edu
% % Model    : x86_64 x86_64
% % CPU      : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% % Memory   : 32286.75MB
% % OS       : Linux 2.6.32-431.20.3.el6.x86_64
% % CPULimit : 300
% % DateTime : Thu Jul 17 08:36:26 CDT 2014
% % CPUTime  : 300.02 
% Python 2.7.5
% Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% FOF formula (forall (K:((fofType->Prop)->(fofType->Prop))), ((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_pme
% Conjecture to prove = (forall (K:((fofType->Prop)->(fofType->Prop))), ((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))), ((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))), ((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 x2:(Xx0 Xx00)
% Found x2 as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (x2:(Xx0 Xx00))=> x2) 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) (x2:(Xx0 Xx00))=> x2) 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) (x2:(Xx0 Xx00))=> x2) 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 x2:(Xx0 Xx00)
% Found x2 as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (x2:(Xx0 Xx00))=> x2) 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) (x2:(Xx0 Xx00))=> x2) 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) (x2:(Xx0 Xx00))=> x2) 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 x4:(Xx0 Xx00)
% Found x4 as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (x4:(Xx0 Xx00))=> x4) 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) (x4:(Xx0 Xx00))=> x4) 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) (x4:(Xx0 Xx00))=> x4) 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 x40:=(x4 Xx):((x1 Xx)->((K x1) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((K Xx0) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((K Xx0) Xx))
% Found (fun (x4:(forall (Xx00:fofType), ((x1 Xx00)->((K x1) Xx00))))=> (x4 Xx)) as proof of ((x1 Xx)->((K Xx0) Xx))
% Found (fun (x4:(forall (Xx00:fofType), ((x1 Xx00)->((K x1) Xx00))))=> (x4 Xx)) as proof of ((forall (Xx00:fofType), ((x1 Xx00)->((K x1) Xx00)))->((x1 Xx)->((K Xx0) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx00:fofType), ((x1 Xx00)->((K x1) Xx00))))=> (x4 Xx))) as proof of ((K Xx0) Xx)
% Found ((and_rect0 ((K Xx0) Xx)) (fun (x4:(forall (Xx00:fofType), ((x1 Xx00)->((K x1) Xx00))))=> (x4 Xx))) as proof of ((K Xx0) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((K Xx0) Xx)) (fun (x4:(forall (Xx00:fofType), ((x1 Xx00)->((K x1) Xx00))))=> (x4 Xx))) as proof of ((K Xx0) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((K Xx0) Xx)) (fun (x4:(forall (Xx00:fofType), ((x1 Xx00)->((K x1) Xx00))))=> (x4 Xx))) as proof of ((K Xx0) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx0) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx0) Xx))
% Found (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx0) Xx))
% Found (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx)) as proof of ((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->((K Xx0) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx0) Xx)
% Found ((and_rect0 ((K Xx0) Xx)) (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx0) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)) P) x4) x3)) ((K Xx0) Xx)) (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx0) Xx)
% Found (fun (x3:((and (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)) P) x4) x3)) ((K Xx0) Xx)) (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx)))) as proof of ((K Xx0) Xx)
% Found x4:(Xx0 Xx00)
% Found x4 as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (x4:(Xx0 Xx00))=> x4) 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) (x4:(Xx0 Xx00))=> x4) 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) (x4:(Xx0 Xx00))=> x4) 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 x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx0) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx0) Xx))
% Found (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx0) Xx))
% Found (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx)) as proof of ((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->((K Xx0) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx0) Xx)
% Found ((and_rect0 ((K Xx0) Xx)) (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx0) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)) P) x4) x3)) ((K Xx0) Xx)) (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx0) Xx)
% Found (fun (x3:((and (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)) P) x4) x3)) ((K Xx0) Xx)) (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx)))) as proof of ((K Xx0) Xx)
% Found x40:=(x4 Xx):((x1 Xx)->((K x1) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((K Xx0) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((K Xx0) Xx))
% Found (fun (x4:(forall (Xx00:fofType), ((x1 Xx00)->((K x1) Xx00))))=> (x4 Xx)) as proof of ((x1 Xx)->((K Xx0) Xx))
% Found (fun (x4:(forall (Xx00:fofType), ((x1 Xx00)->((K x1) Xx00))))=> (x4 Xx)) as proof of ((forall (Xx00:fofType), ((x1 Xx00)->((K x1) Xx00)))->((x1 Xx)->((K Xx0) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx00:fofType), ((x1 Xx00)->((K x1) Xx00))))=> (x4 Xx))) as proof of ((K Xx0) Xx)
% Found ((and_rect0 ((K Xx0) Xx)) (fun (x4:(forall (Xx00:fofType), ((x1 Xx00)->((K x1) Xx00))))=> (x4 Xx))) as proof of ((K Xx0) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((K Xx0) Xx)) (fun (x4:(forall (Xx00:fofType), ((x1 Xx00)->((K x1) Xx00))))=> (x4 Xx))) as proof of ((K Xx0) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((K Xx0) Xx)) (fun (x4:(forall (Xx00:fofType), ((x1 Xx00)->((K x1) Xx00))))=> (x4 Xx))) as proof of ((K Xx0) Xx)
% Found x6:(Xx0 Xx00)
% Found x6 as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (x6:(Xx0 Xx00))=> x6) 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) (x6:(Xx0 Xx00))=> x6) 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) (x6:(Xx0 Xx00))=> x6) 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 x6:(Xx0 Xx00)
% Found x6 as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (x6:(Xx0 Xx00))=> x6) 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) (x6:(Xx0 Xx00))=> x6) 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) (x6:(Xx0 Xx00))=> x6) 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 x2:(Xx00 Xx000)
% Found x2 as proof of (Xx0 Xx000)
% Found (fun (x2:(Xx00 Xx000))=> x2) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x2:(Xx00 Xx000))=> x2) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x2:(Xx00 Xx000))=> x2) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x2:(Xx00 Xx000)
% Found x2 as proof of (Xx0 Xx000)
% Found (fun (x2:(Xx00 Xx000))=> x2) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x2:(Xx00 Xx000))=> x2) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x2:(Xx00 Xx000))=> x2) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x4:(Xx00 Xx000)
% Found x4 as proof of (Xx0 Xx000)
% Found (fun (x4:(Xx00 Xx000))=> x4) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx00 Xx000))=> x4) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx00 Xx000))=> x4) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x4:(Xx00 Xx000)
% Found x4 as proof of (Xx0 Xx000)
% Found (fun (x4:(Xx00 Xx000))=> x4) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx00 Xx000))=> x4) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx00 Xx000))=> x4) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x00:(x1 Xx0)
% Instantiate: x1:=(K Xx1):(fofType->Prop)
% Found x00 as proof of ((K Xx1) Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx00) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx00) Xx))
% Found (fun (x4:(forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx00) Xx))
% Found (fun (x4:(forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000))))=> (x4 Xx)) as proof of ((forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000)))->((x2 Xx)->((K Xx00) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found ((and_rect0 ((K Xx00) Xx)) (fun (x4:(forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)) P) x4) x3)) ((K Xx00) Xx)) (fun (x4:(forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)) P) x4) x3)) ((K Xx00) Xx)) (fun (x4:(forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found x40:=(x4 Xx):((x1 Xx)->((K x1) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((K Xx00) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((K Xx00) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx)) as proof of ((x1 Xx)->((K Xx00) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->((K Xx00) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found ((and_rect0 ((K Xx00) Xx)) (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((K Xx00) Xx)) (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((K Xx00) Xx)) (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx00) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx00) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx00) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx00) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found ((and_rect0 ((K Xx00) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx00) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx00) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx00) Xx)
% Found x4:(Xx00 Xx000)
% Found x4 as proof of (Xx0 Xx000)
% Found (fun (x4:(Xx00 Xx000))=> x4) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx00 Xx000))=> x4) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx00 Xx000))=> x4) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x4:(Xx00 Xx000)
% Found x4 as proof of (Xx0 Xx000)
% Found (fun (x4:(Xx00 Xx000))=> x4) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx00 Xx000))=> x4) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx00 Xx000))=> x4) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x00:(x1 Xx0)
% Instantiate: x1:=(K Xx1):(fofType->Prop)
% Found x00 as proof of ((K Xx1) Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx00) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx00) Xx))
% Found (fun (x4:(forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx00) Xx))
% Found (fun (x4:(forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000))))=> (x4 Xx)) as proof of ((forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000)))->((x2 Xx)->((K Xx00) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found ((and_rect0 ((K Xx00) Xx)) (fun (x4:(forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)) P) x4) x3)) ((K Xx00) Xx)) (fun (x4:(forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)) P) x4) x3)) ((K Xx00) Xx)) (fun (x4:(forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx00) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx00) Xx))
% Found (fun (x4:(forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx00) Xx))
% Found (fun (x4:(forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000))))=> (x4 Xx)) as proof of ((forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000)))->((x2 Xx)->((K Xx00) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found ((and_rect0 ((K Xx00) Xx)) (fun (x4:(forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)) P) x4) x3)) ((K Xx00) Xx)) (fun (x4:(forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)) P) x4) x3)) ((K Xx00) Xx)) (fun (x4:(forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found x4:(Xx00 Xx000)
% Instantiate: Xx0:=Xx00:(fofType->Prop)
% Found (fun (x4:(Xx00 Xx000))=> x4) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx00 Xx000))=> x4) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx00 Xx000))=> x4) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found ((x110 (fun (Xx000:fofType) (x4:(Xx00 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)) P) x4) x3)) ((K Xx00) Xx)) (fun (x4:(forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000))))=> (x4 Xx)))) as proof of ((K Xx0) Xx)
% Found (((x11 Xx0) (fun (Xx000:fofType) (x4:(Xx00 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)) P) x4) x3)) ((K Xx00) Xx)) (fun (x4:(forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000))))=> (x4 Xx)))) as proof of ((K Xx0) Xx)
% Found ((((x1 x2) Xx0) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000))))=> (x4 Xx)))) as proof of ((K Xx0) Xx)
% Found (fun (x3:((and (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)))=> ((((x1 x2) Xx0) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000))))=> (x4 Xx))))) as proof of ((K Xx0) Xx)
% Found x6:(Xx00 Xx000)
% Found x6 as proof of (Xx0 Xx000)
% Found (fun (x6:(Xx00 Xx000))=> x6) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx00 Xx000))=> x6) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx00 Xx000))=> x6) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x400:=(x40 x5):((K x1) Xx)
% Found (x40 x5) as proof of ((K Xx00) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx00) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx00) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx00) Xx)
% Found x6:(Xx00 Xx000)
% Found x6 as proof of (Xx0 Xx000)
% Found (fun (x6:(Xx00 Xx000))=> x6) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx00 Xx000))=> x6) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx00 Xx000))=> x6) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx00) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx00) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx00) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx00) Xx)
% Found x40:=(x4 Xx):((x1 Xx)->((K x1) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((K Xx00) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((K Xx00) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx)) as proof of ((x1 Xx)->((K Xx00) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->((K Xx00) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found ((and_rect0 ((K Xx00) Xx)) (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((K Xx00) Xx)) (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((K Xx00) Xx)) (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx00) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx00) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx00) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx00) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found ((and_rect0 ((K Xx00) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx00) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx00) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx00) Xx)
% Found x6:(Xx00 Xx000)
% Found x6 as proof of (Xx0 Xx000)
% Found (fun (x6:(Xx00 Xx000))=> x6) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx00 Xx000))=> x6) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx00 Xx000))=> x6) 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 x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx00) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx00) Xx))
% Found (fun (x4:(forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx00) Xx))
% Found (fun (x4:(forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000))))=> (x4 Xx)) as proof of ((forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000)))->((x2 Xx)->((K Xx00) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found ((and_rect0 ((K Xx00) Xx)) (fun (x4:(forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)) P) x4) x3)) ((K Xx00) Xx)) (fun (x4:(forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)) P) x4) x3)) ((K Xx00) Xx)) (fun (x4:(forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found x4:(Xx00 Xx000)
% Instantiate: Xx0:=Xx00:(fofType->Prop)
% Found (fun (x4:(Xx00 Xx000))=> x4) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx00 Xx000))=> x4) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx00 Xx000))=> x4) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found ((x110 (fun (Xx000:fofType) (x4:(Xx00 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)) P) x4) x3)) ((K Xx00) Xx)) (fun (x4:(forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000))))=> (x4 Xx)))) as proof of ((K Xx0) Xx)
% Found (((x11 Xx0) (fun (Xx000:fofType) (x4:(Xx00 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)) P) x4) x3)) ((K Xx00) Xx)) (fun (x4:(forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000))))=> (x4 Xx)))) as proof of ((K Xx0) Xx)
% Found ((((x1 x2) Xx0) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000))))=> (x4 Xx)))) as proof of ((K Xx0) Xx)
% Found (fun (x3:((and (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)))=> ((((x1 x2) Xx0) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000))))=> (x4 Xx))))) as proof of ((K Xx0) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx00) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx00) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx00) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx00) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found ((and_rect0 ((K Xx00) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx00) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx00) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx00) Xx)
% Found x6:(Xx00 Xx000)
% Found x6 as proof of (Xx0 Xx000)
% Found (fun (x6:(Xx00 Xx000))=> x6) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx00 Xx000))=> x6) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx00 Xx000))=> x6) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x400:=(x40 x5):((K x1) Xx)
% Found (x40 x5) as proof of ((K Xx00) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx00) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx00) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx00) Xx)
% Found x6:(Xx00 Xx000)
% Found x6 as proof of (Xx0 Xx000)
% Found (fun (x6:(Xx00 Xx000))=> x6) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx00 Xx000))=> x6) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx00 Xx000))=> x6) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx00) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx00) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx00) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx00) Xx)
% Found x6:(Xx00 Xx000)
% Found x6 as proof of (Xx0 Xx000)
% Found (fun (x6:(Xx00 Xx000))=> x6) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx00 Xx000))=> x6) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx00 Xx000))=> x6) 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 x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx00) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx00) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx00) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx00) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found ((and_rect0 ((K Xx00) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx00) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx00) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx00) Xx)
% Found x2:(Xx00 Xx000)
% Instantiate: Xx00:=(K x3):(fofType->Prop)
% Found x2 as proof of (Xx0 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx0 Xx000)
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx0 Xx000))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->(Xx0 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (Xx0 Xx000)
% Found ((and_rect0 (Xx0 Xx000)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (Xx0 Xx000)
% 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)) (Xx0 Xx000)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (Xx0 Xx000)
% 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)) (Xx0 Xx000)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (Xx0 Xx000)
% Found x2:(Xx00 Xx000)
% Found x2 as proof of (Xx0 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx0 Xx000)
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx0 Xx000))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->(Xx0 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (Xx0 Xx000)
% Found ((and_rect0 (Xx0 Xx000)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (Xx0 Xx000)
% 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)) (Xx0 Xx000)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (Xx0 Xx000)
% 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)) (Xx0 Xx000)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (Xx0 Xx000)
% Found x2:(Xx00 Xx000)
% Instantiate: Xx00:=(K x3):(fofType->Prop)
% Found x2 as proof of (Xx0 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx0 Xx000)
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx0 Xx000))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->(Xx0 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (Xx0 Xx000)
% Found ((and_rect0 (Xx0 Xx000)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (Xx0 Xx000)
% 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)) (Xx0 Xx000)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (Xx0 Xx000)
% 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)) (Xx0 Xx000)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (Xx0 Xx000)
% Found x2:(Xx01 Xx000)
% Found x2 as proof of (Xx00 Xx000)
% Found (fun (x2:(Xx01 Xx000))=> x2) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x2:(Xx01 Xx000))=> x2) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x2:(Xx01 Xx000))=> x2) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x2:(Xx00 Xx000)
% Found x2 as proof of (Xx0 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx0 Xx000)
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx0 Xx000))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->(Xx0 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (Xx0 Xx000)
% Found ((and_rect0 (Xx0 Xx000)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (Xx0 Xx000)
% 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)) (Xx0 Xx000)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (Xx0 Xx000)
% 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)) (Xx0 Xx000)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (Xx0 Xx000)
% Found x2:(Xx01 Xx000)
% Found x2 as proof of (Xx00 Xx000)
% Found (fun (x2:(Xx01 Xx000))=> x2) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x2:(Xx01 Xx000))=> x2) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x2:(Xx01 Xx000))=> x2) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x4:(Xx01 Xx000)
% Found x4 as proof of (Xx00 Xx000)
% Found (fun (x4:(Xx01 Xx000))=> x4) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx01 Xx000))=> x4) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx01 Xx000))=> x4) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x4:(Xx01 Xx000)
% Found x4 as proof of (Xx00 Xx000)
% Found (fun (x4:(Xx01 Xx000))=> x4) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx01 Xx000))=> x4) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx01 Xx000))=> x4) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x4:(Xx01 Xx000)
% Found x4 as proof of (Xx00 Xx000)
% Found (fun (x4:(Xx01 Xx000))=> x4) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx01 Xx000))=> x4) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx01 Xx000))=> x4) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx)) as proof of ((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->((K Xx01) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect0 ((K Xx01) Xx)) (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx01) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect0 ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found x4:(Xx01 Xx000)
% Found x4 as proof of (Xx00 Xx000)
% Found (fun (x4:(Xx01 Xx000))=> x4) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx01 Xx000))=> x4) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx01 Xx000))=> x4) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x40:=(x4 Xx):((x1 Xx)->((K x1) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((K Xx01) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((K Xx01) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx)) as proof of ((x1 Xx)->((K Xx01) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->((K Xx01) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect0 ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx01) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect0 ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx01) Xx)
% Found x4:(Xx01 Xx000)
% Found x4 as proof of (Xx00 Xx000)
% Found (fun (x4:(Xx01 Xx000))=> x4) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx01 Xx000))=> x4) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx01 Xx000))=> x4) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x4:(Xx01 Xx000)
% Found x4 as proof of (Xx00 Xx000)
% Found (fun (x4:(Xx01 Xx000))=> x4) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx01 Xx000))=> x4) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx01 Xx000))=> x4) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x6:(Xx01 Xx000)
% Found x6 as proof of (Xx00 Xx000)
% Found (fun (x6:(Xx01 Xx000))=> x6) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx01 Xx000))=> x6) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx01 Xx000))=> x6) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx01) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx01) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx01) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx01) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx01) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect0 ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found x4:(Xx01 Xx000)
% Instantiate: Xx00:=Xx01:(fofType->Prop)
% Found (fun (x4:(Xx01 Xx000))=> x4) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx01 Xx000))=> x4) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx01 Xx000))=> x4) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found ((x120 (fun (Xx000:fofType) (x4:(Xx01 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx00) Xx)
% Found (((x12 Xx00) (fun (Xx000:fofType) (x4:(Xx01 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx00) Xx)
% Found ((((x1 x2) Xx00) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx00) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) Xx00) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))))) as proof of ((K Xx00) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx)) as proof of ((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->((K Xx01) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect0 ((K Xx01) Xx)) (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx01) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect0 ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found x3:(Xx1 Xx00)
% Instantiate: Xx1:=(K Xx2):(fofType->Prop)
% Found x3 as proof of ((K Xx2) Xx00)
% Found x6:(Xx01 Xx000)
% Found x6 as proof of (Xx00 Xx000)
% Found (fun (x6:(Xx01 Xx000))=> x6) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx01 Xx000))=> x6) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx01 Xx000))=> x6) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x400:=(x40 x5):((K x1) Xx)
% Found (x40 x5) as proof of ((K Xx01) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx01) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx01) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx01) Xx)
% Found x6:(Xx01 Xx000)
% Found x6 as proof of (Xx00 Xx000)
% Found (fun (x6:(Xx01 Xx000))=> x6) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx01 Xx000))=> x6) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx01 Xx000))=> x6) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx01) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx01) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx01) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx01) Xx)
% Found x6:(Xx01 Xx000)
% Found x6 as proof of (Xx00 Xx000)
% Found (fun (x6:(Xx01 Xx000))=> x6) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx01 Xx000))=> x6) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx01 Xx000))=> x6) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x400:=(x40 x5):((K x1) Xx)
% Found (x40 x5) as proof of ((K Xx01) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx01) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx01) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx01) Xx)
% Found x6:(Xx01 Xx000)
% Found x6 as proof of (Xx00 Xx000)
% Found (fun (x6:(Xx01 Xx000))=> x6) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx01 Xx000))=> x6) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx01 Xx000))=> x6) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx01) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx01) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx01) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx01) Xx)
% Found x6:(Xx01 Xx000)
% Found x6 as proof of (Xx00 Xx000)
% Found (fun (x6:(Xx01 Xx000))=> x6) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx01 Xx000))=> x6) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx01 Xx000))=> x6) 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 x40:=(x4 Xx):((x1 Xx)->((K x1) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((K Xx01) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((K Xx01) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx)) as proof of ((x1 Xx)->((K Xx01) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->((K Xx01) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect0 ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx01) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect0 ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx01) Xx)
% Found x6:(Xx01 Xx000)
% Found x6 as proof of (Xx00 Xx000)
% Found (fun (x6:(Xx01 Xx000))=> x6) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx01 Xx000))=> x6) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx01 Xx000))=> x6) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx01) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx01) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx01) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx01) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx01) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect0 ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found x4:(Xx01 Xx000)
% Instantiate: Xx00:=Xx01:(fofType->Prop)
% Found (fun (x4:(Xx01 Xx000))=> x4) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx01 Xx000))=> x4) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx01 Xx000))=> x4) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found ((x120 (fun (Xx000:fofType) (x4:(Xx01 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx00) Xx)
% Found (((x12 Xx00) (fun (Xx000:fofType) (x4:(Xx01 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx00) Xx)
% Found ((((x1 x2) Xx00) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx00) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) Xx00) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))))) as proof of ((K Xx00) Xx)
% Found x3:(Xx1 Xx00)
% Instantiate: Xx1:=(K Xx2):(fofType->Prop)
% Found x3 as proof of ((K Xx2) Xx00)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx01) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect0 ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx01) Xx)
% Found x6:(Xx01 Xx000)
% Found x6 as proof of (Xx00 Xx000)
% Found (fun (x6:(Xx01 Xx000))=> x6) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx01 Xx000))=> x6) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx01 Xx000))=> x6) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x400:=(x40 x5):((K x1) Xx)
% Found (x40 x5) as proof of ((K Xx01) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx01) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx01) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx01) Xx)
% Found x6:(Xx01 Xx000)
% Found x6 as proof of (Xx00 Xx000)
% Found (fun (x6:(Xx01 Xx000))=> x6) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx01 Xx000))=> x6) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx01 Xx000))=> x6) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx01) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx01) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx01) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx01) Xx)
% Found x6:(Xx01 Xx000)
% Found x6 as proof of (Xx00 Xx000)
% Found (fun (x6:(Xx01 Xx000))=> x6) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx01 Xx000))=> x6) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx01 Xx000))=> x6) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x400:=(x40 x5):((K x1) Xx)
% Found (x40 x5) as proof of ((K Xx01) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx01) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx01) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx01) Xx)
% Found x6:(Xx01 Xx000)
% Found x6 as proof of (Xx00 Xx000)
% Found (fun (x6:(Xx01 Xx000))=> x6) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx01 Xx000))=> x6) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx01 Xx000))=> x6) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx01) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx01) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx01) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx01) Xx)
% Found x6:(Xx01 Xx000)
% Found x6 as proof of (Xx00 Xx000)
% Found (fun (x6:(Xx01 Xx000))=> x6) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx01 Xx000))=> x6) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx01 Xx000))=> x6) 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 x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx01) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect0 ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx01) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx01) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect0 ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found x4:(Xx01 Xx000)
% Instantiate: Xx00:=Xx01:(fofType->Prop)
% Found (fun (x4:(Xx01 Xx000))=> x4) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx01 Xx000))=> x4) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx01 Xx000))=> x4) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found ((x120 (fun (Xx000:fofType) (x4:(Xx01 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx00) Xx)
% Found (((x12 Xx00) (fun (Xx000:fofType) (x4:(Xx01 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx00) Xx)
% Found ((((x1 x2) Xx00) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx00) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) Xx00) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))))) as proof of ((K Xx00) Xx)
% Found x2:(Xx01 Xx000)
% Instantiate: Xx01:=(K x3):(fofType->Prop)
% Found x2 as proof of (Xx00 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx00 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx00 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx00 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx00 Xx000)
% Found ((and_rect0 (Xx00 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx00 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx00 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx00 Xx000)
% 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)) (Xx00 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx00 Xx000)
% Found x2:(Xx01 Xx000)
% Found x2 as proof of (Xx00 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx00 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx00 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx00 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx00 Xx000)
% Found ((and_rect0 (Xx00 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx00 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx00 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx00 Xx000)
% 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)) (Xx00 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx00 Xx000)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx01) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect0 ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found x4:(Xx01 Xx000)
% Instantiate: Xx00:=Xx01:(fofType->Prop)
% Found (fun (x4:(Xx01 Xx000))=> x4) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx01 Xx000))=> x4) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx01 Xx000))=> x4) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found ((x120 (fun (Xx000:fofType) (x4:(Xx01 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx00) Xx)
% Found (((x12 Xx00) (fun (Xx000:fofType) (x4:(Xx01 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx00) Xx)
% Found ((((x1 x2) Xx00) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx00) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) Xx00) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))))) as proof of ((K Xx00) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx01) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect0 ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx01) Xx)
% Found x2:(Xx01 Xx000)
% Instantiate: Xx01:=(K x3):(fofType->Prop)
% Found x2 as proof of (Xx00 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx00 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx00 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx00 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx00 Xx000)
% Found ((and_rect0 (Xx00 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx00 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx00 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx00 Xx000)
% 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)) (Xx00 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx00 Xx000)
% Found x2:(Xx01 Xx000)
% Found x2 as proof of (Xx00 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx00 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx00 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx00 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx00 Xx000)
% Found ((and_rect0 (Xx00 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx00 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx00 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx00 Xx000)
% 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)) (Xx00 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx00 Xx000)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx01) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect0 ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx01) Xx)
% Found x3:(Xx1 Xx00)
% Instantiate: Xx1:=(K Xx2):(fofType->Prop)
% Found x3 as proof of ((K Xx2) Xx00)
% Found x2:(Xx01 Xx000)
% Instantiate: Xx01:=(K x3):(fofType->Prop)
% Found x2 as proof of (Xx00 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx00 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx00 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx00 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx00 Xx000)
% Found ((and_rect0 (Xx00 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx00 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx00 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx00 Xx000)
% 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)) (Xx00 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx00 Xx000)
% Found x2:(Xx01 Xx000)
% Found x2 as proof of (Xx00 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx00 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx00 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx00 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx00 Xx000)
% Found ((and_rect0 (Xx00 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx00 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx00 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx00 Xx000)
% 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)) (Xx00 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx00 Xx000)
% Found x2:(Xx02 Xx000)
% Found x2 as proof of (Xx01 Xx000)
% Found (fun (x2:(Xx02 Xx000))=> x2) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x2:(Xx02 Xx000))=> x2) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x2:(Xx02 Xx000))=> x2) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x3:(Xx1 Xx00)
% Instantiate: Xx1:=(K Xx2):(fofType->Prop)
% Found x3 as proof of ((K Xx2) Xx00)
% Found x2:(Xx01 Xx000)
% Instantiate: Xx01:=(K x3):(fofType->Prop)
% Found x2 as proof of (Xx00 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx00 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx00 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx00 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx00 Xx000)
% Found ((and_rect0 (Xx00 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx00 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx00 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx00 Xx000)
% 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)) (Xx00 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx00 Xx000)
% Found x2:(Xx02 Xx000)
% Found x2 as proof of (Xx01 Xx000)
% Found (fun (x2:(Xx02 Xx000))=> x2) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x2:(Xx02 Xx000))=> x2) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x2:(Xx02 Xx000))=> x2) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x2:(Xx01 Xx000)
% Found x2 as proof of (Xx00 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx00 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx00 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx00 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx00 Xx000)
% Found ((and_rect0 (Xx00 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx00 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx00 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx00 Xx000)
% 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)) (Xx00 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx00 Xx000)
% Found x4:(Xx02 Xx000)
% Found x4 as proof of (Xx01 Xx000)
% Found (fun (x4:(Xx02 Xx000))=> x4) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x4:(Xx02 Xx000)
% Found x4 as proof of (Xx01 Xx000)
% Found (fun (x4:(Xx02 Xx000))=> x4) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x4:(Xx02 Xx000)
% Found x4 as proof of (Xx01 Xx000)
% Found (fun (x4:(Xx02 Xx000))=> x4) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x4:(Xx02 Xx000)
% Found x4 as proof of (Xx01 Xx000)
% Found (fun (x4:(Xx02 Xx000))=> x4) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx)) as proof of ((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->((K Xx02) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect0 ((K Xx02) Xx)) (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx02) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect0 ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx02) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect0 ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found x4:(Xx02 Xx000)
% Found x4 as proof of (Xx01 Xx000)
% Found (fun (x4:(Xx02 Xx000))=> x4) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x4:(Xx02 Xx000)
% Found x4 as proof of (Xx01 Xx000)
% Found (fun (x4:(Xx02 Xx000))=> x4) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x4:(Xx02 Xx000)
% Found x4 as proof of (Xx01 Xx000)
% Found (fun (x4:(Xx02 Xx000))=> x4) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x40:=(x4 Xx):((x1 Xx)->((K x1) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((K Xx02) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx)) as proof of ((x1 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->((K Xx02) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect0 ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx02) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect0 ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx02) Xx)
% Found x4:(Xx02 Xx000)
% Found x4 as proof of (Xx01 Xx000)
% Found (fun (x4:(Xx02 Xx000))=> x4) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x6:(Xx02 Xx000)
% Found x6 as proof of (Xx01 Xx000)
% Found (fun (x6:(Xx02 Xx000))=> x6) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found x6:(Xx02 Xx000)
% Found x6 as proof of (Xx01 Xx000)
% Found (fun (x6:(Xx02 Xx000))=> x6) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found x6:(Xx02 Xx000)
% Found x6 as proof of (Xx01 Xx000)
% Found (fun (x6:(Xx02 Xx000))=> x6) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx02) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect0 ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found x4:(Xx02 Xx000)
% Instantiate: Xx01:=Xx02:(fofType->Prop)
% Found (fun (x4:(Xx02 Xx000))=> x4) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found ((x130 (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx01) Xx)
% Found (((x13 Xx01) (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx01) Xx)
% Found ((((x1 x2) Xx01) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx01) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) Xx01) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))))) as proof of ((K Xx01) Xx)
% Found x6:(Xx02 Xx000)
% Found x6 as proof of (Xx01 Xx000)
% Found (fun (x6:(Xx02 Xx000))=> x6) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x400:=(x40 x5):((K x1) Xx)
% Found (x40 x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found x6:(Xx02 Xx000)
% Found x6 as proof of (Xx01 Xx000)
% Found (fun (x6:(Xx02 Xx000))=> x6) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx)) as proof of ((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->((K Xx02) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect0 ((K Xx02) Xx)) (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx02) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect0 ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx02) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect0 ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found x6:(Xx02 Xx000)
% Found x6 as proof of (Xx01 Xx000)
% Found (fun (x6:(Xx02 Xx000))=> x6) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x400:=(x40 x5):((K x1) Xx)
% Found (x40 x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found x6:(Xx02 Xx000)
% Found x6 as proof of (Xx01 Xx000)
% Found (fun (x6:(Xx02 Xx000))=> x6) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found x6:(Xx02 Xx000)
% Found x6 as proof of (Xx01 Xx000)
% Found (fun (x6:(Xx02 Xx000))=> x6) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) 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 x6:(Xx02 Xx000)
% Found x6 as proof of (Xx01 Xx000)
% Found (fun (x6:(Xx02 Xx000))=> x6) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x400:=(x40 x5):((K x1) Xx)
% Found (x40 x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found x6:(Xx02 Xx000)
% Found x6 as proof of (Xx01 Xx000)
% Found (fun (x6:(Xx02 Xx000))=> x6) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found x40:=(x4 Xx):((x1 Xx)->((K x1) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((K Xx02) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx)) as proof of ((x1 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->((K Xx02) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect0 ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx02) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect0 ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx02) Xx)
% Found x6:(Xx02 Xx000)
% Found x6 as proof of (Xx01 Xx000)
% Found (fun (x6:(Xx02 Xx000))=> x6) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx02) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect0 ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found x4:(Xx02 Xx000)
% Instantiate: Xx01:=Xx02:(fofType->Prop)
% Found (fun (x4:(Xx02 Xx000))=> x4) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found ((x130 (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx01) Xx)
% Found (((x13 Xx01) (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx01) Xx)
% Found ((((x1 x2) Xx01) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx01) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) Xx01) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))))) as proof of ((K Xx01) Xx)
% Found x6:(Xx02 Xx000)
% Found x6 as proof of (Xx01 Xx000)
% Found (fun (x6:(Xx02 Xx000))=> x6) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found x6:(Xx02 Xx000)
% Found x6 as proof of (Xx01 Xx000)
% Found (fun (x6:(Xx02 Xx000))=> x6) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found x6:(Xx02 Xx000)
% Found x6 as proof of (Xx01 Xx000)
% Found (fun (x6:(Xx02 Xx000))=> x6) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x400:=(x40 x5):((K x1) Xx)
% Found (x40 x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found x6:(Xx02 Xx000)
% Found x6 as proof of (Xx01 Xx000)
% Found (fun (x6:(Xx02 Xx000))=> x6) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx02) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect0 ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx02) Xx)
% Found x5:(Xx2 Xx01)
% Instantiate: Xx2:=(K Xx3):(fofType->Prop)
% Found x5 as proof of ((K Xx3) Xx01)
% Found x6:(Xx02 Xx000)
% Found x6 as proof of (Xx01 Xx000)
% Found (fun (x6:(Xx02 Xx000))=> x6) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x400:=(x40 x5):((K x1) Xx)
% Found (x40 x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found x6:(Xx02 Xx000)
% Found x6 as proof of (Xx01 Xx000)
% Found (fun (x6:(Xx02 Xx000))=> x6) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found x6:(Xx02 Xx000)
% Found x6 as proof of (Xx01 Xx000)
% Found (fun (x6:(Xx02 Xx000))=> x6) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) 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 x6:(Xx02 Xx000)
% Found x6 as proof of (Xx01 Xx000)
% Found (fun (x6:(Xx02 Xx000))=> x6) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x400:=(x40 x5):((K x1) Xx)
% Found (x40 x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found x6:(Xx02 Xx000)
% Found x6 as proof of (Xx01 Xx000)
% Found (fun (x6:(Xx02 Xx000))=> x6) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx02) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect0 ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx02) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx02) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect0 ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found x4:(Xx02 Xx000)
% Instantiate: Xx01:=Xx02:(fofType->Prop)
% Found (fun (x4:(Xx02 Xx000))=> x4) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found ((x130 (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx01) Xx)
% Found (((x13 Xx01) (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx01) Xx)
% Found ((((x1 x2) Xx01) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx01) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) Xx01) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))))) as proof of ((K Xx01) Xx)
% Found x5:(Xx2 Xx01)
% Instantiate: Xx2:=(K Xx3):(fofType->Prop)
% Found x5 as proof of ((K Xx3) Xx01)
% Found x2:(Xx02 Xx000)
% Instantiate: Xx02:=(K x3):(fofType->Prop)
% Found x2 as proof of (Xx01 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx01 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx01 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx01 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% Found ((and_rect0 (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% 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)) (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx01 Xx000)
% Found x2:(Xx02 Xx000)
% Found x2 as proof of (Xx01 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx01 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx01 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx01 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% Found ((and_rect0 (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% 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)) (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx01 Xx000)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx02) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect0 ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found x4:(Xx02 Xx000)
% Instantiate: Xx01:=Xx02:(fofType->Prop)
% Found (fun (x4:(Xx02 Xx000))=> x4) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found ((x130 (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx01) Xx)
% Found (((x13 Xx01) (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx01) Xx)
% Found ((((x1 x2) Xx01) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx01) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) Xx01) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))))) as proof of ((K Xx01) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx02) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect0 ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx02) Xx)
% Found x2:(Xx02 Xx000)
% Instantiate: Xx02:=(K x3):(fofType->Prop)
% Found x2 as proof of (Xx01 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx01 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx01 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx01 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% Found ((and_rect0 (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% 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)) (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx01 Xx000)
% Found x2:(Xx02 Xx000)
% Found x2 as proof of (Xx01 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx01 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx01 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx01 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% Found ((and_rect0 (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% 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)) (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx01 Xx000)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx02) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect0 ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx02) Xx)
% Found x2:(Xx02 Xx000)
% Instantiate: Xx02:=(K x3):(fofType->Prop)
% Found x2 as proof of (Xx01 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx01 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx01 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx01 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% Found ((and_rect0 (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% 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)) (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx01 Xx000)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx02) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect0 ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found x4:(Xx02 Xx000)
% Instantiate: Xx01:=Xx02:(fofType->Prop)
% Found (fun (x4:(Xx02 Xx000))=> x4) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found ((x130 (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx01) Xx)
% Found (((x13 Xx01) (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx01) Xx)
% Found ((((x1 x2) Xx01) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx01) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) Xx01) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))))) as proof of ((K Xx01) Xx)
% Found x2:(Xx02 Xx000)
% Found x2 as proof of (Xx01 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx01 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx01 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx01 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% Found ((and_rect0 (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% 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)) (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx01 Xx000)
% Found x5:(Xx2 Xx01)
% Instantiate: Xx2:=(K Xx3):(fofType->Prop)
% Found x5 as proof of ((K Xx3) Xx01)
% Found x5:(Xx2 Xx01)
% Instantiate: Xx2:=(K Xx3):(fofType->Prop)
% Found x5 as proof of ((K Xx3) Xx01)
% Found x2:(Xx02 Xx000)
% Instantiate: Xx02:=(K x3):(fofType->Prop)
% Found x2 as proof of (Xx01 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx01 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx01 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx01 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% Found ((and_rect0 (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% 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)) (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx01 Xx000)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx02) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect0 ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found x4:(Xx02 Xx000)
% Instantiate: Xx01:=Xx02:(fofType->Prop)
% Found (fun (x4:(Xx02 Xx000))=> x4) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found ((x130 (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx01) Xx)
% Found (((x13 Xx01) (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx01) Xx)
% Found ((((x1 x2) Xx01) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx01) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) Xx01) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))))) as proof of ((K Xx01) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx02) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect0 ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx02) Xx)
% Found x2:(Xx02 Xx000)
% Found x2 as proof of (Xx01 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx01 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx01 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx01 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% Found ((and_rect0 (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% 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)) (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx01 Xx000)
% Found x5:(Xx2 Xx01)
% Instantiate: Xx2:=(K Xx3):(fofType->Prop)
% Found x5 as proof of ((K Xx3) Xx01)
% Found x5:(Xx2 Xx01)
% Instantiate: Xx2:=(K Xx3):(fofType->Prop)
% Found x5 as proof of ((K Xx3) Xx01)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx02) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect0 ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx02) Xx)
% Found x2:(Xx03 Xx000)
% Found x2 as proof of (Xx02 Xx000)
% Found (fun (x2:(Xx03 Xx000))=> x2) as proof of (Xx02 Xx000)
% Found (fun (Xx000:fofType) (x2:(Xx03 Xx000))=> x2) as proof of ((Xx03 Xx000)->(Xx02 Xx000))
% Found (fun (Xx000:fofType) (x2:(Xx03 Xx000))=> x2) as proof of (forall (Xx00:fofType), ((Xx03 Xx00)->(Xx02 Xx00)))
% Found x2:(Xx02 Xx000)
% Instantiate: Xx02:=(K x3):(fofType->Prop)
% Found x2 as proof of (Xx01 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx01 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx01 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx01 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% Found ((and_rect0 (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% 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)) (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx01 Xx000)
% Found x2:(Xx03 Xx000)
% Found x2 as proof of (Xx02 Xx000)
% Found (fun (x2:(Xx03 Xx000))=> x2) as proof of (Xx02 Xx000)
% Found (fun (Xx000:fofType) (x2:(Xx03 Xx000))=> x2) as proof of ((Xx03 Xx000)->(Xx02 Xx000))
% Found (fun (Xx000:fofType) (x2:(Xx03 Xx000))=> x2) as proof of (forall (Xx00:fofType), ((Xx03 Xx00)->(Xx02 Xx00)))
% Found x2:(Xx02 Xx000)
% Found x2 as proof of (Xx01 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx01 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx01 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx01 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% Found ((and_rect0 (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% 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)) (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx01 Xx000)
% Found x4:(Xx03 Xx000)
% Found x4 as proof of (Xx02 Xx000)
% Found (fun (x4:(Xx03 Xx000))=> x4) as proof of (Xx02 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4) as proof of ((Xx03 Xx000)->(Xx02 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx03 Xx00)->(Xx02 Xx00)))
% Found x4:(Xx03 Xx000)
% Found x4 as proof of (Xx02 Xx000)
% Found (fun (x4:(Xx03 Xx000))=> x4) as proof of (Xx02 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4) as proof of ((Xx03 Xx000)->(Xx02 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx03 Xx00)->(Xx02 Xx00)))
% Found x2:(Xx02 Xx000)
% Instantiate: Xx02:=(K x3):(fofType->Prop)
% Found x2 as proof of (Xx01 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx01 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx01 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx01 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% Found ((and_rect0 (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% 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)) (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx01 Xx000)
% Found x4:(Xx03 Xx000)
% Found x4 as proof of (Xx02 Xx000)
% Found (fun (x4:(Xx03 Xx000))=> x4) as proof of (Xx02 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4) as proof of ((Xx03 Xx000)->(Xx02 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx03 Xx00)->(Xx02 Xx00)))
% Found x4:(Xx03 Xx000)
% Found x4 as proof of (Xx02 Xx000)
% Found (fun (x4:(Xx03 Xx000))=> x4) as proof of (Xx02 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4) as proof of ((Xx03 Xx000)->(Xx02 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx03 Xx00)->(Xx02 Xx00)))
% Found x4:(Xx03 Xx000)
% Found x4 as proof of (Xx02 Xx000)
% Found (fun (x4:(Xx03 Xx000))=> x4) as proof of (Xx02 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4) as proof of ((Xx03 Xx000)->(Xx02 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx03 Xx00)->(Xx02 Xx00)))
% Found x2:(Xx02 Xx000)
% Found x2 as proof of (Xx01 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx01 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx01 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx01 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% Found ((and_rect0 (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% 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)) (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx01 Xx000)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx)) as proof of ((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->((K Xx03) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found ((and_rect0 ((K Xx03) Xx)) (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx03) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found ((and_rect0 ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx03) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found ((and_rect0 ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx03) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found ((and_rect0 ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found x4:(Xx03 Xx000)
% Found x4 as proof of (Xx02 Xx000)
% Found (fun (x4:(Xx03 Xx000))=> x4) as proof of (Xx02 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4) as proof of ((Xx03 Xx000)->(Xx02 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx03 Xx00)->(Xx02 Xx00)))
% Found x4:(Xx03 Xx000)
% Found x4 as proof of (Xx02 Xx000)
% Found (fun (x4:(Xx03 Xx000))=> x4) as proof of (Xx02 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4) as proof of ((Xx03 Xx000)->(Xx02 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx03 Xx00)->(Xx02 Xx00)))
% Found x4:(Xx03 Xx000)
% Found x4 as proof of (Xx02 Xx000)
% Found (fun (x4:(Xx03 Xx000))=> x4) as proof of (Xx02 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4) as proof of ((Xx03 Xx000)->(Xx02 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx03 Xx00)->(Xx02 Xx00)))
% Found x4:(Xx03 Xx000)
% Found x4 as proof of (Xx02 Xx000)
% Found (fun (x4:(Xx03 Xx000))=> x4) as proof of (Xx02 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4) as proof of ((Xx03 Xx000)->(Xx02 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx03 Xx00)->(Xx02 Xx00)))
% Found x40:=(x4 Xx):((x1 Xx)->((K x1) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((K Xx03) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((K Xx03) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx)) as proof of ((x1 Xx)->((K Xx03) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->((K Xx03) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found ((and_rect0 ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx03) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found ((and_rect0 ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx03) Xx)
% Found x5:(Xx2 Xx01)
% Instantiate: Xx2:=(K Xx3):(fofType->Prop)
% Found x5 as proof of ((K Xx3) Xx01)
% Found x4:(Xx03 Xx000)
% Found x4 as proof of (Xx02 Xx000)
% Found (fun (x4:(Xx03 Xx000))=> x4) as proof of (Xx02 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4) as proof of ((Xx03 Xx000)->(Xx02 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx03 Xx00)->(Xx02 Xx00)))
% Found x6:(Xx03 Xx000)
% Found x6 as proof of (Xx02 Xx000)
% Found (fun (x6:(Xx03 Xx000))=> x6) as proof of (Xx02 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx03 Xx000))=> x6) as proof of ((Xx03 Xx000)->(Xx02 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx03 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx03 Xx00)->(Xx02 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found x6:(Xx03 Xx000)
% Found x6 as proof of (Xx02 Xx000)
% Found (fun (x6:(Xx03 Xx000))=> x6) as proof of (Xx02 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx03 Xx000))=> x6) as proof of ((Xx03 Xx000)->(Xx02 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx03 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx03 Xx00)->(Xx02 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found x6:(Xx03 Xx000)
% Found x6 as proof of (Xx02 Xx000)
% Found (fun (x6:(Xx03 Xx000))=> x6) as proof of (Xx02 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx03 Xx000))=> x6) as proof of ((Xx03 Xx000)->(Xx02 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx03 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx03 Xx00)->(Xx02 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found x6:(Xx03 Xx000)
% Found x6 as proof of (Xx02 Xx000)
% Found (fun (x6:(Xx03 Xx000))=> x6) as proof of (Xx02 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx03 Xx000))=> x6) as proof of ((Xx03 Xx000)->(Xx02 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx03 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx03 Xx00)->(Xx02 Xx00)))
% Found x400:=(x40 x5):((K x1) Xx)
% Found (x40 x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found x6:(Xx03 Xx000)
% Found x6 as proof of (Xx02 Xx000)
% Found (fun (x6:(Xx03 Xx000))=> x6) as proof of (Xx02 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx03 Xx000))=> x6) as proof of ((Xx03 Xx000)->(Xx02 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx03 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx03 Xx00)->(Xx02 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx03) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found ((and_rect0 ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found x4:(Xx03 Xx000)
% Instantiate: Xx02:=Xx03:(fofType->Prop)
% Found (fun (x4:(Xx03 Xx000))=> x4) as proof of (Xx02 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4) as proof of ((Xx03 Xx000)->(Xx02 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx03 Xx00)->(Xx02 Xx00)))
% Found ((x140 (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx02) Xx)
% Found (((x14 Xx02) (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx02) Xx)
% Found ((((x1 x2) Xx02) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx02) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) Xx02) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))))) as proof of ((K Xx02) Xx)
% Found x6:(Xx03 Xx000)
% Found x6 as proof of (Xx02 Xx000)
% Found (fun (x6:(Xx03 Xx000))=> x6) as proof of (Xx02 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx03 Xx000))=> x6) as proof of ((Xx03 Xx000)->(Xx02 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx03 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx03 Xx00)->(Xx02 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found x6:(Xx03 Xx000)
% Found x6 as proof of (Xx02 Xx000)
% Found (fun (x6:(Xx03 Xx000))=> x6) as proof of (Xx02 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx03 Xx000))=> x6) as proof of ((Xx03 Xx000)->(Xx02 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx03 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx03 Xx00)->(Xx02 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found x6:(Xx03 Xx000)
% Found x6 as proof of (Xx02 Xx000)
% Found (fun (x6:(Xx03 Xx000))=> x6) as proof of (Xx02 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx03 Xx000))=> x6) as proof of ((Xx03 Xx000)->(Xx02 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx03 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx03 Xx00)->(Xx02 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found x6:(Xx03 Xx000)
% Found x6 as proof of (Xx02 Xx000)
% Found (fun (x6:(Xx03 Xx000))=> x6) as proof of (Xx02 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx03 Xx000))=> x6) as proof of ((Xx03 Xx000)->(Xx02 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx03 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx03 Xx00)->(Xx02 Xx00)))
% Found x400:=(x40 x5):((K x1) Xx)
% Found (x40 x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found x6:(Xx03 Xx000)
% Found x6 as proof of (Xx02 Xx000)
% Found (fun (x6:(Xx03 Xx000))=> x6) as proof of (Xx02 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx03 Xx000))=> x6) as proof of ((Xx03 Xx000)->(Xx02 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx03 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx03 Xx00)->(Xx02 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found x6:(Xx03 Xx000)
% Found x6 as proof of (Xx02 Xx000)
% Found (fun (x6:(Xx03 Xx000))=> x6) as proof of (Xx02 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx03 Xx000))=> x6) as proof of ((Xx03 Xx000)->(Xx02 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx03 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx03 Xx00)->(Xx02 Xx00)))
% Found x300:=(x30 x4):((K x1) Xx)
% Found (x30 x4) as proof of ((K Xx03) Xx)
% Found ((x3 Xx) x4) as proof of ((K Xx03) Xx)
% Found ((x3 Xx) x4) as proof of ((K Xx03) Xx)
% Found ((x3 Xx) x4) as proof of ((K Xx03) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx)) as proof of ((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->((K Xx03) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found ((and_rect0 ((K Xx03) Xx)) (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx03) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found ((and_rect0 ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx03) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found ((and_rect0 ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx03) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found ((and_rect0 ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found x6:(Xx03 Xx000)
% Found x6 as proof of (Xx02 Xx000)
% Found (fun (x6:(Xx03 Xx000))=> x6) as proof of (Xx02 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx03 Xx000))=> x6) as proof of ((Xx03 Xx000)->(Xx02 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx03 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx03 Xx00)->(Xx02 Xx00)))
% Found x400:=(x40 x5):((K x1) Xx)
% Found (x40 x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found x6:(Xx03 Xx000)
% Found x6 as proof of (Xx02 Xx000)
% Found (fun (x6:(Xx03 Xx000))=> x6) as proof of (Xx02 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx03 Xx000))=> x6) as proof of ((Xx03 Xx000)->(Xx02 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx03 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx03 Xx00)->(Xx02 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found x6:(Xx03 Xx000)
% Found x6 as proof of (Xx02 Xx000)
% Found (fun (x6:(Xx03 Xx000))=> x6) as proof of (Xx02 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx03 Xx000))=> x6) as proof of ((Xx03 Xx000)->(Xx02 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx03 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx03 Xx00)->(Xx02 Xx00)))
% Found x400:=(x40 x5):((K x1) Xx)
% Found (x40 x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found x6:(Xx03 Xx000)
% Found x6 as proof of (Xx02 Xx000)
% Found (fun (x6:(Xx03 Xx000))=> x6) as proof of (Xx02 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx03 Xx000))=> x6) as proof of ((Xx03 Xx000)->(Xx02 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx03 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx03 Xx00)->(Xx02 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found x40:=(x4 Xx):((x1 Xx)->((K x1) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((K Xx03) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((K Xx03) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx)) as proof of ((x1 Xx)->((K Xx03) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->((K Xx03) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found ((and_rect0 ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx03) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found ((and_rect0 ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx03) Xx)
% Found x5:(Xx2 Xx01)
% Instantiate: Xx2:=(K Xx3):(fofType->Prop)
% Found x5 as proof of ((K Xx3) Xx01)
% Found x6:(Xx03 Xx000)
% Found x6 as proof of (Xx02 Xx000)
% Found (fun (x6:(Xx03 Xx000))=> x6) as proof of (Xx02 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx03 Xx000))=> x6) as proof of ((Xx03 Xx000)->(Xx02 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx03 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx03 Xx00)->(Xx02 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found x6:(Xx03 Xx000)
% Found x6 as proof of (Xx02 Xx000)
% Found (fun (x6:(Xx03 Xx000))=> x6) as proof of (Xx02 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx03 Xx000))=> x6) as proof of ((Xx03 Xx000)->(Xx02 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx03 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx03 Xx00)->(Xx02 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found x6:(Xx03 Xx000)
% Found x6 as proof of (Xx02 Xx000)
% Found (fun (x6:(Xx03 Xx000))=> x6) as proof of (Xx02 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx03 Xx000))=> x6) as proof of ((Xx03 Xx000)->(Xx02 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx03 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx03 Xx00)->(Xx02 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found x6:(Xx03 Xx000)
% Found x6 as proof of (Xx02 Xx000)
% Found (fun (x6:(Xx03 Xx000))=> x6) as proof of (Xx02 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx03 Xx000))=> x6) as proof of ((Xx03 Xx000)->(Xx02 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx03 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx03 Xx00)->(Xx02 Xx00)))
% Found x400:=(x40 x5):((K x1) Xx)
% Found (x40 x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found x6:(Xx03 Xx000)
% Found x6 as proof of (Xx02 Xx000)
% Found (fun (x6:(Xx03 Xx000))=> x6) as proof of (Xx02 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx03 Xx000))=> x6) as proof of ((Xx03 Xx000)->(Xx02 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx03 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx03 Xx00)->(Xx02 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx03) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found ((and_rect0 ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found x4:(Xx03 Xx000)
% Instantiate: Xx02:=Xx03:(fofType->Prop)
% Found (fun (x4:(Xx03 Xx000))=> x4) as proof of (Xx02 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4) as proof of ((Xx03 Xx000)->(Xx02 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx03 Xx00)->(Xx02 Xx00)))
% Found ((x140 (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx02) Xx)
% Found (((x14 Xx02) (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx02) Xx)
% Found ((((x1 x2) Xx02) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx02) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) Xx02) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))))) as proof of ((K Xx02) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx03) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found ((and_rect0 ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx03) Xx)
% Found x6:(Xx03 Xx000)
% Found x6 as proof of (Xx02 Xx000)
% Found (fun (x6:(Xx03 Xx000))=> x6) as proof of (Xx02 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx03 Xx000))=> x6) as proof of ((Xx03 Xx000)->(Xx02 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx03 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx03 Xx00)->(Xx02 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found x6:(Xx03 Xx000)
% Found x6 as proof of (Xx02 Xx000)
% Found (fun (x6:(Xx03 Xx000))=> x6) as proof of (Xx02 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx03 Xx000))=> x6) as proof of ((Xx03 Xx000)->(Xx02 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx03 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx03 Xx00)->(Xx02 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found x6:(Xx03 Xx000)
% Found x6 as proof of (Xx02 Xx000)
% Found (fun (x6:(Xx03 Xx000))=> x6) as proof of (Xx02 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx03 Xx000))=> x6) as proof of ((Xx03 Xx000)->(Xx02 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx03 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx03 Xx00)->(Xx02 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found x6:(Xx03 Xx000)
% Found x6 as proof of (Xx02 Xx000)
% Found (fun (x6:(Xx03 Xx000))=> x6) as proof of (Xx02 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx03 Xx000))=> x6) as proof of ((Xx03 Xx000)->(Xx02 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx03 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx03 Xx00)->(Xx02 Xx00)))
% Found x400:=(x40 x5):((K x1) Xx)
% Found (x40 x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found x6:(Xx03 Xx000)
% Found x6 as proof of (Xx02 Xx000)
% Found (fun (x6:(Xx03 Xx000))=> x6) as proof of (Xx02 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx03 Xx000))=> x6) as proof of ((Xx03 Xx000)->(Xx02 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx03 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx03 Xx00)->(Xx02 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found x6:(Xx03 Xx000)
% Found x6 as proof of (Xx02 Xx000)
% Found (fun (x6:(Xx03 Xx000))=> x6) as proof of (Xx02 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx03 Xx000))=> x6) as proof of ((Xx03 Xx000)->(Xx02 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx03 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx03 Xx00)->(Xx02 Xx00)))
% Found x300:=(x30 x4):((K x1) Xx)
% Found (x30 x4) as proof of ((K Xx03) Xx)
% Found ((x3 Xx) x4) as proof of ((K Xx03) Xx)
% Found ((x3 Xx) x4) as proof of ((K Xx03) Xx)
% Found ((x3 Xx) x4) as proof of ((K Xx03) Xx)
% Found x6:(Xx03 Xx000)
% Found x6 as proof of (Xx02 Xx000)
% Found (fun (x6:(Xx03 Xx000))=> x6) as proof of (Xx02 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx03 Xx000))=> x6) as proof of ((Xx03 Xx000)->(Xx02 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx03 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx03 Xx00)->(Xx02 Xx00)))
% Found x400:=(x40 x5):((K x1) Xx)
% Found (x40 x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found x6:(Xx03 Xx000)
% Found x6 as proof of (Xx02 Xx000)
% Found (fun (x6:(Xx03 Xx000))=> x6) as proof of (Xx02 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx03 Xx000))=> x6) as proof of ((Xx03 Xx000)->(Xx02 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx03 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx03 Xx00)->(Xx02 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found x6:(Xx03 Xx000)
% Found x6 as proof of (Xx02 Xx000)
% Found (fun (x6:(Xx03 Xx000))=> x6) as proof of (Xx02 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx03 Xx000))=> x6) as proof of ((Xx03 Xx000)->(Xx02 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx03 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx03 Xx00)->(Xx02 Xx00)))
% Found x400:=(x40 x5):((K x1) Xx)
% Found (x40 x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found x6:(Xx03 Xx000)
% Found x6 as proof of (Xx02 Xx000)
% Found (fun (x6:(Xx03 Xx000))=> x6) as proof of (Xx02 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx03 Xx000))=> x6) as proof of ((Xx03 Xx000)->(Xx02 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx03 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx03 Xx00)->(Xx02 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx03) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found ((and_rect0 ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found x4:(Xx03 Xx000)
% Instantiate: Xx02:=Xx03:(fofType->Prop)
% Found (fun (x4:(Xx03 Xx000))=> x4) as proof of (Xx02 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4) as proof of ((Xx03 Xx000)->(Xx02 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx03 Xx00)->(Xx02 Xx00)))
% Found ((x140 (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx02) Xx)
% Found (((x14 Xx02) (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx02) Xx)
% Found ((((x1 x2) Xx02) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx02) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) Xx02) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))))) as proof of ((K Xx02) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx03) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found ((and_rect0 ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx03) Xx)
% Found x2:(Xx03 Xx000)
% Instantiate: Xx03:=(K x3):(fofType->Prop)
% Found x2 as proof of (Xx02 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx02 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx02 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx02 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx02 Xx000)
% Found ((and_rect0 (Xx02 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx02 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx02 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx02 Xx000)
% 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)) (Xx02 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx02 Xx000)
% Found x7:(Xx3 Xx02)
% Instantiate: Xx3:=(K Xx4):(fofType->Prop)
% Found x7 as proof of ((K Xx4) Xx02)
% Found x2:(Xx03 Xx000)
% Found x2 as proof of (Xx02 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx02 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx02 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx02 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx02 Xx000)
% Found ((and_rect0 (Xx02 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx02 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx02 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx02 Xx000)
% 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)) (Xx02 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx02 Xx000)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx03) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found ((and_rect0 ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found x4:(Xx03 Xx000)
% Instantiate: Xx02:=Xx03:(fofType->Prop)
% Found (fun (x4:(Xx03 Xx000))=> x4) as proof of (Xx02 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4) as proof of ((Xx03 Xx000)->(Xx02 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx03 Xx00)->(Xx02 Xx00)))
% Found ((x140 (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx02) Xx)
% Found (((x14 Xx02) (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx02) Xx)
% Found ((((x1 x2) Xx02) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx02) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) Xx02) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))))) as proof of ((K Xx02) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx03) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found ((and_rect0 ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx03) Xx)
% Found x2:(Xx03 Xx000)
% Instantiate: Xx03:=(K x3):(fofType->Prop)
% Found x2 as proof of (Xx02 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx02 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx02 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx02 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx02 Xx000)
% Found ((and_rect0 (Xx02 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx02 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx02 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx02 Xx000)
% 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)) (Xx02 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx02 Xx000)
% Found x7:(Xx3 Xx02)
% Instantiate: Xx3:=(K Xx4):(fofType->Prop)
% Found x7 as proof of ((K Xx4) Xx02)
% Found x2:(Xx03 Xx000)
% Found x2 as proof of (Xx02 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx02 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx02 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx02 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx02 Xx000)
% Found ((and_rect0 (Xx02 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx02 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx02 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx02 Xx000)
% 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)) (Xx02 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx02 Xx000)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx03) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found ((and_rect0 ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx03) Xx)
% Found x2:(Xx03 Xx000)
% Instantiate: Xx03:=(K x3):(fofType->Prop)
% Found x2 as proof of (Xx02 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx02 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx02 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx02 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx02 Xx000)
% Found ((and_rect0 (Xx02 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx02 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx02 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx02 Xx000)
% 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)) (Xx02 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx02 Xx000)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx03) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found ((and_rect0 ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found x4:(Xx03 Xx000)
% Instantiate: Xx02:=Xx03:(fofType->Prop)
% Found (fun (x4:(Xx03 Xx000))=> x4) as proof of (Xx02 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4) as proof of ((Xx03 Xx000)->(Xx02 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx03 Xx00)->(Xx02 Xx00)))
% Found ((x140 (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx02) Xx)
% Found (((x14 Xx02) (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx02) Xx)
% Found ((((x1 x2) Xx02) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx02) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) Xx02) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))))) as proof of ((K Xx02) Xx)
% Found x2:(Xx03 Xx000)
% Found x2 as proof of (Xx02 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx02 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx02 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx02 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx02 Xx000)
% Found ((and_rect0 (Xx02 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx02 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx02 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx02 Xx000)
% 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)) (Xx02 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx02 Xx000)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx03) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found ((and_rect0 ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found x4:(Xx03 Xx000)
% Instantiate: Xx02:=Xx03:(fofType->Prop)
% Found (fun (x4:(Xx03 Xx000))=> x4) as proof of (Xx02 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4) as proof of ((Xx03 Xx000)->(Xx02 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx03 Xx00)->(Xx02 Xx00)))
% Found ((x140 (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx02) Xx)
% Found (((x14 Xx02) (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx02) Xx)
% Found ((((x1 x2) Xx02) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx02) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) Xx02) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))))) as proof of ((K Xx02) Xx)
% Found x2:(Xx03 Xx000)
% Instantiate: Xx03:=(K x3):(fofType->Prop)
% Found x2 as proof of (Xx02 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx02 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx02 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx02 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx02 Xx000)
% Found ((and_rect0 (Xx02 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx02 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx02 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx02 Xx000)
% 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)) (Xx02 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx02 Xx000)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx03) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found ((and_rect0 ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx03) Xx)
% Found x2:(Xx03 Xx000)
% Found x2 as proof of (Xx02 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx02 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx02 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx02 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx02 Xx000)
% Found ((and_rect0 (Xx02 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx02 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx02 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx02 Xx000)
% 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)) (Xx02 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx02 Xx000)
% Found x7:(Xx3 Xx02)
% Instantiate: Xx3:=(K Xx4):(fofType->Prop)
% Found x7 as proof of ((K Xx4) Xx02)
% Found x7:(Xx3 Xx02)
% Instantiate: Xx3:=(K Xx4):(fofType->Prop)
% Found x7 as proof of ((K Xx4) Xx02)
% Found x7:(Xx3 Xx02)
% Instantiate: Xx3:=(K Xx4):(fofType->Prop)
% Found x7 as proof of ((K Xx4) Xx02)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx03) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found ((and_rect0 ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx03) Xx)
% Found x2:(Xx03 Xx000)
% Instantiate: Xx03:=(K x3):(fofType->Prop)
% Found x2 as proof of (Xx02 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx02 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx02 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx02 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx02 Xx000)
% Found ((and_rect0 (Xx02 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx02 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx02 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx02 Xx000)
% 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)) (Xx02 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx02 Xx000)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx03) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found ((and_rect0 ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found x4:(Xx03 Xx000)
% Instantiate: Xx02:=Xx03:(fofType->Prop)
% Found (fun (x4:(Xx03 Xx000))=> x4) as proof of (Xx02 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4) as proof of ((Xx03 Xx000)->(Xx02 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx03 Xx00)->(Xx02 Xx00)))
% Found ((x140 (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx02) Xx)
% Found (((x14 Xx02) (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx02) Xx)
% Found ((((x1 x2) Xx02) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx02) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) Xx02) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))))) as proof of ((K Xx02) Xx)
% Found x7:(Xx3 Xx02)
% Instantiate: Xx3:=(K Xx4):(fofType->Prop)
% Found x7 as proof of ((K Xx4) Xx02)
% Found x7:(Xx3 Xx02)
% Instantiate: Xx3:=(K Xx4):(fofType->Prop)
% Found x7 as proof of ((K Xx4) Xx02)
% Found x7:(Xx3 Xx02)
% Instantiate: Xx3:=(K Xx4):(fofType->Prop)
% Found x7 as proof of ((K Xx4) Xx02)
% Found x2:(Xx03 Xx000)
% Found x2 as proof of (Xx02 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx02 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx02 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx02 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx02 Xx000)
% Found ((and_rect0 (Xx02 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx02 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx02 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx02 Xx000)
% 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)) (Xx02 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx02 Xx000)
% Found x2:(Xx04 Xx000)
% Found x2 as proof of (Xx03 Xx000)
% Found (fun (x2:(Xx04 Xx000))=> x2) as proof of (Xx03 Xx000)
% Found (fun (Xx000:fofType) (x2:(Xx04 Xx000))=> x2) as proof of ((Xx04 Xx000)->(Xx03 Xx000))
% Found (fun (Xx000:fofType) (x2:(Xx04 Xx000))=> x2) as proof of (forall (Xx00:fofType), ((Xx04 Xx00)->(Xx03 Xx00)))
% Found x2:(Xx03 Xx000)
% Instantiate: Xx03:=(K x3):(fofType->Prop)
% Found x2 as proof of (Xx02 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx02 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx02 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx02 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx02 Xx000)
% Found ((and_rect0 (Xx02 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx02 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx02 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx02 Xx000)
% 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)) (Xx02 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx02 Xx000)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx03) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found ((and_rect0 ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found x4:(Xx03 Xx000)
% Instantiate: Xx02:=Xx03:(fofType->Prop)
% Found (fun (x4:(Xx03 Xx000))=> x4) as proof of (Xx02 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4) as proof of ((Xx03 Xx000)->(Xx02 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx03 Xx00)->(Xx02 Xx00)))
% Found ((x140 (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx02) Xx)
% Found (((x14 Xx02) (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx02) Xx)
% Found ((((x1 x2) Xx02) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx02) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) Xx02) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))))) as proof of ((K Xx02) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx03) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found ((and_rect0 ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx03) Xx)
% Found x2:(Xx03 Xx000)
% Found x2 as proof of (Xx02 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx02 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx02 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx02 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx02 Xx000)
% Found ((and_rect0 (Xx02 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx02 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx02 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx02 Xx000)
% 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)) (Xx02 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx02 Xx000)
% Found x2:(Xx04 Xx000)
% Found x2 as proof of (Xx03 Xx000)
% Found (fun (x2:(Xx04 Xx000))=> x2) as proof of (Xx03 Xx000)
% Found (fun (Xx000:fofType) (x2:(Xx04 Xx000))=> x2) as proof of ((Xx04 Xx000)->(Xx03 Xx000))
% Found (fun (Xx000:fofType) (x2:(Xx04 Xx000))=> x2) as proof of (forall (Xx00:fofType), ((Xx04 Xx00)->(Xx03 Xx00)))
% Found x2:(Xx0 Xx00)
% Found x2 as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (x2:(Xx0 Xx00))=> x2) 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) (x2:(Xx0 Xx00))=> x2) 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) (x2:(Xx0 Xx00))=> x2) 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 x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx03) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found ((and_rect0 ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx03) Xx)
% Found x4:(Xx04 Xx000)
% Found x4 as proof of (Xx03 Xx000)
% Found (fun (x4:(Xx04 Xx000))=> x4) as proof of (Xx03 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx04 Xx000))=> x4) as proof of ((Xx04 Xx000)->(Xx03 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx04 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx04 Xx00)->(Xx03 Xx00)))
% Found x4:(Xx04 Xx000)
% Found x4 as proof of (Xx03 Xx000)
% Found (fun (x4:(Xx04 Xx000))=> x4) as proof of (Xx03 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx04 Xx000))=> x4) as proof of ((Xx04 Xx000)->(Xx03 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx04 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx04 Xx00)->(Xx03 Xx00)))
% Found x4:(Xx04 Xx000)
% Found x4 as proof of (Xx03 Xx000)
% Found (fun (x4:(Xx04 Xx000))=> x4) as proof of (Xx03 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx04 Xx000))=> x4) as proof of ((Xx04 Xx000)->(Xx03 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx04 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx04 Xx00)->(Xx03 Xx00)))
% Found x2:(Xx0 Xx00)
% Found x2 as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (x2:(Xx0 Xx00))=> x2) 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) (x2:(Xx0 Xx00))=> x2) 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) (x2:(Xx0 Xx00))=> x2) 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 x2:(Xx0 Xx00)
% Found x2 as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (x2:(Xx0 Xx00))=> x2) 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) (x2:(Xx0 Xx00))=> x2) 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) (x2:(Xx0 Xx00))=> x2) 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 x4:(Xx04 Xx000)
% Found x4 as proof of (Xx03 Xx000)
% Found (fun (x4:(Xx04 Xx000))=> x4) as proof of (Xx03 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx04 Xx000))=> x4) as proof of ((Xx04 Xx000)->(Xx03 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx04 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx04 Xx00)->(Xx03 Xx00)))
% Found x4:(Xx04 Xx000)
% Found x4 as proof of (Xx03 Xx000)
% Found (fun (x4:(Xx04 Xx000))=> x4) as proof of (Xx03 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx04 Xx000))=> x4) as proof of ((Xx04 Xx000)->(Xx03 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx04 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx04 Xx00)->(Xx03 Xx00)))
% Found x4:(Xx04 Xx000)
% Found x4 as proof of (Xx03 Xx000)
% Found (fun (x4:(Xx04 Xx000))=> x4) as proof of (Xx03 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx04 Xx000))=> x4) as proof of ((Xx04 Xx000)->(Xx03 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx04 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx04 Xx00)->(Xx03 Xx00)))
% Found x2:(Xx03 Xx000)
% Instantiate: Xx03:=(K x3):(fofType->Prop)
% Found x2 as proof of (Xx02 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx02 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx02 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx02 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx02 Xx000)
% Found ((and_rect0 (Xx02 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx02 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx02 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx02 Xx000)
% 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)) (Xx02 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx02 Xx000)
% Found x4:(Xx0 Xx00)
% Found x4 as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (x4:(Xx0 Xx00))=> x4) 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) (x4:(Xx0 Xx00))=> x4) 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) (x4:(Xx0 Xx00))=> x4) 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:(Xx3 Xx02)
% Instantiate: Xx3:=(K Xx4):(fofType->Prop)
% Found x7 as proof of ((K Xx4) Xx02)
% Found x7:(Xx3 Xx02)
% Instantiate: Xx3:=(K Xx4):(fofType->Prop)
% Found x7 as proof of ((K Xx4) Xx02)
% Found x7:(Xx3 Xx02)
% Instantiate: Xx3:=(K Xx4):(fofType->Prop)
% Found x7 as proof of ((K Xx4) Xx02)
% Found x4:(Xx04 Xx000)
% Found x4 as proof of (Xx03 Xx000)
% Found (fun (x4:(Xx04 Xx000))=> x4) as proof of (Xx03 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx04 Xx000))=> x4) as proof of ((Xx04 Xx000)->(Xx03 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx04 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx04 Xx00)->(Xx03 Xx00)))
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx)) as proof of ((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->((K Xx04) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found ((and_rect0 ((K Xx04) Xx)) (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx04) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found ((and_rect0 ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx04) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found ((and_rect0 ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx04) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found ((and_rect0 ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx04) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found ((and_rect0 ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found x4:(Xx04 Xx000)
% Found x4 as proof of (Xx03 Xx000)
% Found (fun (x4:(Xx04 Xx000))=> x4) as proof of (Xx03 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx04 Xx000))=> x4) as proof of ((Xx04 Xx000)->(Xx03 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx04 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx04 Xx00)->(Xx03 Xx00)))
% Found x4:(Xx04 Xx000)
% Found x4 as proof of (Xx03 Xx000)
% Found (fun (x4:(Xx04 Xx000))=> x4) as proof of (Xx03 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx04 Xx000))=> x4) as proof of ((Xx04 Xx000)->(Xx03 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx04 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx04 Xx00)->(Xx03 Xx00)))
% Found x40:=(x4 Xx):((x1 Xx)->((K x1) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((K Xx0) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((K Xx0) Xx))
% Found (fun (x4:(forall (Xx00:fofType), ((x1 Xx00)->((K x1) Xx00))))=> (x4 Xx)) as proof of ((x1 Xx)->((K Xx0) Xx))
% Found (fun (x4:(forall (Xx00:fofType), ((x1 Xx00)->((K x1) Xx00))))=> (x4 Xx)) as proof of ((forall (Xx00:fofType), ((x1 Xx00)->((K x1) Xx00)))->((x1 Xx)->((K Xx0) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx00:fofType), ((x1 Xx00)->((K x1) Xx00))))=> (x4 Xx))) as proof of ((K Xx0) Xx)
% Found ((and_rect0 ((K Xx0) Xx)) (fun (x4:(forall (Xx00:fofType), ((x1 Xx00)->((K x1) Xx00))))=> (x4 Xx))) as proof of ((K Xx0) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((K Xx0) Xx)) (fun (x4:(forall (Xx00:fofType), ((x1 Xx00)->((K x1) Xx00))))=> (x4 Xx))) as proof of ((K Xx0) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((K Xx0) Xx)) (fun (x4:(forall (Xx00:fofType), ((x1 Xx00)->((K x1) Xx00))))=> (x4 Xx))) as proof of ((K Xx0) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx0) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx0) Xx))
% Found (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx0) Xx))
% Found (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx)) as proof of ((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->((K Xx0) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx0) Xx)
% Found ((and_rect0 ((K Xx0) Xx)) (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx0) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)) P) x4) x3)) ((K Xx0) Xx)) (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx0) Xx)
% Found (fun (x3:((and (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)) P) x4) x3)) ((K Xx0) Xx)) (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx)))) as proof of ((K Xx0) Xx)
% Found x4:(Xx04 Xx000)
% Found x4 as proof of (Xx03 Xx000)
% Found (fun (x4:(Xx04 Xx000))=> x4) as proof of (Xx03 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx04 Xx000))=> x4) as proof of ((Xx04 Xx000)->(Xx03 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx04 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx04 Xx00)->(Xx03 Xx00)))
% Found x2:(Xx03 Xx000)
% Found x2 as proof of (Xx02 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx02 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx02 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx02 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx02 Xx000)
% Found ((and_rect0 (Xx02 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx02 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx02 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx02 Xx000)
% 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)) (Xx02 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx02 Xx000)
% Found x4:(Xx04 Xx000)
% Found x4 as proof of (Xx03 Xx000)
% Found (fun (x4:(Xx04 Xx000))=> x4) as proof of (Xx03 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx04 Xx000))=> x4) as proof of ((Xx04 Xx000)->(Xx03 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx04 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx04 Xx00)->(Xx03 Xx00)))
% Found x40:=(x4 Xx):((x1 Xx)->((K x1) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((K Xx04) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((K Xx04) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx)) as proof of ((x1 Xx)->((K Xx04) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->((K Xx04) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found ((and_rect0 ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx04) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found ((and_rect0 ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx04) Xx)
% Found x6:(Xx04 Xx000)
% Found x6 as proof of (Xx03 Xx000)
% Found (fun (x6:(Xx04 Xx000))=> x6) as proof of (Xx03 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of ((Xx04 Xx000)->(Xx03 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx04 Xx00)->(Xx03 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found x4:(Xx0 Xx00)
% Found x4 as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (x4:(Xx0 Xx00))=> x4) 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) (x4:(Xx0 Xx00))=> x4) 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) (x4:(Xx0 Xx00))=> x4) 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 x4:(Xx0 Xx00)
% Found x4 as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (x4:(Xx0 Xx00))=> x4) 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) (x4:(Xx0 Xx00))=> x4) 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) (x4:(Xx0 Xx00))=> x4) 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 x4:(Xx04 Xx000)
% Found x4 as proof of (Xx03 Xx000)
% Found (fun (x4:(Xx04 Xx000))=> x4) as proof of (Xx03 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx04 Xx000))=> x4) as proof of ((Xx04 Xx000)->(Xx03 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx04 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx04 Xx00)->(Xx03 Xx00)))
% Found x2:(Xx03 Xx000)
% Instantiate: Xx03:=(K x3):(fofType->Prop)
% Found x2 as proof of (Xx02 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx02 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx02 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx02 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx02 Xx000)
% Found ((and_rect0 (Xx02 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx02 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx02 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx02 Xx000)
% 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)) (Xx02 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx02 Xx000)
% Found x6:(Xx04 Xx000)
% Found x6 as proof of (Xx03 Xx000)
% Found (fun (x6:(Xx04 Xx000))=> x6) as proof of (Xx03 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of ((Xx04 Xx000)->(Xx03 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx04 Xx00)->(Xx03 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found x6:(Xx04 Xx000)
% Found x6 as proof of (Xx03 Xx000)
% Found (fun (x6:(Xx04 Xx000))=> x6) as proof of (Xx03 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of ((Xx04 Xx000)->(Xx03 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx04 Xx00)->(Xx03 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found x6:(Xx04 Xx000)
% Found x6 as proof of (Xx03 Xx000)
% Found (fun (x6:(Xx04 Xx000))=> x6) as proof of (Xx03 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of ((Xx04 Xx000)->(Xx03 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx04 Xx00)->(Xx03 Xx00)))
% Found x400:=(x40 x5):((K x1) Xx)
% Found (x40 x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found x6:(Xx04 Xx000)
% Found x6 as proof of (Xx03 Xx000)
% Found (fun (x6:(Xx04 Xx000))=> x6) as proof of (Xx03 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of ((Xx04 Xx000)->(Xx03 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx04 Xx00)->(Xx03 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found x6:(Xx04 Xx000)
% Found x6 as proof of (Xx03 Xx000)
% Found (fun (x6:(Xx04 Xx000))=> x6) as proof of (Xx03 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of ((Xx04 Xx000)->(Xx03 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx04 Xx00)->(Xx03 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found x6:(Xx04 Xx000)
% Found x6 as proof of (Xx03 Xx000)
% Found (fun (x6:(Xx04 Xx000))=> x6) as proof of (Xx03 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of ((Xx04 Xx000)->(Xx03 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx04 Xx00)->(Xx03 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found x6:(Xx04 Xx000)
% Found x6 as proof of (Xx03 Xx000)
% Found (fun (x6:(Xx04 Xx000))=> x6) as proof of (Xx03 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of ((Xx04 Xx000)->(Xx03 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx04 Xx00)->(Xx03 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found x6:(Xx04 Xx000)
% Found x6 as proof of (Xx03 Xx000)
% Found (fun (x6:(Xx04 Xx000))=> x6) as proof of (Xx03 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of ((Xx04 Xx000)->(Xx03 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx04 Xx00)->(Xx03 Xx00)))
% Found x400:=(x40 x5):((K x1) Xx)
% Found (x40 x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found x6:(Xx04 Xx000)
% Found x6 as proof of (Xx03 Xx000)
% Found (fun (x6:(Xx04 Xx000))=> x6) as proof of (Xx03 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of ((Xx04 Xx000)->(Xx03 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx04 Xx00)->(Xx03 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found x6:(Xx04 Xx000)
% Found x6 as proof of (Xx03 Xx000)
% Found (fun (x6:(Xx04 Xx000))=> x6) as proof of (Xx03 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of ((Xx04 Xx000)->(Xx03 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx04 Xx00)->(Xx03 Xx00)))
% Found x300:=(x30 x4):((K x1) Xx)
% Found (x30 x4) as proof of ((K Xx04) Xx)
% Found ((x3 Xx) x4) as proof of ((K Xx04) Xx)
% Found ((x3 Xx) x4) as proof of ((K Xx04) Xx)
% Found ((x3 Xx) x4) as proof of ((K Xx04) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx04) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found ((and_rect0 ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found x4:(Xx04 Xx000)
% Instantiate: Xx03:=Xx04:(fofType->Prop)
% Found (fun (x4:(Xx04 Xx000))=> x4) as proof of (Xx03 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx04 Xx000))=> x4) as proof of ((Xx04 Xx000)->(Xx03 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx04 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx04 Xx00)->(Xx03 Xx00)))
% Found ((x150 (fun (Xx000:fofType) (x4:(Xx04 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx03) Xx)
% Found (((x15 Xx03) (fun (Xx000:fofType) (x4:(Xx04 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx03) Xx)
% Found ((((x1 x2) Xx03) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx03) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) Xx03) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))))) as proof of ((K Xx03) Xx)
% Found x40:=(x4 Xx):((x1 Xx)->((K x1) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((K Xx0) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((K Xx0) Xx))
% Found (fun (x4:(forall (Xx00:fofType), ((x1 Xx00)->((K x1) Xx00))))=> (x4 Xx)) as proof of ((x1 Xx)->((K Xx0) Xx))
% Found (fun (x4:(forall (Xx00:fofType), ((x1 Xx00)->((K x1) Xx00))))=> (x4 Xx)) as proof of ((forall (Xx00:fofType), ((x1 Xx00)->((K x1) Xx00)))->((x1 Xx)->((K Xx0) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx00:fofType), ((x1 Xx00)->((K x1) Xx00))))=> (x4 Xx))) as proof of ((K Xx0) Xx)
% Found ((and_rect0 ((K Xx0) Xx)) (fun (x4:(forall (Xx00:fofType), ((x1 Xx00)->((K x1) Xx00))))=> (x4 Xx))) as proof of ((K Xx0) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((K Xx0) Xx)) (fun (x4:(forall (Xx00:fofType), ((x1 Xx00)->((K x1) Xx00))))=> (x4 Xx))) as proof of ((K Xx0) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((K Xx0) Xx)) (fun (x4:(forall (Xx00:fofType), ((x1 Xx00)->((K x1) Xx00))))=> (x4 Xx))) as proof of ((K Xx0) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx0) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx0) Xx))
% Found (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx0) Xx))
% Found (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx)) as proof of ((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->((K Xx0) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx0) Xx)
% Found ((and_rect0 ((K Xx0) Xx)) (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx0) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)) P) x4) x3)) ((K Xx0) Xx)) (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx0) Xx)
% Found (fun (x3:((and (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)) P) x4) x3)) ((K Xx0) Xx)) (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx)))) as proof of ((K Xx0) Xx)
% Found x40:=(x4 Xx):((x1 Xx)->((K x1) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((K Xx0) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((K Xx0) Xx))
% Found (fun (x4:(forall (Xx00:fofType), ((x1 Xx00)->((K x1) Xx00))))=> (x4 Xx)) as proof of ((x1 Xx)->((K Xx0) Xx))
% Found (fun (x4:(forall (Xx00:fofType), ((x1 Xx00)->((K x1) Xx00))))=> (x4 Xx)) as proof of ((forall (Xx00:fofType), ((x1 Xx00)->((K x1) Xx00)))->((x1 Xx)->((K Xx0) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx00:fofType), ((x1 Xx00)->((K x1) Xx00))))=> (x4 Xx))) as proof of ((K Xx0) Xx)
% Found ((and_rect0 ((K Xx0) Xx)) (fun (x4:(forall (Xx00:fofType), ((x1 Xx00)->((K x1) Xx00))))=> (x4 Xx))) as proof of ((K Xx0) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((K Xx0) Xx)) (fun (x4:(forall (Xx00:fofType), ((x1 Xx00)->((K x1) Xx00))))=> (x4 Xx))) as proof of ((K Xx0) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((K Xx0) Xx)) (fun (x4:(forall (Xx00:fofType), ((x1 Xx00)->((K x1) Xx00))))=> (x4 Xx))) as proof of ((K Xx0) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx0) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx0) Xx))
% Found (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx0) Xx))
% Found (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx)) as proof of ((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->((K Xx0) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx0) Xx)
% Found ((and_rect0 ((K Xx0) Xx)) (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx0) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)) P) x4) x3)) ((K Xx0) Xx)) (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx0) Xx)
% Found (fun (x3:((and (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)) P) x4) x3)) ((K Xx0) Xx)) (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx)))) as proof of ((K Xx0) Xx)
% Found x7:(Xx3 Xx02)
% Instantiate: Xx3:=(K Xx4):(fofType->Prop)
% Found x7 as proof of ((K Xx4) Xx02)
% Found x7:(Xx3 Xx02)
% Instantiate: Xx3:=(K Xx4):(fofType->Prop)
% Found x7 as proof of ((K Xx4) Xx02)
% Found x7:(Xx3 Xx02)
% Instantiate: Xx3:=(K Xx4):(fofType->Prop)
% Found x7 as proof of ((K Xx4) Xx02)
% Found x6:(Xx04 Xx000)
% Found x6 as proof of (Xx03 Xx000)
% Found (fun (x6:(Xx04 Xx000))=> x6) as proof of (Xx03 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of ((Xx04 Xx000)->(Xx03 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx04 Xx00)->(Xx03 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found x6:(Xx04 Xx000)
% Found x6 as proof of (Xx03 Xx000)
% Found (fun (x6:(Xx04 Xx000))=> x6) as proof of (Xx03 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of ((Xx04 Xx000)->(Xx03 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx04 Xx00)->(Xx03 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found x6:(Xx04 Xx000)
% Found x6 as proof of (Xx03 Xx000)
% Found (fun (x6:(Xx04 Xx000))=> x6) as proof of (Xx03 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of ((Xx04 Xx000)->(Xx03 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx04 Xx00)->(Xx03 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found x6:(Xx04 Xx000)
% Found x6 as proof of (Xx03 Xx000)
% Found (fun (x6:(Xx04 Xx000))=> x6) as proof of (Xx03 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of ((Xx04 Xx000)->(Xx03 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx04 Xx00)->(Xx03 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found x6:(Xx04 Xx000)
% Found x6 as proof of (Xx03 Xx000)
% Found (fun (x6:(Xx04 Xx000))=> x6) as proof of (Xx03 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of ((Xx04 Xx000)->(Xx03 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx04 Xx00)->(Xx03 Xx00)))
% Found x400:=(x40 x5):((K x1) Xx)
% Found (x40 x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found x6:(Xx04 Xx000)
% Found x6 as proof of (Xx03 Xx000)
% Found (fun (x6:(Xx04 Xx000))=> x6) as proof of (Xx03 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of ((Xx04 Xx000)->(Xx03 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx04 Xx00)->(Xx03 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx)) as proof of ((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->((K Xx04) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found ((and_rect0 ((K Xx04) Xx)) (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx04) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found ((and_rect0 ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx04) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found ((and_rect0 ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx04) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found ((and_rect0 ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx04) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found ((and_rect0 ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found x6:(Xx04 Xx000)
% Found x6 as proof of (Xx03 Xx000)
% Found (fun (x6:(Xx04 Xx000))=> x6) as proof of (Xx03 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of ((Xx04 Xx000)->(Xx03 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx04 Xx00)->(Xx03 Xx00)))
% Found x400:=(x40 x5):((K x1) Xx)
% Found (x40 x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found x6:(Xx0 Xx00)
% Found x6 as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (x6:(Xx0 Xx00))=> x6) 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) (x6:(Xx0 Xx00))=> x6) 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) (x6:(Xx0 Xx00))=> x6) 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 x6:(Xx04 Xx000)
% Found x6 as proof of (Xx03 Xx000)
% Found (fun (x6:(Xx04 Xx000))=> x6) as proof of (Xx03 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of ((Xx04 Xx000)->(Xx03 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx04 Xx00)->(Xx03 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found x6:(Xx04 Xx000)
% Found x6 as proof of (Xx03 Xx000)
% Found (fun (x6:(Xx04 Xx000))=> x6) as proof of (Xx03 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of ((Xx04 Xx000)->(Xx03 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx04 Xx00)->(Xx03 Xx00)))
% Found x400:=(x40 x5):((K x1) Xx)
% Found (x40 x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found x6:(Xx04 Xx000)
% Found x6 as proof of (Xx03 Xx000)
% Found (fun (x6:(Xx04 Xx000))=> x6) as proof of (Xx03 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of ((Xx04 Xx000)->(Xx03 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx04 Xx00)->(Xx03 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found x2:(Xx03 Xx000)
% Found x2 as proof of (Xx02 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx02 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx02 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx02 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx02 Xx000)
% Found ((and_rect0 (Xx02 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx02 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx02 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx02 Xx000)
% 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)) (Xx02 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx02 Xx000)
% Found x40:=(x4 Xx):((x1 Xx)->((K x1) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((K Xx04) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((K Xx04) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx)) as proof of ((x1 Xx)->((K Xx04) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->((K Xx04) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found ((and_rect0 ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx04) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found ((and_rect0 ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx04) Xx)
% Found x6:(Xx04 Xx000)
% Found x6 as proof of (Xx03 Xx000)
% Found (fun (x6:(Xx04 Xx000))=> x6) as proof of (Xx03 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of ((Xx04 Xx000)->(Xx03 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx04 Xx00)->(Xx03 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found x6:(Xx04 Xx000)
% Found x6 as proof of (Xx03 Xx000)
% Found (fun (x6:(Xx04 Xx000))=> x6) as proof of (Xx03 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of ((Xx04 Xx000)->(Xx03 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx04 Xx00)->(Xx03 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found x6:(Xx04 Xx000)
% Found x6 as proof of (Xx03 Xx000)
% Found (fun (x6:(Xx04 Xx000))=> x6) as proof of (Xx03 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of ((Xx04 Xx000)->(Xx03 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx04 Xx00)->(Xx03 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found x6:(Xx04 Xx000)
% Found x6 as proof of (Xx03 Xx000)
% Found (fun (x6:(Xx04 Xx000))=> x6) as proof of (Xx03 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of ((Xx04 Xx000)->(Xx03 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx04 Xx00)->(Xx03 Xx00)))
% Found x400:=(x40 x5):((K x1) Xx)
% Found (x40 x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found x6:(Xx04 Xx000)
% Found x6 as proof of (Xx03 Xx000)
% Found (fun (x6:(Xx04 Xx000))=> x6) as proof of (Xx03 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of ((Xx04 Xx000)->(Xx03 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx04 Xx00)->(Xx03 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found x6:(Xx04 Xx000)
% Found x6 as proof of (Xx03 Xx000)
% Found (fun (x6:(Xx04 Xx000))=> x6) as proof of (Xx03 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of ((Xx04 Xx000)->(Xx03 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx04 Xx00)->(Xx03 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found x6:(Xx04 Xx000)
% Found x6 as proof of (Xx03 Xx000)
% Found (fun (x6:(Xx04 Xx000))=> x6) as proof of (Xx03 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of ((Xx04 Xx000)->(Xx03 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx04 Xx00)->(Xx03 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found x6:(Xx04 Xx000)
% Found x6 as proof of (Xx03 Xx000)
% Found (fun (x6:(Xx04 Xx000))=> x6) as proof of (Xx03 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of ((Xx04 Xx000)->(Xx03 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx04 Xx00)->(Xx03 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx04) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found ((and_rect0 ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx04) Xx)
% Found x6:(Xx04 Xx000)
% Found x6 as proof of (Xx03 Xx000)
% Found (fun (x6:(Xx04 Xx000))=> x6) as proof of (Xx03 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of ((Xx04 Xx000)->(Xx03 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx04 Xx00)->(Xx03 Xx00)))
% Found x400:=(x40 x5):((K x1) Xx)
% Found (x40 x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx04) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found ((and_rect0 ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found x4:(Xx04 Xx000)
% Instantiate: Xx03:=Xx04:(fofType->Prop)
% Found (fun (x4:(Xx04 Xx000))=> x4) as proof of (Xx03 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx04 Xx000))=> x4) as proof of ((Xx04 Xx000)->(Xx03 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx04 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx04 Xx00)->(Xx03 Xx00)))
% Found ((x150 (fun (Xx000:fofType) (x4:(Xx04 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx03) Xx)
% Found (((x15 Xx03) (fun (Xx000:fofType) (x4:(Xx04 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx03) Xx)
% Found ((((x1 x2) Xx03) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx03) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) Xx03) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))))) as proof of ((K Xx03) Xx)
% Found x6:(Xx04 Xx000)
% Found x6 as proof of (Xx03 Xx000)
% Found (fun (x6:(Xx04 Xx000))=> x6) as proof of (Xx03 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of ((Xx04 Xx000)->(Xx03 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx04 Xx00)->(Xx03 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found x6:(Xx0 Xx00)
% Found x6 as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (x6:(Xx0 Xx00))=> x6) 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) (x6:(Xx0 Xx00))=> x6) 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) (x6:(Xx0 Xx00))=> x6) 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 x6:(Xx0 Xx00)
% Found x6 as proof of ((ex (fofType->Prop)) (fun (S:(fofType->Prop))=> ((and (forall (Xx1:fofType), ((S Xx1)->((K S) Xx1)))) (S Xx00))))
% Found (fun (x6:(Xx0 Xx00))=> x6) 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) (x6:(Xx0 Xx00))=> x6) 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) (x6:(Xx0 Xx00))=> x6) 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 x6:(Xx04 Xx000)
% Found x6 as proof of (Xx03 Xx000)
% Found (fun (x6:(Xx04 Xx000))=> x6) as proof of (Xx03 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of ((Xx04 Xx000)->(Xx03 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx04 Xx00)->(Xx03 Xx00)))
% Found x300:=(x30 x4):((K x1) Xx)
% Found (x30 x4) as proof of ((K Xx04) Xx)
% Found ((x3 Xx) x4) as proof of ((K Xx04) Xx)
% Found ((x3 Xx) x4) as proof of ((K Xx04) Xx)
% Found ((x3 Xx) x4) as proof of ((K Xx04) Xx)
% Found x6:(Xx04 Xx000)
% Found x6 as proof of (Xx03 Xx000)
% Found (fun (x6:(Xx04 Xx000))=> x6) as proof of (Xx03 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of ((Xx04 Xx000)->(Xx03 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx04 Xx00)->(Xx03 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found x6:(Xx04 Xx000)
% Found x6 as proof of (Xx03 Xx000)
% Found (fun (x6:(Xx04 Xx000))=> x6) as proof of (Xx03 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of ((Xx04 Xx000)->(Xx03 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx04 Xx00)->(Xx03 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found x6:(Xx04 Xx000)
% Found x6 as proof of (Xx03 Xx000)
% Found (fun (x6:(Xx04 Xx000))=> x6) as proof of (Xx03 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of ((Xx04 Xx000)->(Xx03 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx04 Xx00)->(Xx03 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found x6:(Xx04 Xx000)
% Found x6 as proof of (Xx03 Xx000)
% Found (fun (x6:(Xx04 Xx000))=> x6) as proof of (Xx03 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of ((Xx04 Xx000)->(Xx03 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx04 Xx00)->(Xx03 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found x6:(Xx04 Xx000)
% Found x6 as proof of (Xx03 Xx000)
% Found (fun (x6:(Xx04 Xx000))=> x6) as proof of (Xx03 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of ((Xx04 Xx000)->(Xx03 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx04 Xx00)->(Xx03 Xx00)))
% Found x400:=(x40 x5):((K x1) Xx)
% Found (x40 x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found x6:(Xx04 Xx000)
% Found x6 as proof of (Xx03 Xx000)
% Found (fun (x6:(Xx04 Xx000))=> x6) as proof of (Xx03 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of ((Xx04 Xx000)->(Xx03 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx04 Xx00)->(Xx03 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found x6:(Xx04 Xx000)
% Found x6 as proof of (Xx03 Xx000)
% Found (fun (x6:(Xx04 Xx000))=> x6) as proof of (Xx03 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of ((Xx04 Xx000)->(Xx03 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx04 Xx00)->(Xx03 Xx00)))
% Found x400:=(x40 x5):((K x1) Xx)
% Found (x40 x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found x6:(Xx04 Xx000)
% Found x6 as proof of (Xx03 Xx000)
% Found (fun (x6:(Xx04 Xx000))=> x6) as proof of (Xx03 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of ((Xx04 Xx000)->(Xx03 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx04 Xx00)->(Xx03 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found x2:(Xx00 Xx000)
% Found x2 as proof of (Xx0 Xx000)
% Found (fun (x2:(Xx00 Xx000))=> x2) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x2:(Xx00 Xx000))=> x2) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x2:(Xx00 Xx000))=> x2) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x6:(Xx04 Xx000)
% Found x6 as proof of (Xx03 Xx000)
% Found (fun (x6:(Xx04 Xx000))=> x6) as proof of (Xx03 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of ((Xx04 Xx000)->(Xx03 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx04 Xx00)->(Xx03 Xx00)))
% Found x400:=(x40 x5):((K x1) Xx)
% Found (x40 x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found x6:(Xx04 Xx000)
% Found x6 as proof of (Xx03 Xx000)
% Found (fun (x6:(Xx04 Xx000))=> x6) as proof of (Xx03 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of ((Xx04 Xx000)->(Xx03 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx04 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx04 Xx00)->(Xx03 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx04) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx04) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found ((and_rect0 ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found x4:(Xx04 Xx000)
% Instantiate: Xx03:=Xx04:(fofType->Prop)
% Found (fun (x4:(Xx04 Xx000))=> x4) as proof of (Xx03 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx04 Xx000))=> x4) as proof of ((Xx04 Xx000)->(Xx03 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx04 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx04 Xx00)->(Xx03 Xx00)))
% Found ((x150 (fun (Xx000:fofType) (x4:(Xx04 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx03) Xx)
% Found (((x15 Xx03) (fun (Xx000:fofType) (x4:(Xx04 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx03) Xx)
% Found ((((x1 x2) Xx03) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx03) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) Xx03) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))))) as proof of ((K Xx03) Xx)
% Found x2:(Xx00 Xx000)
% Found x2 as proof of (Xx0 Xx000)
% Found (fun (x2:(Xx00 Xx000))=> x2) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x2:(Xx00 Xx000))=> x2) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x2:(Xx00 Xx000))=> x2) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x2:(Xx00 Xx000)
% Found x2 as proof of (Xx0 Xx000)
% Found (fun (x2:(Xx00 Xx000))=> x2) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x2:(Xx00 Xx000))=> x2) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x2:(Xx00 Xx000))=> x2) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx04) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found ((and_rect0 ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx04) Xx)
% Found x2:(Xx04 Xx000)
% Instantiate: Xx04:=(K x3):(fofType->Prop)
% Found x2 as proof of (Xx03 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx03 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx03 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx03 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx03 Xx000)
% Found ((and_rect0 (Xx03 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx03 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx03 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx03 Xx000)
% 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)) (Xx03 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx03 Xx000)
% Found x4:(Xx00 Xx000)
% Found x4 as proof of (Xx0 Xx000)
% Found (fun (x4:(Xx00 Xx000))=> x4) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx00 Xx000))=> x4) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx00 Xx000))=> x4) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x4:(Xx00 Xx000)
% Found x4 as proof of (Xx0 Xx000)
% Found (fun (x4:(Xx00 Xx000))=> x4) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx00 Xx000))=> x4) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx00 Xx000))=> x4) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x2:(Xx04 Xx000)
% Found x2 as proof of (Xx03 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx03 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx03 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx03 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx03 Xx000)
% Found ((and_rect0 (Xx03 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx03 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx03 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx03 Xx000)
% 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)) (Xx03 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx03 Xx000)
% Found x00:(x1 Xx0)
% Instantiate: x1:=(K Xx1):(fofType->Prop)
% Found x00 as proof of ((K Xx1) Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx00) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx00) Xx))
% Found (fun (x4:(forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx00) Xx))
% Found (fun (x4:(forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000))))=> (x4 Xx)) as proof of ((forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000)))->((x2 Xx)->((K Xx00) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found ((and_rect0 ((K Xx00) Xx)) (fun (x4:(forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)) P) x4) x3)) ((K Xx00) Xx)) (fun (x4:(forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)) P) x4) x3)) ((K Xx00) Xx)) (fun (x4:(forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx04) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found ((and_rect0 ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx04) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx04) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found ((and_rect0 ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found x4:(Xx04 Xx000)
% Instantiate: Xx03:=Xx04:(fofType->Prop)
% Found (fun (x4:(Xx04 Xx000))=> x4) as proof of (Xx03 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx04 Xx000))=> x4) as proof of ((Xx04 Xx000)->(Xx03 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx04 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx04 Xx00)->(Xx03 Xx00)))
% Found ((x150 (fun (Xx000:fofType) (x4:(Xx04 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx03) Xx)
% Found (((x15 Xx03) (fun (Xx000:fofType) (x4:(Xx04 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx03) Xx)
% Found ((((x1 x2) Xx03) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx03) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) Xx03) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))))) as proof of ((K Xx03) Xx)
% Found x7:(Xx3 Xx02)
% Instantiate: Xx3:=(K Xx4):(fofType->Prop)
% Found x7 as proof of ((K Xx4) Xx02)
% Found x40:=(x4 Xx):((x1 Xx)->((K x1) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((K Xx00) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((K Xx00) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx)) as proof of ((x1 Xx)->((K Xx00) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->((K Xx00) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found ((and_rect0 ((K Xx00) Xx)) (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((K Xx00) Xx)) (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((K Xx00) Xx)) (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx00) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx00) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx00) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx00) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found ((and_rect0 ((K Xx00) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx00) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx00) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx00) Xx)
% Found x4:(Xx00 Xx000)
% Found x4 as proof of (Xx0 Xx000)
% Found (fun (x4:(Xx00 Xx000))=> x4) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx00 Xx000))=> x4) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx00 Xx000))=> x4) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x4:(Xx00 Xx000)
% Found x4 as proof of (Xx0 Xx000)
% Found (fun (x4:(Xx00 Xx000))=> x4) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx00 Xx000))=> x4) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx00 Xx000))=> x4) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x2:(Xx04 Xx000)
% Instantiate: Xx04:=(K x3):(fofType->Prop)
% Found x2 as proof of (Xx03 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx03 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx03 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx03 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx03 Xx000)
% Found ((and_rect0 (Xx03 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx03 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx03 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx03 Xx000)
% 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)) (Xx03 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx03 Xx000)
% Found x4:(Xx00 Xx000)
% Found x4 as proof of (Xx0 Xx000)
% Found (fun (x4:(Xx00 Xx000))=> x4) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx00 Xx000))=> x4) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx00 Xx000))=> x4) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x4:(Xx00 Xx000)
% Found x4 as proof of (Xx0 Xx000)
% Found (fun (x4:(Xx00 Xx000))=> x4) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx00 Xx000))=> x4) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx00 Xx000))=> x4) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% 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 x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx00) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx00) Xx))
% Found (fun (x4:(forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx00) Xx))
% Found (fun (x4:(forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000))))=> (x4 Xx)) as proof of ((forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000)))->((x2 Xx)->((K Xx00) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found ((and_rect0 ((K Xx00) Xx)) (fun (x4:(forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)) P) x4) x3)) ((K Xx00) Xx)) (fun (x4:(forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)) P) x4) x3)) ((K Xx00) Xx)) (fun (x4:(forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found x4:(Xx00 Xx000)
% Instantiate: Xx0:=Xx00:(fofType->Prop)
% Found (fun (x4:(Xx00 Xx000))=> x4) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx00 Xx000))=> x4) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx00 Xx000))=> x4) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found ((x110 (fun (Xx000:fofType) (x4:(Xx00 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)) P) x4) x3)) ((K Xx00) Xx)) (fun (x4:(forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000))))=> (x4 Xx)))) as proof of ((K Xx0) Xx)
% Found (((x11 Xx0) (fun (Xx000:fofType) (x4:(Xx00 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)) P) x4) x3)) ((K Xx00) Xx)) (fun (x4:(forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000))))=> (x4 Xx)))) as proof of ((K Xx0) Xx)
% Found ((((x1 x2) Xx0) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000))))=> (x4 Xx)))) as proof of ((K Xx0) Xx)
% Found (fun (x3:((and (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)))=> ((((x1 x2) Xx0) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000))))=> (x4 Xx))))) as proof of ((K Xx0) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx00) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx00) Xx))
% Found (fun (x4:(forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx00) Xx))
% Found (fun (x4:(forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000))))=> (x4 Xx)) as proof of ((forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000)))->((x2 Xx)->((K Xx00) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found ((and_rect0 ((K Xx00) Xx)) (fun (x4:(forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)) P) x4) x3)) ((K Xx00) Xx)) (fun (x4:(forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)) P) x4) x3)) ((K Xx00) Xx)) (fun (x4:(forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx00) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx00) Xx))
% Found (fun (x4:(forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx00) Xx))
% Found (fun (x4:(forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000))))=> (x4 Xx)) as proof of ((forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000)))->((x2 Xx)->((K Xx00) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found ((and_rect0 ((K Xx00) Xx)) (fun (x4:(forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)) P) x4) x3)) ((K Xx00) Xx)) (fun (x4:(forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)) P) x4) x3)) ((K Xx00) Xx)) (fun (x4:(forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found x9:(Xx4 Xx03)
% Instantiate: Xx4:=(K Xx5):(fofType->Prop)
% Found x9 as proof of ((K Xx5) Xx03)
% Found x2:(Xx04 Xx000)
% Found x2 as proof of (Xx03 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx03 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx03 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx03 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx03 Xx000)
% Found ((and_rect0 (Xx03 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx03 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx03 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx03 Xx000)
% 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)) (Xx03 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx03 Xx000)
% Found x6:(Xx00 Xx000)
% Found x6 as proof of (Xx0 Xx000)
% Found (fun (x6:(Xx00 Xx000))=> x6) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx00 Xx000))=> x6) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx00 Xx000))=> x6) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x400:=(x40 x5):((K x1) Xx)
% Found (x40 x5) as proof of ((K Xx00) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx00) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx00) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx00) Xx)
% Found x6:(Xx00 Xx000)
% Found x6 as proof of (Xx0 Xx000)
% Found (fun (x6:(Xx00 Xx000))=> x6) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx00 Xx000))=> x6) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx00 Xx000))=> x6) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx00) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx00) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx00) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx00) Xx)
% Found x40:=(x4 Xx):((x1 Xx)->((K x1) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((K Xx00) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((K Xx00) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx)) as proof of ((x1 Xx)->((K Xx00) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->((K Xx00) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found ((and_rect0 ((K Xx00) Xx)) (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((K Xx00) Xx)) (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((K Xx00) Xx)) (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx00) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx00) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx00) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx00) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found ((and_rect0 ((K Xx00) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx00) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx00) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx00) Xx)
% Found x40:=(x4 Xx):((x1 Xx)->((K x1) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((K Xx00) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((K Xx00) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx)) as proof of ((x1 Xx)->((K Xx00) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->((K Xx00) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found ((and_rect0 ((K Xx00) Xx)) (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((K Xx00) Xx)) (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((K Xx00) Xx)) (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx00) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx00) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx00) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx00) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found ((and_rect0 ((K Xx00) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx00) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx00) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx00) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx04) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found ((and_rect0 ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx04) Xx)
% Found x6:(Xx00 Xx000)
% Found x6 as proof of (Xx0 Xx000)
% Found (fun (x6:(Xx00 Xx000))=> x6) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx00 Xx000))=> x6) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx00 Xx000))=> x6) 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:(Xx3 Xx02)
% Instantiate: Xx3:=(K Xx4):(fofType->Prop)
% Found x7 as proof of ((K Xx4) Xx02)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx00) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx00) Xx))
% Found (fun (x4:(forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx00) Xx))
% Found (fun (x4:(forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000))))=> (x4 Xx)) as proof of ((forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000)))->((x2 Xx)->((K Xx00) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found ((and_rect0 ((K Xx00) Xx)) (fun (x4:(forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)) P) x4) x3)) ((K Xx00) Xx)) (fun (x4:(forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)) P) x4) x3)) ((K Xx00) Xx)) (fun (x4:(forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found x4:(Xx00 Xx000)
% Instantiate: Xx0:=Xx00:(fofType->Prop)
% Found (fun (x4:(Xx00 Xx000))=> x4) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx00 Xx000))=> x4) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx00 Xx000))=> x4) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found ((x110 (fun (Xx000:fofType) (x4:(Xx00 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)) P) x4) x3)) ((K Xx00) Xx)) (fun (x4:(forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000))))=> (x4 Xx)))) as proof of ((K Xx0) Xx)
% Found (((x11 Xx0) (fun (Xx000:fofType) (x4:(Xx00 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)) P) x4) x3)) ((K Xx00) Xx)) (fun (x4:(forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000))))=> (x4 Xx)))) as proof of ((K Xx0) Xx)
% Found ((((x1 x2) Xx0) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000))))=> (x4 Xx)))) as proof of ((K Xx0) Xx)
% Found (fun (x3:((and (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)))=> ((((x1 x2) Xx0) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000))))=> (x4 Xx))))) as proof of ((K Xx0) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx00) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx00) Xx))
% Found (fun (x4:(forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx00) Xx))
% Found (fun (x4:(forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000))))=> (x4 Xx)) as proof of ((forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000)))->((x2 Xx)->((K Xx00) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found ((and_rect0 ((K Xx00) Xx)) (fun (x4:(forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)) P) x4) x3)) ((K Xx00) Xx)) (fun (x4:(forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)) P) x4) x3)) ((K Xx00) Xx)) (fun (x4:(forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found x4:(Xx00 Xx000)
% Instantiate: Xx0:=Xx00:(fofType->Prop)
% Found (fun (x4:(Xx00 Xx000))=> x4) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx00 Xx000))=> x4) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx00 Xx000))=> x4) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found ((x110 (fun (Xx000:fofType) (x4:(Xx00 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)) P) x4) x3)) ((K Xx00) Xx)) (fun (x4:(forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000))))=> (x4 Xx)))) as proof of ((K Xx0) Xx)
% Found (((x11 Xx0) (fun (Xx000:fofType) (x4:(Xx00 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)) P) x4) x3)) ((K Xx00) Xx)) (fun (x4:(forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000))))=> (x4 Xx)))) as proof of ((K Xx0) Xx)
% Found ((((x1 x2) Xx0) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000))))=> (x4 Xx)))) as proof of ((K Xx0) Xx)
% Found (fun (x3:((and (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)))=> ((((x1 x2) Xx0) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx000:fofType), ((x2 Xx000)->((K x2) Xx000))))=> (x4 Xx))))) as proof of ((K Xx0) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx04) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found ((and_rect0 ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found x4:(Xx04 Xx000)
% Instantiate: Xx03:=Xx04:(fofType->Prop)
% Found (fun (x4:(Xx04 Xx000))=> x4) as proof of (Xx03 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx04 Xx000))=> x4) as proof of ((Xx04 Xx000)->(Xx03 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx04 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx04 Xx00)->(Xx03 Xx00)))
% Found ((x150 (fun (Xx000:fofType) (x4:(Xx04 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx03) Xx)
% Found (((x15 Xx03) (fun (Xx000:fofType) (x4:(Xx04 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx03) Xx)
% Found ((((x1 x2) Xx03) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx03) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) Xx03) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))))) as proof of ((K Xx03) Xx)
% Found x2:(Xx04 Xx000)
% Instantiate: Xx04:=(K x3):(fofType->Prop)
% Found x2 as proof of (Xx03 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx03 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx03 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx03 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx03 Xx000)
% Found ((and_rect0 (Xx03 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx03 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx03 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx03 Xx000)
% 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)) (Xx03 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx03 Xx000)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx00) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx00) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx00) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx00) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found ((and_rect0 ((K Xx00) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx00) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx00) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx00) Xx)
% Found x6:(Xx00 Xx000)
% Found x6 as proof of (Xx0 Xx000)
% Found (fun (x6:(Xx00 Xx000))=> x6) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx00 Xx000))=> x6) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx00 Xx000))=> x6) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x400:=(x40 x5):((K x1) Xx)
% Found (x40 x5) as proof of ((K Xx00) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx00) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx00) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx00) Xx)
% Found x6:(Xx00 Xx000)
% Found x6 as proof of (Xx0 Xx000)
% Found (fun (x6:(Xx00 Xx000))=> x6) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx00 Xx000))=> x6) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx00 Xx000))=> x6) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx00) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx00) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx00) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx00) Xx)
% Found x6:(Xx00 Xx000)
% Found x6 as proof of (Xx0 Xx000)
% Found (fun (x6:(Xx00 Xx000))=> x6) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx00 Xx000))=> x6) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx00 Xx000))=> x6) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x400:=(x40 x5):((K x1) Xx)
% Found (x40 x5) as proof of ((K Xx00) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx00) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx00) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx00) Xx)
% Found x6:(Xx00 Xx000)
% Found x6 as proof of (Xx0 Xx000)
% Found (fun (x6:(Xx00 Xx000))=> x6) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx00 Xx000))=> x6) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx00 Xx000))=> x6) as proof of (forall (Xx000:fofType), ((Xx00 Xx000)->(Xx0 Xx000)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx00) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx00) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx00) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx00) Xx)
% Found x9:(Xx4 Xx03)
% Instantiate: Xx4:=(K Xx5):(fofType->Prop)
% Found x9 as proof of ((K Xx5) Xx03)
% Found x6:(Xx00 Xx000)
% Found x6 as proof of (Xx0 Xx000)
% Found (fun (x6:(Xx00 Xx000))=> x6) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx00 Xx000))=> x6) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx00 Xx000))=> x6) 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 x6:(Xx00 Xx000)
% Found x6 as proof of (Xx0 Xx000)
% Found (fun (x6:(Xx00 Xx000))=> x6) as proof of (Xx0 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx00 Xx000))=> x6) as proof of ((Xx00 Xx000)->(Xx0 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx00 Xx000))=> x6) 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 x2:(Xx04 Xx000)
% Found x2 as proof of (Xx03 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx03 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx03 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx03 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx03 Xx000)
% Found ((and_rect0 (Xx03 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx03 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx03 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx03 Xx000)
% 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)) (Xx03 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx03 Xx000)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx00) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx00) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx00) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx00) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found ((and_rect0 ((K Xx00) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx00) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx00) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx00) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx00) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx00) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx00) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx00) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found ((and_rect0 ((K Xx00) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx00) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx00) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx00) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx00) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx04) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found ((and_rect0 ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx04) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx04) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found ((and_rect0 ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found x4:(Xx04 Xx000)
% Instantiate: Xx03:=Xx04:(fofType->Prop)
% Found (fun (x4:(Xx04 Xx000))=> x4) as proof of (Xx03 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx04 Xx000))=> x4) as proof of ((Xx04 Xx000)->(Xx03 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx04 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx04 Xx00)->(Xx03 Xx00)))
% Found ((x150 (fun (Xx000:fofType) (x4:(Xx04 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx03) Xx)
% Found (((x15 Xx03) (fun (Xx000:fofType) (x4:(Xx04 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx03) Xx)
% Found ((((x1 x2) Xx03) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx03) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) Xx03) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))))) as proof of ((K Xx03) Xx)
% Found x2:(Xx04 Xx000)
% Instantiate: Xx04:=(K x3):(fofType->Prop)
% Found x2 as proof of (Xx03 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx03 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx03 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx03 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx03 Xx000)
% Found ((and_rect0 (Xx03 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx03 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx03 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx03 Xx000)
% 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)) (Xx03 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx03 Xx000)
% Found x2:(Xx00 Xx000)
% Instantiate: Xx00:=(K x3):(fofType->Prop)
% Found x2 as proof of (Xx0 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx0 Xx000)
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx0 Xx000))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->(Xx0 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (Xx0 Xx000)
% Found ((and_rect0 (Xx0 Xx000)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (Xx0 Xx000)
% 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)) (Xx0 Xx000)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (Xx0 Xx000)
% 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)) (Xx0 Xx000)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (Xx0 Xx000)
% Found x2:(Xx04 Xx000)
% Found x2 as proof of (Xx03 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx03 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx03 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx03 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx03 Xx000)
% Found ((and_rect0 (Xx03 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx03 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx03 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx03 Xx000)
% 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)) (Xx03 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx03 Xx000)
% Found x2:(Xx00 Xx000)
% Found x2 as proof of (Xx0 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx0 Xx000)
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx0 Xx000))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->(Xx0 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (Xx0 Xx000)
% Found ((and_rect0 (Xx0 Xx000)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (Xx0 Xx000)
% 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)) (Xx0 Xx000)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (Xx0 Xx000)
% 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)) (Xx0 Xx000)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (Xx0 Xx000)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx04) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found ((and_rect0 ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx04) Xx)
% Found x2:(Xx00 Xx000)
% Instantiate: Xx00:=(K x3):(fofType->Prop)
% Found x2 as proof of (Xx0 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx0 Xx000)
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx0 Xx000))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->(Xx0 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (Xx0 Xx000)
% Found ((and_rect0 (Xx0 Xx000)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (Xx0 Xx000)
% 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)) (Xx0 Xx000)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (Xx0 Xx000)
% 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)) (Xx0 Xx000)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (Xx0 Xx000)
% Found x2:(Xx00 Xx000)
% Instantiate: Xx00:=(K x3):(fofType->Prop)
% Found x2 as proof of (Xx0 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx0 Xx000)
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx0 Xx000))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->(Xx0 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (Xx0 Xx000)
% Found ((and_rect0 (Xx0 Xx000)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (Xx0 Xx000)
% 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)) (Xx0 Xx000)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (Xx0 Xx000)
% 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)) (Xx0 Xx000)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (Xx0 Xx000)
% Found x2:(Xx01 Xx000)
% Found x2 as proof of (Xx00 Xx000)
% Found (fun (x2:(Xx01 Xx000))=> x2) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x2:(Xx01 Xx000))=> x2) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x2:(Xx01 Xx000))=> x2) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x2:(Xx00 Xx000)
% Found x2 as proof of (Xx0 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx0 Xx000)
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx0 Xx000))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->(Xx0 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (Xx0 Xx000)
% Found ((and_rect0 (Xx0 Xx000)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (Xx0 Xx000)
% 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)) (Xx0 Xx000)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (Xx0 Xx000)
% 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)) (Xx0 Xx000)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (Xx0 Xx000)
% Found x2:(Xx00 Xx000)
% Found x2 as proof of (Xx0 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx0 Xx000)
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx0 Xx000))
% Found (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))->((x3 Xx)->(Xx0 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (Xx0 Xx000)
% Found ((and_rect0 (Xx0 Xx000)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (Xx0 Xx000)
% 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)) (Xx0 Xx000)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x6:(x3 Xx))=> x2)) as proof of (Xx0 Xx000)
% 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)) (Xx0 Xx000)) (fun (x5:(forall (Xx00:fofType), ((x3 Xx00)->((K x3) Xx00)))) (x6:(x3 Xx))=> x2))) as proof of (Xx0 Xx000)
% Found x2:(Xx04 Xx000)
% Instantiate: Xx04:=(K x3):(fofType->Prop)
% Found x2 as proof of (Xx03 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx03 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx03 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx03 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx03 Xx000)
% Found ((and_rect0 (Xx03 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx03 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx03 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx03 Xx000)
% 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)) (Xx03 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx03 Xx000)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx04) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found ((and_rect0 ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found x4:(Xx04 Xx000)
% Instantiate: Xx03:=Xx04:(fofType->Prop)
% Found (fun (x4:(Xx04 Xx000))=> x4) as proof of (Xx03 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx04 Xx000))=> x4) as proof of ((Xx04 Xx000)->(Xx03 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx04 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx04 Xx00)->(Xx03 Xx00)))
% Found ((x150 (fun (Xx000:fofType) (x4:(Xx04 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx03) Xx)
% Found (((x15 Xx03) (fun (Xx000:fofType) (x4:(Xx04 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx03) Xx)
% Found ((((x1 x2) Xx03) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx03) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) Xx03) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))))) as proof of ((K Xx03) Xx)
% Found x2:(Xx01 Xx000)
% Found x2 as proof of (Xx00 Xx000)
% Found (fun (x2:(Xx01 Xx000))=> x2) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x2:(Xx01 Xx000))=> x2) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x2:(Xx01 Xx000))=> x2) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x2:(Xx01 Xx000)
% Found x2 as proof of (Xx00 Xx000)
% Found (fun (x2:(Xx01 Xx000))=> x2) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x2:(Xx01 Xx000))=> x2) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x2:(Xx01 Xx000))=> x2) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x9:(Xx4 Xx03)
% Instantiate: Xx4:=(K Xx5):(fofType->Prop)
% Found x9 as proof of ((K Xx5) Xx03)
% Found x9:(Xx4 Xx03)
% Instantiate: Xx4:=(K Xx5):(fofType->Prop)
% Found x9 as proof of ((K Xx5) Xx03)
% Found x9:(Xx4 Xx03)
% Instantiate: Xx4:=(K Xx5):(fofType->Prop)
% Found x9 as proof of ((K Xx5) Xx03)
% Found x9:(Xx4 Xx03)
% Instantiate: Xx4:=(K Xx5):(fofType->Prop)
% Found x9 as proof of ((K Xx5) Xx03)
% Found x2:(Xx04 Xx000)
% Found x2 as proof of (Xx03 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx03 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx03 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx03 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx03 Xx000)
% Found ((and_rect0 (Xx03 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx03 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx03 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx03 Xx000)
% 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)) (Xx03 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx03 Xx000)
% Found x4:(Xx01 Xx000)
% Found x4 as proof of (Xx00 Xx000)
% Found (fun (x4:(Xx01 Xx000))=> x4) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx01 Xx000))=> x4) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx01 Xx000))=> x4) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x2:(Xx04 Xx000)
% Instantiate: Xx04:=(K x3):(fofType->Prop)
% Found x2 as proof of (Xx03 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx03 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx03 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx03 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx03 Xx000)
% Found ((and_rect0 (Xx03 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx03 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx03 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx03 Xx000)
% 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)) (Xx03 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx03 Xx000)
% Found x4:(Xx01 Xx000)
% Found x4 as proof of (Xx00 Xx000)
% Found (fun (x4:(Xx01 Xx000))=> x4) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx01 Xx000))=> x4) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx01 Xx000))=> x4) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x4:(Xx01 Xx000)
% Found x4 as proof of (Xx00 Xx000)
% Found (fun (x4:(Xx01 Xx000))=> x4) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx01 Xx000))=> x4) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx01 Xx000))=> x4) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx04) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found ((and_rect0 ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx04) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx04) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found ((and_rect0 ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found x4:(Xx04 Xx000)
% Instantiate: Xx03:=Xx04:(fofType->Prop)
% Found (fun (x4:(Xx04 Xx000))=> x4) as proof of (Xx03 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx04 Xx000))=> x4) as proof of ((Xx04 Xx000)->(Xx03 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx04 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx04 Xx00)->(Xx03 Xx00)))
% Found ((x150 (fun (Xx000:fofType) (x4:(Xx04 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx03) Xx)
% Found (((x15 Xx03) (fun (Xx000:fofType) (x4:(Xx04 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx03) Xx)
% Found ((((x1 x2) Xx03) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx03) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) Xx03) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))))) as proof of ((K Xx03) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx)) as proof of ((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->((K Xx01) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect0 ((K Xx01) Xx)) (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx01) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect0 ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found x9:(Xx4 Xx03)
% Instantiate: Xx4:=(K Xx5):(fofType->Prop)
% Found x9 as proof of ((K Xx5) Xx03)
% Found x9:(Xx4 Xx03)
% Instantiate: Xx4:=(K Xx5):(fofType->Prop)
% Found x9 as proof of ((K Xx5) Xx03)
% Found x9:(Xx4 Xx03)
% Instantiate: Xx4:=(K Xx5):(fofType->Prop)
% Found x9 as proof of ((K Xx5) Xx03)
% Found x9:(Xx4 Xx03)
% Instantiate: Xx4:=(K Xx5):(fofType->Prop)
% Found x9 as proof of ((K Xx5) Xx03)
% Found x2:(Xx04 Xx000)
% Found x2 as proof of (Xx03 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx03 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx03 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx03 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx03 Xx000)
% Found ((and_rect0 (Xx03 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx03 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx03 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx03 Xx000)
% 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)) (Xx03 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx03 Xx000)
% Found x4:(Xx01 Xx000)
% Found x4 as proof of (Xx00 Xx000)
% Found (fun (x4:(Xx01 Xx000))=> x4) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx01 Xx000))=> x4) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx01 Xx000))=> x4) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x4:(Xx01 Xx000)
% Found x4 as proof of (Xx00 Xx000)
% Found (fun (x4:(Xx01 Xx000))=> x4) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx01 Xx000))=> x4) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx01 Xx000))=> x4) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x40:=(x4 Xx):((x1 Xx)->((K x1) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((K Xx01) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((K Xx01) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx)) as proof of ((x1 Xx)->((K Xx01) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->((K Xx01) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect0 ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx01) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect0 ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx01) Xx)
% Found x4:(Xx01 Xx000)
% Found x4 as proof of (Xx00 Xx000)
% Found (fun (x4:(Xx01 Xx000))=> x4) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx01 Xx000))=> x4) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx01 Xx000))=> x4) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x4:(Xx01 Xx000)
% Found x4 as proof of (Xx00 Xx000)
% Found (fun (x4:(Xx01 Xx000))=> x4) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx01 Xx000))=> x4) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx01 Xx000))=> x4) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x4:(Xx01 Xx000)
% Found x4 as proof of (Xx00 Xx000)
% Found (fun (x4:(Xx01 Xx000))=> x4) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx01 Xx000))=> x4) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx01 Xx000))=> x4) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x4:(Xx01 Xx000)
% Found x4 as proof of (Xx00 Xx000)
% Found (fun (x4:(Xx01 Xx000))=> x4) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx01 Xx000))=> x4) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx01 Xx000))=> x4) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx04) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found ((and_rect0 ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx04) Xx)
% Found x6:(Xx01 Xx000)
% Found x6 as proof of (Xx00 Xx000)
% Found (fun (x6:(Xx01 Xx000))=> x6) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx01 Xx000))=> x6) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx01 Xx000))=> x6) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx01) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx01) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx01) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx01) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx01) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect0 ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found x4:(Xx01 Xx000)
% Instantiate: Xx00:=Xx01:(fofType->Prop)
% Found (fun (x4:(Xx01 Xx000))=> x4) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx01 Xx000))=> x4) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx01 Xx000))=> x4) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found ((x120 (fun (Xx000:fofType) (x4:(Xx01 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx00) Xx)
% Found (((x12 Xx00) (fun (Xx000:fofType) (x4:(Xx01 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx00) Xx)
% Found ((((x1 x2) Xx00) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx00) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) Xx00) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))))) as proof of ((K Xx00) Xx)
% Found x3:(Xx1 Xx00)
% Instantiate: Xx1:=(K Xx2):(fofType->Prop)
% Found x3 as proof of ((K Xx2) Xx00)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx)) as proof of ((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->((K Xx01) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect0 ((K Xx01) Xx)) (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx)) as proof of ((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->((K Xx01) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect0 ((K Xx01) Xx)) (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx01) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect0 ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx01) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect0 ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found x6:(Xx01 Xx000)
% Found x6 as proof of (Xx00 Xx000)
% Found (fun (x6:(Xx01 Xx000))=> x6) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx01 Xx000))=> x6) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx01 Xx000))=> x6) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x400:=(x40 x5):((K x1) Xx)
% Found (x40 x5) as proof of ((K Xx01) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx01) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx01) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx01) Xx)
% Found x6:(Xx01 Xx000)
% Found x6 as proof of (Xx00 Xx000)
% Found (fun (x6:(Xx01 Xx000))=> x6) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx01 Xx000))=> x6) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx01 Xx000))=> x6) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx01) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx01) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx01) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx01) Xx)
% Found x2:(Xx05 Xx000)
% Found x2 as proof of (Xx04 Xx000)
% Found (fun (x2:(Xx05 Xx000))=> x2) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x2:(Xx05 Xx000))=> x2) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x2:(Xx05 Xx000))=> x2) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found x6:(Xx01 Xx000)
% Found x6 as proof of (Xx00 Xx000)
% Found (fun (x6:(Xx01 Xx000))=> x6) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx01 Xx000))=> x6) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx01 Xx000))=> x6) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x400:=(x40 x5):((K x1) Xx)
% Found (x40 x5) as proof of ((K Xx01) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx01) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx01) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx01) Xx)
% Found x6:(Xx01 Xx000)
% Found x6 as proof of (Xx00 Xx000)
% Found (fun (x6:(Xx01 Xx000))=> x6) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx01 Xx000))=> x6) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx01 Xx000))=> x6) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx01) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx01) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx01) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx01) Xx)
% Found x6:(Xx01 Xx000)
% Found x6 as proof of (Xx00 Xx000)
% Found (fun (x6:(Xx01 Xx000))=> x6) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx01 Xx000))=> x6) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx01 Xx000))=> x6) 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 x40:=(x4 Xx):((x1 Xx)->((K x1) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((K Xx01) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((K Xx01) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx)) as proof of ((x1 Xx)->((K Xx01) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->((K Xx01) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect0 ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found x40:=(x4 Xx):((x1 Xx)->((K x1) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((K Xx01) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((K Xx01) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx)) as proof of ((x1 Xx)->((K Xx01) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->((K Xx01) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect0 ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx01) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect0 ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx01) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx01) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect0 ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx01) Xx)
% Found x2:(Xx04 Xx000)
% Instantiate: Xx04:=(K x3):(fofType->Prop)
% Found x2 as proof of (Xx03 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx03 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx03 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx03 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx03 Xx000)
% Found ((and_rect0 (Xx03 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx03 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx03 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx03 Xx000)
% 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)) (Xx03 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx03 Xx000)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx01) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect0 ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found x4:(Xx01 Xx000)
% Instantiate: Xx00:=Xx01:(fofType->Prop)
% Found (fun (x4:(Xx01 Xx000))=> x4) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx01 Xx000))=> x4) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx01 Xx000))=> x4) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found ((x120 (fun (Xx000:fofType) (x4:(Xx01 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx00) Xx)
% Found (((x12 Xx00) (fun (Xx000:fofType) (x4:(Xx01 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx00) Xx)
% Found ((((x1 x2) Xx00) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx00) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) Xx00) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))))) as proof of ((K Xx00) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx01) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect0 ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found x4:(Xx01 Xx000)
% Instantiate: Xx00:=Xx01:(fofType->Prop)
% Found (fun (x4:(Xx01 Xx000))=> x4) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx01 Xx000))=> x4) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx01 Xx000))=> x4) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found ((x120 (fun (Xx000:fofType) (x4:(Xx01 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx00) Xx)
% Found (((x12 Xx00) (fun (Xx000:fofType) (x4:(Xx01 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx00) Xx)
% Found ((((x1 x2) Xx00) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx00) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) Xx00) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))))) as proof of ((K Xx00) Xx)
% Found x6:(Xx01 Xx000)
% Found x6 as proof of (Xx00 Xx000)
% Found (fun (x6:(Xx01 Xx000))=> x6) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx01 Xx000))=> x6) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx01 Xx000))=> x6) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx01) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx01) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx01) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx01) Xx)
% Found x6:(Xx01 Xx000)
% Found x6 as proof of (Xx00 Xx000)
% Found (fun (x6:(Xx01 Xx000))=> x6) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx01 Xx000))=> x6) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx01 Xx000))=> x6) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx01) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx01) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx01) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx01) Xx)
% Found x3:(Xx1 Xx00)
% Instantiate: Xx1:=(K Xx2):(fofType->Prop)
% Found x3 as proof of ((K Xx2) Xx00)
% Found x3:(Xx1 Xx00)
% Instantiate: Xx1:=(K Xx2):(fofType->Prop)
% Found x3 as proof of ((K Xx2) Xx00)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx01) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect0 ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx01) Xx)
% Found x6:(Xx01 Xx000)
% Found x6 as proof of (Xx00 Xx000)
% Found (fun (x6:(Xx01 Xx000))=> x6) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx01 Xx000))=> x6) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx01 Xx000))=> x6) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x400:=(x40 x5):((K x1) Xx)
% Found (x40 x5) as proof of ((K Xx01) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx01) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx01) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx01) Xx)
% Found x6:(Xx01 Xx000)
% Found x6 as proof of (Xx00 Xx000)
% Found (fun (x6:(Xx01 Xx000))=> x6) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx01 Xx000))=> x6) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx01 Xx000))=> x6) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x400:=(x40 x5):((K x1) Xx)
% Found (x40 x5) as proof of ((K Xx01) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx01) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx01) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx01) Xx)
% Found x6:(Xx01 Xx000)
% Found x6 as proof of (Xx00 Xx000)
% Found (fun (x6:(Xx01 Xx000))=> x6) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx01 Xx000))=> x6) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx01 Xx000))=> x6) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx01) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx01) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx01) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx01) Xx)
% Found x6:(Xx01 Xx000)
% Found x6 as proof of (Xx00 Xx000)
% Found (fun (x6:(Xx01 Xx000))=> x6) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx01 Xx000))=> x6) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx01 Xx000))=> x6) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx01) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx01) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx01) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx01) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx04) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found ((and_rect0 ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found x4:(Xx04 Xx000)
% Instantiate: Xx03:=Xx04:(fofType->Prop)
% Found (fun (x4:(Xx04 Xx000))=> x4) as proof of (Xx03 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx04 Xx000))=> x4) as proof of ((Xx04 Xx000)->(Xx03 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx04 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx04 Xx00)->(Xx03 Xx00)))
% Found ((x150 (fun (Xx000:fofType) (x4:(Xx04 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx03) Xx)
% Found (((x15 Xx03) (fun (Xx000:fofType) (x4:(Xx04 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx03) Xx)
% Found ((((x1 x2) Xx03) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx03) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) Xx03) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))))) as proof of ((K Xx03) Xx)
% Found x2:(Xx05 Xx000)
% Found x2 as proof of (Xx04 Xx000)
% Found (fun (x2:(Xx05 Xx000))=> x2) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x2:(Xx05 Xx000))=> x2) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x2:(Xx05 Xx000))=> x2) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found x6:(Xx01 Xx000)
% Found x6 as proof of (Xx00 Xx000)
% Found (fun (x6:(Xx01 Xx000))=> x6) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx01 Xx000))=> x6) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx01 Xx000))=> x6) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x400:=(x40 x5):((K x1) Xx)
% Found (x40 x5) as proof of ((K Xx01) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx01) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx01) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx01) Xx)
% Found x6:(Xx01 Xx000)
% Found x6 as proof of (Xx00 Xx000)
% Found (fun (x6:(Xx01 Xx000))=> x6) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx01 Xx000))=> x6) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx01 Xx000))=> x6) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x400:=(x40 x5):((K x1) Xx)
% Found (x40 x5) as proof of ((K Xx01) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx01) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx01) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx01) Xx)
% Found x6:(Xx01 Xx000)
% Found x6 as proof of (Xx00 Xx000)
% Found (fun (x6:(Xx01 Xx000))=> x6) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx01 Xx000))=> x6) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx01 Xx000))=> x6) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx01) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx01) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx01) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx01) Xx)
% Found x6:(Xx01 Xx000)
% Found x6 as proof of (Xx00 Xx000)
% Found (fun (x6:(Xx01 Xx000))=> x6) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx01 Xx000))=> x6) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx01 Xx000))=> x6) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx01) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx01) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx01) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx01) Xx)
% Found x6:(Xx01 Xx000)
% Found x6 as proof of (Xx00 Xx000)
% Found (fun (x6:(Xx01 Xx000))=> x6) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx01 Xx000))=> x6) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx01 Xx000))=> x6) 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 x6:(Xx01 Xx000)
% Found x6 as proof of (Xx00 Xx000)
% Found (fun (x6:(Xx01 Xx000))=> x6) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx01 Xx000))=> x6) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx01 Xx000))=> x6) 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 x2:(Xx04 Xx000)
% Found x2 as proof of (Xx03 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx03 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx03 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx03 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx03 Xx000)
% Found ((and_rect0 (Xx03 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx03 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx03 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx03 Xx000)
% 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)) (Xx03 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx03 Xx000)
% Found x4:(Xx05 Xx000)
% Found x4 as proof of (Xx04 Xx000)
% Found (fun (x4:(Xx05 Xx000))=> x4) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx05 Xx000))=> x4) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx05 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found x2:(Xx04 Xx000)
% Instantiate: Xx04:=(K x3):(fofType->Prop)
% Found x2 as proof of (Xx03 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx03 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx03 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx03 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx03 Xx000)
% Found ((and_rect0 (Xx03 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx03 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx03 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx03 Xx000)
% 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)) (Xx03 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx03 Xx000)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx01) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect0 ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx01) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx01) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect0 ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx01) Xx)
% Found x4:(Xx05 Xx000)
% Found x4 as proof of (Xx04 Xx000)
% Found (fun (x4:(Xx05 Xx000))=> x4) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx05 Xx000))=> x4) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx05 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found x4:(Xx05 Xx000)
% Found x4 as proof of (Xx04 Xx000)
% Found (fun (x4:(Xx05 Xx000))=> x4) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx05 Xx000))=> x4) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx05 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx01) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect0 ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found x4:(Xx01 Xx000)
% Instantiate: Xx00:=Xx01:(fofType->Prop)
% Found (fun (x4:(Xx01 Xx000))=> x4) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx01 Xx000))=> x4) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx01 Xx000))=> x4) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found ((x120 (fun (Xx000:fofType) (x4:(Xx01 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx00) Xx)
% Found (((x12 Xx00) (fun (Xx000:fofType) (x4:(Xx01 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx00) Xx)
% Found ((((x1 x2) Xx00) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx00) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) Xx00) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))))) as proof of ((K Xx00) Xx)
% Found x4:(Xx05 Xx000)
% Found x4 as proof of (Xx04 Xx000)
% Found (fun (x4:(Xx05 Xx000))=> x4) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx05 Xx000))=> x4) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx05 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found x2:(Xx01 Xx000)
% Instantiate: Xx01:=(K x3):(fofType->Prop)
% Found x2 as proof of (Xx00 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx00 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx00 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx00 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx00 Xx000)
% Found ((and_rect0 (Xx00 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx00 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx00 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx00 Xx000)
% 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)) (Xx00 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx00 Xx000)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx04) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found ((and_rect0 ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx04) Xx)
% Found x4:(Xx05 Xx000)
% Found x4 as proof of (Xx04 Xx000)
% Found (fun (x4:(Xx05 Xx000))=> x4) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx05 Xx000))=> x4) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx05 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx04) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found ((and_rect0 ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found x4:(Xx04 Xx000)
% Instantiate: Xx03:=Xx04:(fofType->Prop)
% Found (fun (x4:(Xx04 Xx000))=> x4) as proof of (Xx03 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx04 Xx000))=> x4) as proof of ((Xx04 Xx000)->(Xx03 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx04 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx04 Xx00)->(Xx03 Xx00)))
% Found ((x150 (fun (Xx000:fofType) (x4:(Xx04 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx03) Xx)
% Found (((x15 Xx03) (fun (Xx000:fofType) (x4:(Xx04 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx03) Xx)
% Found ((((x1 x2) Xx03) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx03) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) Xx03) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))))) as proof of ((K Xx03) Xx)
% Found x4:(Xx05 Xx000)
% Found x4 as proof of (Xx04 Xx000)
% Found (fun (x4:(Xx05 Xx000))=> x4) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx05 Xx000))=> x4) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx05 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found x9:(Xx4 Xx03)
% Instantiate: Xx4:=(K Xx5):(fofType->Prop)
% Found x9 as proof of ((K Xx5) Xx03)
% Found x9:(Xx4 Xx03)
% Instantiate: Xx4:=(K Xx5):(fofType->Prop)
% Found x9 as proof of ((K Xx5) Xx03)
% Found x9:(Xx4 Xx03)
% Instantiate: Xx4:=(K Xx5):(fofType->Prop)
% Found x9 as proof of ((K Xx5) Xx03)
% Found x9:(Xx4 Xx03)
% Instantiate: Xx4:=(K Xx5):(fofType->Prop)
% Found x9 as proof of ((K Xx5) Xx03)
% Found x9:(Xx4 Xx03)
% Instantiate: Xx4:=(K Xx5):(fofType->Prop)
% Found x9 as proof of ((K Xx5) Xx03)
% Found x9:(Xx4 Xx03)
% Instantiate: Xx4:=(K Xx5):(fofType->Prop)
% Found x9 as proof of ((K Xx5) Xx03)
% Found x4:(Xx05 Xx000)
% Found x4 as proof of (Xx04 Xx000)
% Found (fun (x4:(Xx05 Xx000))=> x4) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx05 Xx000))=> x4) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx05 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found x2:(Xx01 Xx000)
% Found x2 as proof of (Xx00 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx00 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx00 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx00 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx00 Xx000)
% Found ((and_rect0 (Xx00 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx00 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx00 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx00 Xx000)
% 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)) (Xx00 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx00 Xx000)
% Found x2:(Xx04 Xx000)
% Found x2 as proof of (Xx03 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx03 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx03 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx03 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx03 Xx000)
% Found ((and_rect0 (Xx03 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx03 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx03 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx03 Xx000)
% 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)) (Xx03 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx03 Xx000)
% Found x4:(Xx05 Xx000)
% Found x4 as proof of (Xx04 Xx000)
% Found (fun (x4:(Xx05 Xx000))=> x4) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx05 Xx000))=> x4) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx05 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx01) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect0 ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found x4:(Xx01 Xx000)
% Instantiate: Xx00:=Xx01:(fofType->Prop)
% Found (fun (x4:(Xx01 Xx000))=> x4) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx01 Xx000))=> x4) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx01 Xx000))=> x4) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found ((x120 (fun (Xx000:fofType) (x4:(Xx01 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx00) Xx)
% Found (((x12 Xx00) (fun (Xx000:fofType) (x4:(Xx01 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx00) Xx)
% Found ((((x1 x2) Xx00) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx00) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) Xx00) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))))) as proof of ((K Xx00) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx01) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect0 ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found x4:(Xx01 Xx000)
% Instantiate: Xx00:=Xx01:(fofType->Prop)
% Found (fun (x4:(Xx01 Xx000))=> x4) as proof of (Xx00 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx01 Xx000))=> x4) as proof of ((Xx01 Xx000)->(Xx00 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx01 Xx000))=> x4) as proof of (forall (Xx000:fofType), ((Xx01 Xx000)->(Xx00 Xx000)))
% Found ((x120 (fun (Xx000:fofType) (x4:(Xx01 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx00) Xx)
% Found (((x12 Xx00) (fun (Xx000:fofType) (x4:(Xx01 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx00) Xx)
% Found ((((x1 x2) Xx00) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx00) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) Xx00) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))))) as proof of ((K Xx00) Xx)
% Found x4:(Xx05 Xx000)
% Found x4 as proof of (Xx04 Xx000)
% Found (fun (x4:(Xx05 Xx000))=> x4) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx05 Xx000))=> x4) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx05 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found x4:(Xx05 Xx000)
% Found x4 as proof of (Xx04 Xx000)
% Found (fun (x4:(Xx05 Xx000))=> x4) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx05 Xx000))=> x4) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx05 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx01) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect0 ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx01) Xx)
% Found x2:(Xx01 Xx000)
% Instantiate: Xx01:=(K x3):(fofType->Prop)
% Found x2 as proof of (Xx00 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx00 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx00 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx00 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx00 Xx000)
% Found ((and_rect0 (Xx00 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx00 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx00 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx00 Xx000)
% 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)) (Xx00 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx00 Xx000)
% Found x2:(Xx01 Xx000)
% Instantiate: Xx01:=(K x3):(fofType->Prop)
% Found x2 as proof of (Xx00 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx00 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx00 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx00 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx00 Xx000)
% Found ((and_rect0 (Xx00 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx00 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx00 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx00 Xx000)
% 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)) (Xx00 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx00 Xx000)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx)) as proof of ((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->((K Xx05) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found ((and_rect0 ((K Xx05) Xx)) (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx05) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found ((and_rect0 ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx05) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found ((and_rect0 ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx05) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found ((and_rect0 ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx05) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found ((and_rect0 ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx05) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found ((and_rect0 ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found x4:(Xx05 Xx000)
% Found x4 as proof of (Xx04 Xx000)
% Found (fun (x4:(Xx05 Xx000))=> x4) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx05 Xx000))=> x4) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx05 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx04) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx04) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found ((and_rect0 ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx04) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx04) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx04) Xx)
% Found x4:(Xx05 Xx000)
% Found x4 as proof of (Xx04 Xx000)
% Found (fun (x4:(Xx05 Xx000))=> x4) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx05 Xx000))=> x4) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx05 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found x6:(Xx05 Xx000)
% Found x6 as proof of (Xx04 Xx000)
% Found (fun (x6:(Xx05 Xx000))=> x6) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found x4:(Xx05 Xx000)
% Found x4 as proof of (Xx04 Xx000)
% Found (fun (x4:(Xx05 Xx000))=> x4) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx05 Xx000))=> x4) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx05 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found x40:=(x4 Xx):((x1 Xx)->((K x1) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((K Xx05) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((K Xx05) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx)) as proof of ((x1 Xx)->((K Xx05) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->((K Xx05) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found ((and_rect0 ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx05) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found ((and_rect0 ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx05) Xx)
% Found x2:(Xx01 Xx000)
% Found x2 as proof of (Xx00 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx00 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx00 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx00 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx00 Xx000)
% Found ((and_rect0 (Xx00 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx00 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx00 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx00 Xx000)
% 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)) (Xx00 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx00 Xx000)
% Found x2:(Xx01 Xx000)
% Found x2 as proof of (Xx00 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx00 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx00 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx00 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx00 Xx000)
% Found ((and_rect0 (Xx00 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx00 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx00 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx00 Xx000)
% 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)) (Xx00 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx00 Xx000)
% Found x9:(Xx4 Xx03)
% Instantiate: Xx4:=(K Xx5):(fofType->Prop)
% Found x9 as proof of ((K Xx5) Xx03)
% Found x9:(Xx4 Xx03)
% Instantiate: Xx4:=(K Xx5):(fofType->Prop)
% Found x9 as proof of ((K Xx5) Xx03)
% Found x9:(Xx4 Xx03)
% Instantiate: Xx4:=(K Xx5):(fofType->Prop)
% Found x9 as proof of ((K Xx5) Xx03)
% Found x9:(Xx4 Xx03)
% Instantiate: Xx4:=(K Xx5):(fofType->Prop)
% Found x9 as proof of ((K Xx5) Xx03)
% Found x9:(Xx4 Xx03)
% Instantiate: Xx4:=(K Xx5):(fofType->Prop)
% Found x9 as proof of ((K Xx5) Xx03)
% Found x9:(Xx4 Xx03)
% Instantiate: Xx4:=(K Xx5):(fofType->Prop)
% Found x9 as proof of ((K Xx5) Xx03)
% Found x6:(Xx05 Xx000)
% Found x6 as proof of (Xx04 Xx000)
% Found (fun (x6:(Xx05 Xx000))=> x6) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found x6:(Xx05 Xx000)
% Found x6 as proof of (Xx04 Xx000)
% Found (fun (x6:(Xx05 Xx000))=> x6) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found x4:(Xx05 Xx000)
% Found x4 as proof of (Xx04 Xx000)
% Found (fun (x4:(Xx05 Xx000))=> x4) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx05 Xx000))=> x4) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx05 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found x6:(Xx05 Xx000)
% Found x6 as proof of (Xx04 Xx000)
% Found (fun (x6:(Xx05 Xx000))=> x6) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found x400:=(x40 x5):((K x1) Xx)
% Found (x40 x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found x6:(Xx05 Xx000)
% Found x6 as proof of (Xx04 Xx000)
% Found (fun (x6:(Xx05 Xx000))=> x6) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found x6:(Xx05 Xx000)
% Found x6 as proof of (Xx04 Xx000)
% Found (fun (x6:(Xx05 Xx000))=> x6) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found x6:(Xx05 Xx000)
% Found x6 as proof of (Xx04 Xx000)
% Found (fun (x6:(Xx05 Xx000))=> x6) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found x6:(Xx05 Xx000)
% Found x6 as proof of (Xx04 Xx000)
% Found (fun (x6:(Xx05 Xx000))=> x6) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found x6:(Xx05 Xx000)
% Found x6 as proof of (Xx04 Xx000)
% Found (fun (x6:(Xx05 Xx000))=> x6) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found x400:=(x40 x5):((K x1) Xx)
% Found (x40 x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found x6:(Xx05 Xx000)
% Found x6 as proof of (Xx04 Xx000)
% Found (fun (x6:(Xx05 Xx000))=> x6) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found x6:(Xx05 Xx000)
% Found x6 as proof of (Xx04 Xx000)
% Found (fun (x6:(Xx05 Xx000))=> x6) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found x300:=(x30 x4):((K x1) Xx)
% Found (x30 x4) as proof of ((K Xx05) Xx)
% Found ((x3 Xx) x4) as proof of ((K Xx05) Xx)
% Found ((x3 Xx) x4) as proof of ((K Xx05) Xx)
% Found ((x3 Xx) x4) as proof of ((K Xx05) Xx)
% Found x6:(Xx05 Xx000)
% Found x6 as proof of (Xx04 Xx000)
% Found (fun (x6:(Xx05 Xx000))=> x6) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found x6:(Xx05 Xx000)
% Found x6 as proof of (Xx04 Xx000)
% Found (fun (x6:(Xx05 Xx000))=> x6) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found x6:(Xx05 Xx000)
% Found x6 as proof of (Xx04 Xx000)
% Found (fun (x6:(Xx05 Xx000))=> x6) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found x6:(Xx05 Xx000)
% Found x6 as proof of (Xx04 Xx000)
% Found (fun (x6:(Xx05 Xx000))=> x6) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx01) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect0 ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx01) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx01) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx01) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found ((and_rect0 ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx01) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx01) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx01) Xx)
% Found x6:(Xx05 Xx000)
% Found x6 as proof of (Xx04 Xx000)
% Found (fun (x6:(Xx05 Xx000))=> x6) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found x400:=(x40 x5):((K x1) Xx)
% Found (x40 x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found x6:(Xx05 Xx000)
% Found x6 as proof of (Xx04 Xx000)
% Found (fun (x6:(Xx05 Xx000))=> x6) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx05) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found ((and_rect0 ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found x4:(Xx05 Xx000)
% Instantiate: Xx04:=Xx05:(fofType->Prop)
% Found (fun (x4:(Xx05 Xx000))=> x4) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx05 Xx000))=> x4) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx05 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found ((x160 (fun (Xx000:fofType) (x4:(Xx05 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx04) Xx)
% Found (((x16 Xx04) (fun (Xx000:fofType) (x4:(Xx05 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx04) Xx)
% Found ((((x1 x2) Xx04) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx04) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) Xx04) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))))) as proof of ((K Xx04) Xx)
% Found x6:(Xx05 Xx000)
% Found x6 as proof of (Xx04 Xx000)
% Found (fun (x6:(Xx05 Xx000))=> x6) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found x6:(Xx05 Xx000)
% Found x6 as proof of (Xx04 Xx000)
% Found (fun (x6:(Xx05 Xx000))=> x6) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found x6:(Xx05 Xx000)
% Found x6 as proof of (Xx04 Xx000)
% Found (fun (x6:(Xx05 Xx000))=> x6) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found x6:(Xx05 Xx000)
% Found x6 as proof of (Xx04 Xx000)
% Found (fun (x6:(Xx05 Xx000))=> x6) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found x6:(Xx05 Xx000)
% Found x6 as proof of (Xx04 Xx000)
% Found (fun (x6:(Xx05 Xx000))=> x6) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found x6:(Xx05 Xx000)
% Found x6 as proof of (Xx04 Xx000)
% Found (fun (x6:(Xx05 Xx000))=> x6) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found x400:=(x40 x5):((K x1) Xx)
% Found (x40 x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found x3:(Xx1 Xx00)
% Instantiate: Xx1:=(K Xx2):(fofType->Prop)
% Found x3 as proof of ((K Xx2) Xx00)
% Found x6:(Xx05 Xx000)
% Found x6 as proof of (Xx04 Xx000)
% Found (fun (x6:(Xx05 Xx000))=> x6) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx)) as proof of ((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->((K Xx05) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found ((and_rect0 ((K Xx05) Xx)) (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx05) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found ((and_rect0 ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx05) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found ((and_rect0 ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx05) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found ((and_rect0 ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx05) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found ((and_rect0 ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx05) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found ((and_rect0 ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found x6:(Xx05 Xx000)
% Found x6 as proof of (Xx04 Xx000)
% Found (fun (x6:(Xx05 Xx000))=> x6) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found x400:=(x40 x5):((K x1) Xx)
% Found (x40 x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found x6:(Xx05 Xx000)
% Found x6 as proof of (Xx04 Xx000)
% Found (fun (x6:(Xx05 Xx000))=> x6) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found x2:(Xx04 Xx000)
% Instantiate: Xx04:=(K x3):(fofType->Prop)
% Found x2 as proof of (Xx03 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx03 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx03 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx03 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx03 Xx000)
% Found ((and_rect0 (Xx03 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx03 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx03 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx03 Xx000)
% 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)) (Xx03 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx03 Xx000)
% Found x6:(Xx05 Xx000)
% Found x6 as proof of (Xx04 Xx000)
% Found (fun (x6:(Xx05 Xx000))=> x6) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found x400:=(x40 x5):((K x1) Xx)
% Found (x40 x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found x2:(Xx01 Xx000)
% Instantiate: Xx01:=(K x3):(fofType->Prop)
% Found x2 as proof of (Xx00 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx00 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx00 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx00 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx00 Xx000)
% Found ((and_rect0 (Xx00 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx00 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx00 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx00 Xx000)
% 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)) (Xx00 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx00 Xx000)
% Found x6:(Xx05 Xx000)
% Found x6 as proof of (Xx04 Xx000)
% Found (fun (x6:(Xx05 Xx000))=> x6) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found x40:=(x4 Xx):((x1 Xx)->((K x1) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((K Xx05) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((K Xx05) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx)) as proof of ((x1 Xx)->((K Xx05) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->((K Xx05) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found ((and_rect0 ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found x6:(Xx05 Xx000)
% Found x6 as proof of (Xx04 Xx000)
% Found (fun (x6:(Xx05 Xx000))=> x6) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx05) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found ((and_rect0 ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx05) Xx)
% Found x6:(Xx05 Xx000)
% Found x6 as proof of (Xx04 Xx000)
% Found (fun (x6:(Xx05 Xx000))=> x6) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found x6:(Xx05 Xx000)
% Found x6 as proof of (Xx04 Xx000)
% Found (fun (x6:(Xx05 Xx000))=> x6) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found x6:(Xx05 Xx000)
% Found x6 as proof of (Xx04 Xx000)
% Found (fun (x6:(Xx05 Xx000))=> x6) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found x400:=(x40 x5):((K x1) Xx)
% Found (x40 x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found x6:(Xx05 Xx000)
% Found x6 as proof of (Xx04 Xx000)
% Found (fun (x6:(Xx05 Xx000))=> x6) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found x6:(Xx05 Xx000)
% Found x6 as proof of (Xx04 Xx000)
% Found (fun (x6:(Xx05 Xx000))=> x6) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found x6:(Xx05 Xx000)
% Found x6 as proof of (Xx04 Xx000)
% Found (fun (x6:(Xx05 Xx000))=> x6) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found x6:(Xx05 Xx000)
% Found x6 as proof of (Xx04 Xx000)
% Found (fun (x6:(Xx05 Xx000))=> x6) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found x2:(Xx02 Xx000)
% Found x2 as proof of (Xx01 Xx000)
% Found (fun (x2:(Xx02 Xx000))=> x2) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x2:(Xx02 Xx000))=> x2) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x2:(Xx02 Xx000))=> x2) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x2:(Xx01 Xx000)
% Found x2 as proof of (Xx00 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx00 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx00 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx00 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx00 Xx000)
% Found ((and_rect0 (Xx00 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx00 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx00 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx00 Xx000)
% 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)) (Xx00 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx00 Xx000)
% Found x6:(Xx05 Xx000)
% Found x6 as proof of (Xx04 Xx000)
% Found (fun (x6:(Xx05 Xx000))=> x6) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found x400:=(x40 x5):((K x1) Xx)
% Found (x40 x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found x6:(Xx05 Xx000)
% Found x6 as proof of (Xx04 Xx000)
% Found (fun (x6:(Xx05 Xx000))=> x6) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found x3:(Xx1 Xx00)
% Instantiate: Xx1:=(K Xx2):(fofType->Prop)
% Found x3 as proof of ((K Xx2) Xx00)
% Found x6:(Xx05 Xx000)
% Found x6 as proof of (Xx04 Xx000)
% Found (fun (x6:(Xx05 Xx000))=> x6) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found x300:=(x30 x4):((K x1) Xx)
% Found (x30 x4) as proof of ((K Xx05) Xx)
% Found ((x3 Xx) x4) as proof of ((K Xx05) Xx)
% Found ((x3 Xx) x4) as proof of ((K Xx05) Xx)
% Found ((x3 Xx) x4) as proof of ((K Xx05) Xx)
% Found x3:(Xx1 Xx00)
% Instantiate: Xx1:=(K Xx2):(fofType->Prop)
% Found x3 as proof of ((K Xx2) Xx00)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx05) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found ((and_rect0 ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx05) Xx)
% Found x6:(Xx05 Xx000)
% Found x6 as proof of (Xx04 Xx000)
% Found (fun (x6:(Xx05 Xx000))=> x6) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found x6:(Xx05 Xx000)
% Found x6 as proof of (Xx04 Xx000)
% Found (fun (x6:(Xx05 Xx000))=> x6) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found x6:(Xx05 Xx000)
% Found x6 as proof of (Xx04 Xx000)
% Found (fun (x6:(Xx05 Xx000))=> x6) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found x6:(Xx05 Xx000)
% Found x6 as proof of (Xx04 Xx000)
% Found (fun (x6:(Xx05 Xx000))=> x6) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx05) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found ((and_rect0 ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found x4:(Xx05 Xx000)
% Instantiate: Xx04:=Xx05:(fofType->Prop)
% Found (fun (x4:(Xx05 Xx000))=> x4) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx05 Xx000))=> x4) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx05 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found ((x160 (fun (Xx000:fofType) (x4:(Xx05 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx04) Xx)
% Found (((x16 Xx04) (fun (Xx000:fofType) (x4:(Xx05 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx04) Xx)
% Found ((((x1 x2) Xx04) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx04) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) Xx04) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))))) as proof of ((K Xx04) Xx)
% Found x6:(Xx05 Xx000)
% Found x6 as proof of (Xx04 Xx000)
% Found (fun (x6:(Xx05 Xx000))=> x6) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found x400:=(x40 x5):((K x1) Xx)
% Found (x40 x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found x6:(Xx05 Xx000)
% Found x6 as proof of (Xx04 Xx000)
% Found (fun (x6:(Xx05 Xx000))=> x6) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found x6:(Xx05 Xx000)
% Found x6 as proof of (Xx04 Xx000)
% Found (fun (x6:(Xx05 Xx000))=> x6) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found x6:(Xx05 Xx000)
% Found x6 as proof of (Xx04 Xx000)
% Found (fun (x6:(Xx05 Xx000))=> x6) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found x6:(Xx05 Xx000)
% Found x6 as proof of (Xx04 Xx000)
% Found (fun (x6:(Xx05 Xx000))=> x6) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found x6:(Xx05 Xx000)
% Found x6 as proof of (Xx04 Xx000)
% Found (fun (x6:(Xx05 Xx000))=> x6) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found x6:(Xx05 Xx000)
% Found x6 as proof of (Xx04 Xx000)
% Found (fun (x6:(Xx05 Xx000))=> x6) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found x6:(Xx05 Xx000)
% Found x6 as proof of (Xx04 Xx000)
% Found (fun (x6:(Xx05 Xx000))=> x6) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found x400:=(x40 x5):((K x1) Xx)
% Found (x40 x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found x6:(Xx05 Xx000)
% Found x6 as proof of (Xx04 Xx000)
% Found (fun (x6:(Xx05 Xx000))=> x6) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found x2:(Xx04 Xx000)
% Found x2 as proof of (Xx03 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx03 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx03 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx03 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx03 Xx000)
% Found ((and_rect0 (Xx03 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx03 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx03 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx03 Xx000)
% 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)) (Xx03 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx03 Xx000)
% Found x2:(Xx01 Xx000)
% Instantiate: Xx01:=(K x3):(fofType->Prop)
% Found x2 as proof of (Xx00 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx00 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx00 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx00 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx00 Xx000)
% Found ((and_rect0 (Xx00 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx00 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx00 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx00 Xx000)
% 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)) (Xx00 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx00 Xx000)
% Found x2:(Xx01 Xx000)
% Instantiate: Xx01:=(K x3):(fofType->Prop)
% Found x2 as proof of (Xx00 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx00 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx00 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx00 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx00 Xx000)
% Found ((and_rect0 (Xx00 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx00 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx00 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx00 Xx000)
% 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)) (Xx00 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx00 Xx000)
% Found x6:(Xx05 Xx000)
% Found x6 as proof of (Xx04 Xx000)
% Found (fun (x6:(Xx05 Xx000))=> x6) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found x400:=(x40 x5):((K x1) Xx)
% Found (x40 x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found x6:(Xx05 Xx000)
% Found x6 as proof of (Xx04 Xx000)
% Found (fun (x6:(Xx05 Xx000))=> x6) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found x2:(Xx04 Xx000)
% Instantiate: Xx04:=(K x3):(fofType->Prop)
% Found x2 as proof of (Xx03 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx03 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx03 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx03 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx03 Xx000)
% Found ((and_rect0 (Xx03 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx03 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx03 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx03 Xx000)
% 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)) (Xx03 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx03 Xx000)
% Found x6:(Xx05 Xx000)
% Found x6 as proof of (Xx04 Xx000)
% Found (fun (x6:(Xx05 Xx000))=> x6) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found x400:=(x40 x5):((K x1) Xx)
% Found (x40 x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found x6:(Xx05 Xx000)
% Found x6 as proof of (Xx04 Xx000)
% Found (fun (x6:(Xx05 Xx000))=> x6) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx05 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx05) Xx)
% Found x2:(Xx02 Xx000)
% Found x2 as proof of (Xx01 Xx000)
% Found (fun (x2:(Xx02 Xx000))=> x2) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x2:(Xx02 Xx000))=> x2) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x2:(Xx02 Xx000))=> x2) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x2:(Xx02 Xx000)
% Found x2 as proof of (Xx01 Xx000)
% Found (fun (x2:(Xx02 Xx000))=> x2) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x2:(Xx02 Xx000))=> x2) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x2:(Xx02 Xx000))=> x2) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x2:(Xx01 Xx000)
% Found x2 as proof of (Xx00 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx00 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx00 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx00 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx00 Xx000)
% Found ((and_rect0 (Xx00 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx00 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx00 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx00 Xx000)
% 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)) (Xx00 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx00 Xx000)
% Found x2:(Xx01 Xx000)
% Found x2 as proof of (Xx00 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx00 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx00 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx00 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx00 Xx000)
% Found ((and_rect0 (Xx00 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx00 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx00 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx00 Xx000)
% 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)) (Xx00 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx00 Xx000)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx05) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found ((and_rect0 ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found x4:(Xx05 Xx000)
% Instantiate: Xx04:=Xx05:(fofType->Prop)
% Found (fun (x4:(Xx05 Xx000))=> x4) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx05 Xx000))=> x4) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx05 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found ((x160 (fun (Xx000:fofType) (x4:(Xx05 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx04) Xx)
% Found (((x16 Xx04) (fun (Xx000:fofType) (x4:(Xx05 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx04) Xx)
% Found ((((x1 x2) Xx04) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx04) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) Xx04) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))))) as proof of ((K Xx04) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx05) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found ((and_rect0 ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx05) Xx)
% Found x4:(Xx02 Xx000)
% Found x4 as proof of (Xx01 Xx000)
% Found (fun (x4:(Xx02 Xx000))=> x4) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x2:(Xx05 Xx000)
% Instantiate: Xx05:=(K x3):(fofType->Prop)
% Found x2 as proof of (Xx04 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx04 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx04 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx04 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx04 Xx000)
% Found ((and_rect0 (Xx04 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx04 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx04 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx04 Xx000)
% 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)) (Xx04 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx04 Xx000)
% Found x2:(Xx04 Xx000)
% Found x2 as proof of (Xx03 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx03 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx03 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx03 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx03 Xx000)
% Found ((and_rect0 (Xx03 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx03 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx03 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx03 Xx000)
% 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)) (Xx03 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx03 Xx000)
% Found x4:(Xx02 Xx000)
% Found x4 as proof of (Xx01 Xx000)
% Found (fun (x4:(Xx02 Xx000))=> x4) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x4:(Xx02 Xx000)
% Found x4 as proof of (Xx01 Xx000)
% Found (fun (x4:(Xx02 Xx000))=> x4) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x4:(Xx02 Xx000)
% Found x4 as proof of (Xx01 Xx000)
% Found (fun (x4:(Xx02 Xx000))=> x4) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x9:(Xx4 Xx03)
% Instantiate: Xx4:=(K Xx5):(fofType->Prop)
% Found x9 as proof of ((K Xx5) Xx03)
% Found x9:(Xx4 Xx03)
% Instantiate: Xx4:=(K Xx5):(fofType->Prop)
% Found x9 as proof of ((K Xx5) Xx03)
% Found x9:(Xx4 Xx03)
% Instantiate: Xx4:=(K Xx5):(fofType->Prop)
% Found x9 as proof of ((K Xx5) Xx03)
% Found x9:(Xx4 Xx03)
% Instantiate: Xx4:=(K Xx5):(fofType->Prop)
% Found x9 as proof of ((K Xx5) Xx03)
% Found x2:(Xx05 Xx000)
% Found x2 as proof of (Xx04 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx04 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx04 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx04 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx04 Xx000)
% Found ((and_rect0 (Xx04 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx04 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx04 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx04 Xx000)
% 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)) (Xx04 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx04 Xx000)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx)) as proof of ((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->((K Xx02) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect0 ((K Xx02) Xx)) (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx02) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect0 ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx02) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect0 ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx05) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found ((and_rect0 ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx05) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx05) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found ((and_rect0 ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found x4:(Xx05 Xx000)
% Instantiate: Xx04:=Xx05:(fofType->Prop)
% Found (fun (x4:(Xx05 Xx000))=> x4) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx05 Xx000))=> x4) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx05 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found ((x160 (fun (Xx000:fofType) (x4:(Xx05 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx04) Xx)
% Found (((x16 Xx04) (fun (Xx000:fofType) (x4:(Xx05 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx04) Xx)
% Found ((((x1 x2) Xx04) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx04) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) Xx04) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))))) as proof of ((K Xx04) Xx)
% Found x4:(Xx02 Xx000)
% Found x4 as proof of (Xx01 Xx000)
% Found (fun (x4:(Xx02 Xx000))=> x4) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x4:(Xx02 Xx000)
% Found x4 as proof of (Xx01 Xx000)
% Found (fun (x4:(Xx02 Xx000))=> x4) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x4:(Xx02 Xx000)
% Found x4 as proof of (Xx01 Xx000)
% Found (fun (x4:(Xx02 Xx000))=> x4) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x4:(Xx02 Xx000)
% Found x4 as proof of (Xx01 Xx000)
% Found (fun (x4:(Xx02 Xx000))=> x4) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x4:(Xx02 Xx000)
% Found x4 as proof of (Xx01 Xx000)
% Found (fun (x4:(Xx02 Xx000))=> x4) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x4:(Xx02 Xx000)
% Found x4 as proof of (Xx01 Xx000)
% Found (fun (x4:(Xx02 Xx000))=> x4) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x40:=(x4 Xx):((x1 Xx)->((K x1) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((K Xx02) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx)) as proof of ((x1 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->((K Xx02) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect0 ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx02) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect0 ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx02) Xx)
% Found x2:(Xx05 Xx000)
% Instantiate: Xx05:=(K x3):(fofType->Prop)
% Found x2 as proof of (Xx04 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx04 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx04 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx04 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx04 Xx000)
% Found ((and_rect0 (Xx04 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx04 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx04 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx04 Xx000)
% 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)) (Xx04 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx04 Xx000)
% Found x4:(Xx02 Xx000)
% Found x4 as proof of (Xx01 Xx000)
% Found (fun (x4:(Xx02 Xx000))=> x4) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x4:(Xx02 Xx000)
% Found x4 as proof of (Xx01 Xx000)
% Found (fun (x4:(Xx02 Xx000))=> x4) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x6:(Xx02 Xx000)
% Found x6 as proof of (Xx01 Xx000)
% Found (fun (x6:(Xx02 Xx000))=> x6) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found x9:(Xx4 Xx03)
% Instantiate: Xx4:=(K Xx5):(fofType->Prop)
% Found x9 as proof of ((K Xx5) Xx03)
% Found x9:(Xx4 Xx03)
% Instantiate: Xx4:=(K Xx5):(fofType->Prop)
% Found x9 as proof of ((K Xx5) Xx03)
% Found x9:(Xx4 Xx03)
% Instantiate: Xx4:=(K Xx5):(fofType->Prop)
% Found x9 as proof of ((K Xx5) Xx03)
% Found x9:(Xx4 Xx03)
% Instantiate: Xx4:=(K Xx5):(fofType->Prop)
% Found x9 as proof of ((K Xx5) Xx03)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx02) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect0 ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found x4:(Xx02 Xx000)
% Instantiate: Xx01:=Xx02:(fofType->Prop)
% Found (fun (x4:(Xx02 Xx000))=> x4) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found ((x130 (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx01) Xx)
% Found (((x13 Xx01) (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx01) Xx)
% Found ((((x1 x2) Xx01) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx01) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) Xx01) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))))) as proof of ((K Xx01) Xx)
% Found x6:(Xx02 Xx000)
% Found x6 as proof of (Xx01 Xx000)
% Found (fun (x6:(Xx02 Xx000))=> x6) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found x6:(Xx02 Xx000)
% Found x6 as proof of (Xx01 Xx000)
% Found (fun (x6:(Xx02 Xx000))=> x6) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found x6:(Xx02 Xx000)
% Found x6 as proof of (Xx01 Xx000)
% Found (fun (x6:(Xx02 Xx000))=> x6) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x400:=(x40 x5):((K x1) Xx)
% Found (x40 x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found x6:(Xx02 Xx000)
% Found x6 as proof of (Xx01 Xx000)
% Found (fun (x6:(Xx02 Xx000))=> x6) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found x2:(Xx05 Xx000)
% Found x2 as proof of (Xx04 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx04 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx04 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx04 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx04 Xx000)
% Found ((and_rect0 (Xx04 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx04 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx04 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx04 Xx000)
% 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)) (Xx04 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx04 Xx000)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx)) as proof of ((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->((K Xx02) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect0 ((K Xx02) Xx)) (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx)) as proof of ((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->((K Xx02) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect0 ((K Xx02) Xx)) (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx02) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect0 ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx02) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect0 ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx02) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect0 ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx02) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect0 ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found x6:(Xx02 Xx000)
% Found x6 as proof of (Xx01 Xx000)
% Found (fun (x6:(Xx02 Xx000))=> x6) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x400:=(x40 x5):((K x1) Xx)
% Found (x40 x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found x6:(Xx02 Xx000)
% Found x6 as proof of (Xx01 Xx000)
% Found (fun (x6:(Xx02 Xx000))=> x6) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found x6:(Xx02 Xx000)
% Found x6 as proof of (Xx01 Xx000)
% Found (fun (x6:(Xx02 Xx000))=> x6) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) 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 x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx05) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found ((and_rect0 ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx05) Xx)
% Found x6:(Xx02 Xx000)
% Found x6 as proof of (Xx01 Xx000)
% Found (fun (x6:(Xx02 Xx000))=> x6) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x400:=(x40 x5):((K x1) Xx)
% Found (x40 x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found x6:(Xx02 Xx000)
% Found x6 as proof of (Xx01 Xx000)
% Found (fun (x6:(Xx02 Xx000))=> x6) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found x40:=(x4 Xx):((x1 Xx)->((K x1) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((K Xx02) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx)) as proof of ((x1 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->((K Xx02) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect0 ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found x40:=(x4 Xx):((x1 Xx)->((K x1) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((K Xx02) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx)) as proof of ((x1 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->((K Xx02) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect0 ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx02) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect0 ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx02) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx02) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect0 ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx02) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx05) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found ((and_rect0 ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found x4:(Xx05 Xx000)
% Instantiate: Xx04:=Xx05:(fofType->Prop)
% Found (fun (x4:(Xx05 Xx000))=> x4) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx05 Xx000))=> x4) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx05 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found ((x160 (fun (Xx000:fofType) (x4:(Xx05 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx04) Xx)
% Found (((x16 Xx04) (fun (Xx000:fofType) (x4:(Xx05 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx04) Xx)
% Found ((((x1 x2) Xx04) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx04) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) Xx04) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))))) as proof of ((K Xx04) Xx)
% Found x2:(Xx05 Xx000)
% Instantiate: Xx05:=(K x3):(fofType->Prop)
% Found x2 as proof of (Xx04 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx04 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx04 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx04 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx04 Xx000)
% Found ((and_rect0 (Xx04 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx04 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx04 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx04 Xx000)
% 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)) (Xx04 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx04 Xx000)
% Found x6:(Xx02 Xx000)
% Found x6 as proof of (Xx01 Xx000)
% Found (fun (x6:(Xx02 Xx000))=> x6) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found x6:(Xx02 Xx000)
% Found x6 as proof of (Xx01 Xx000)
% Found (fun (x6:(Xx02 Xx000))=> x6) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx02) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect0 ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found x4:(Xx02 Xx000)
% Instantiate: Xx01:=Xx02:(fofType->Prop)
% Found (fun (x4:(Xx02 Xx000))=> x4) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found ((x130 (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx01) Xx)
% Found (((x13 Xx01) (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx01) Xx)
% Found ((((x1 x2) Xx01) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx01) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) Xx01) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))))) as proof of ((K Xx01) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx02) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect0 ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found x4:(Xx02 Xx000)
% Instantiate: Xx01:=Xx02:(fofType->Prop)
% Found (fun (x4:(Xx02 Xx000))=> x4) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found ((x130 (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx01) Xx)
% Found (((x13 Xx01) (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx01) Xx)
% Found ((((x1 x2) Xx01) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx01) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) Xx01) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))))) as proof of ((K Xx01) Xx)
% Found x6:(Xx02 Xx000)
% Found x6 as proof of (Xx01 Xx000)
% Found (fun (x6:(Xx02 Xx000))=> x6) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found x6:(Xx02 Xx000)
% Found x6 as proof of (Xx01 Xx000)
% Found (fun (x6:(Xx02 Xx000))=> x6) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found x6:(Xx02 Xx000)
% Found x6 as proof of (Xx01 Xx000)
% Found (fun (x6:(Xx02 Xx000))=> x6) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found x6:(Xx02 Xx000)
% Found x6 as proof of (Xx01 Xx000)
% Found (fun (x6:(Xx02 Xx000))=> x6) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx02) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect0 ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx02) Xx)
% Found x6:(Xx02 Xx000)
% Found x6 as proof of (Xx01 Xx000)
% Found (fun (x6:(Xx02 Xx000))=> x6) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x400:=(x40 x5):((K x1) Xx)
% Found (x40 x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found x6:(Xx02 Xx000)
% Found x6 as proof of (Xx01 Xx000)
% Found (fun (x6:(Xx02 Xx000))=> x6) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x400:=(x40 x5):((K x1) Xx)
% Found (x40 x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found x6:(Xx02 Xx000)
% Found x6 as proof of (Xx01 Xx000)
% Found (fun (x6:(Xx02 Xx000))=> x6) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found x6:(Xx02 Xx000)
% Found x6 as proof of (Xx01 Xx000)
% Found (fun (x6:(Xx02 Xx000))=> x6) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found x5:(Xx2 Xx01)
% Instantiate: Xx2:=(K Xx3):(fofType->Prop)
% Found x5 as proof of ((K Xx3) Xx01)
% Found x6:(Xx02 Xx000)
% Found x6 as proof of (Xx01 Xx000)
% Found (fun (x6:(Xx02 Xx000))=> x6) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x400:=(x40 x5):((K x1) Xx)
% Found (x40 x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found x6:(Xx02 Xx000)
% Found x6 as proof of (Xx01 Xx000)
% Found (fun (x6:(Xx02 Xx000))=> x6) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x400:=(x40 x5):((K x1) Xx)
% Found (x40 x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found x6:(Xx02 Xx000)
% Found x6 as proof of (Xx01 Xx000)
% Found (fun (x6:(Xx02 Xx000))=> x6) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found x6:(Xx02 Xx000)
% Found x6 as proof of (Xx01 Xx000)
% Found (fun (x6:(Xx02 Xx000))=> x6) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found x6:(Xx02 Xx000)
% Found x6 as proof of (Xx01 Xx000)
% Found (fun (x6:(Xx02 Xx000))=> x6) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) 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 x6:(Xx02 Xx000)
% Found x6 as proof of (Xx01 Xx000)
% Found (fun (x6:(Xx02 Xx000))=> x6) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) 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 x2:(Xx05 Xx000)
% Found x2 as proof of (Xx04 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx04 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx04 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx04 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx04 Xx000)
% Found ((and_rect0 (Xx04 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx04 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx04 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx04 Xx000)
% 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)) (Xx04 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx04 Xx000)
% Found x11:(Xx5 Xx04)
% Instantiate: Xx5:=(K Xx6):(fofType->Prop)
% Found x11 as proof of ((K Xx6) Xx04)
% Found x6:(Xx02 Xx000)
% Found x6 as proof of (Xx01 Xx000)
% Found (fun (x6:(Xx02 Xx000))=> x6) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x400:=(x40 x5):((K x1) Xx)
% Found (x40 x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found x6:(Xx02 Xx000)
% Found x6 as proof of (Xx01 Xx000)
% Found (fun (x6:(Xx02 Xx000))=> x6) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x400:=(x40 x5):((K x1) Xx)
% Found (x40 x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found x6:(Xx02 Xx000)
% Found x6 as proof of (Xx01 Xx000)
% Found (fun (x6:(Xx02 Xx000))=> x6) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found x6:(Xx02 Xx000)
% Found x6 as proof of (Xx01 Xx000)
% Found (fun (x6:(Xx02 Xx000))=> x6) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx02 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx02) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx05) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found ((and_rect0 ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx05) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx05) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found ((and_rect0 ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found x4:(Xx05 Xx000)
% Instantiate: Xx04:=Xx05:(fofType->Prop)
% Found (fun (x4:(Xx05 Xx000))=> x4) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx05 Xx000))=> x4) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx05 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found ((x160 (fun (Xx000:fofType) (x4:(Xx05 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx04) Xx)
% Found (((x16 Xx04) (fun (Xx000:fofType) (x4:(Xx05 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx04) Xx)
% Found ((((x1 x2) Xx04) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx04) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) Xx04) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))))) as proof of ((K Xx04) Xx)
% Found x2:(Xx05 Xx000)
% Instantiate: Xx05:=(K x3):(fofType->Prop)
% Found x2 as proof of (Xx04 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx04 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx04 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx04 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx04 Xx000)
% Found ((and_rect0 (Xx04 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx04 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx04 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx04 Xx000)
% 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)) (Xx04 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx04 Xx000)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx02) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect0 ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx02) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx02) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect0 ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx02) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx02) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect0 ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found x4:(Xx02 Xx000)
% Instantiate: Xx01:=Xx02:(fofType->Prop)
% Found (fun (x4:(Xx02 Xx000))=> x4) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found ((x130 (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx01) Xx)
% Found (((x13 Xx01) (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx01) Xx)
% Found ((((x1 x2) Xx01) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx01) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) Xx01) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))))) as proof of ((K Xx01) Xx)
% Found x5:(Xx2 Xx01)
% Instantiate: Xx2:=(K Xx3):(fofType->Prop)
% Found x5 as proof of ((K Xx3) Xx01)
% Found x5:(Xx2 Xx01)
% Instantiate: Xx2:=(K Xx3):(fofType->Prop)
% Found x5 as proof of ((K Xx3) Xx01)
% Found x2:(Xx02 Xx000)
% Instantiate: Xx02:=(K x3):(fofType->Prop)
% Found x2 as proof of (Xx01 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx01 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx01 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx01 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% Found ((and_rect0 (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% 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)) (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx01 Xx000)
% Found x2:(Xx05 Xx000)
% Found x2 as proof of (Xx04 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx04 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx04 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx04 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx04 Xx000)
% Found ((and_rect0 (Xx04 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx04 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx04 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx04 Xx000)
% 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)) (Xx04 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx04 Xx000)
% Found x11:(Xx5 Xx04)
% Instantiate: Xx5:=(K Xx6):(fofType->Prop)
% Found x11 as proof of ((K Xx6) Xx04)
% Found x2:(Xx02 Xx000)
% Found x2 as proof of (Xx01 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx01 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx01 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx01 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% Found ((and_rect0 (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% 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)) (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx01 Xx000)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx05) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found ((and_rect0 ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx05) Xx)
% Found x9:(Xx4 Xx03)
% Instantiate: Xx4:=(K Xx5):(fofType->Prop)
% Found x9 as proof of ((K Xx5) Xx03)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx02) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect0 ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found x4:(Xx02 Xx000)
% Instantiate: Xx01:=Xx02:(fofType->Prop)
% Found (fun (x4:(Xx02 Xx000))=> x4) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found ((x130 (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx01) Xx)
% Found (((x13 Xx01) (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx01) Xx)
% Found ((((x1 x2) Xx01) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx01) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) Xx01) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))))) as proof of ((K Xx01) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx02) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect0 ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found x4:(Xx02 Xx000)
% Instantiate: Xx01:=Xx02:(fofType->Prop)
% Found (fun (x4:(Xx02 Xx000))=> x4) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found ((x130 (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx01) Xx)
% Found (((x13 Xx01) (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx01) Xx)
% Found ((((x1 x2) Xx01) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx01) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) Xx01) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))))) as proof of ((K Xx01) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx02) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect0 ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx02) Xx)
% Found x2:(Xx02 Xx000)
% Instantiate: Xx02:=(K x3):(fofType->Prop)
% Found x2 as proof of (Xx01 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx01 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx01 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx01 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% Found ((and_rect0 (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% 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)) (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx01 Xx000)
% Found x2:(Xx02 Xx000)
% Instantiate: Xx02:=(K x3):(fofType->Prop)
% Found x2 as proof of (Xx01 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx01 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx01 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx01 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% Found ((and_rect0 (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% 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)) (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx01 Xx000)
% Found x2:(Xx05 Xx000)
% Instantiate: Xx05:=(K x3):(fofType->Prop)
% Found x2 as proof of (Xx04 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx04 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx04 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx04 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx04 Xx000)
% Found ((and_rect0 (Xx04 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx04 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx04 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx04 Xx000)
% 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)) (Xx04 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx04 Xx000)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx05) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found ((and_rect0 ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found x4:(Xx05 Xx000)
% Instantiate: Xx04:=Xx05:(fofType->Prop)
% Found (fun (x4:(Xx05 Xx000))=> x4) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx05 Xx000))=> x4) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx05 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found ((x160 (fun (Xx000:fofType) (x4:(Xx05 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx04) Xx)
% Found (((x16 Xx04) (fun (Xx000:fofType) (x4:(Xx05 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx04) Xx)
% Found ((((x1 x2) Xx04) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx04) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) Xx04) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))))) as proof of ((K Xx04) Xx)
% Found x2:(Xx02 Xx000)
% Found x2 as proof of (Xx01 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx01 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx01 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx01 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% Found ((and_rect0 (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% 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)) (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx01 Xx000)
% Found x2:(Xx02 Xx000)
% Found x2 as proof of (Xx01 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx01 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx01 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx01 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% Found ((and_rect0 (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% 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)) (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx01 Xx000)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx02) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect0 ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx02) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx02) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect0 ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx02) Xx)
% Found x2:(Xx05 Xx000)
% Found x2 as proof of (Xx04 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx04 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx04 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx04 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx04 Xx000)
% Found ((and_rect0 (Xx04 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx04 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx04 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx04 Xx000)
% 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)) (Xx04 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx04 Xx000)
% Found x9:(Xx4 Xx03)
% Instantiate: Xx4:=(K Xx5):(fofType->Prop)
% Found x9 as proof of ((K Xx5) Xx03)
% Found x2:(Xx02 Xx000)
% Instantiate: Xx02:=(K x3):(fofType->Prop)
% Found x2 as proof of (Xx01 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx01 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx01 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx01 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% Found ((and_rect0 (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% 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)) (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx01 Xx000)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx02) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect0 ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found x4:(Xx02 Xx000)
% Instantiate: Xx01:=Xx02:(fofType->Prop)
% Found (fun (x4:(Xx02 Xx000))=> x4) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found ((x130 (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx01) Xx)
% Found (((x13 Xx01) (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx01) Xx)
% Found ((((x1 x2) Xx01) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx01) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) Xx01) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))))) as proof of ((K Xx01) Xx)
% Found x2:(Xx05 Xx000)
% Instantiate: Xx05:=(K x3):(fofType->Prop)
% Found x2 as proof of (Xx04 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx04 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx04 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx04 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx04 Xx000)
% Found ((and_rect0 (Xx04 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx04 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx04 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx04 Xx000)
% 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)) (Xx04 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx04 Xx000)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx05) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found ((and_rect0 ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx05) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx05) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found ((and_rect0 ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found x4:(Xx05 Xx000)
% Instantiate: Xx04:=Xx05:(fofType->Prop)
% Found (fun (x4:(Xx05 Xx000))=> x4) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx05 Xx000))=> x4) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx05 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found ((x160 (fun (Xx000:fofType) (x4:(Xx05 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx04) Xx)
% Found (((x16 Xx04) (fun (Xx000:fofType) (x4:(Xx05 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx04) Xx)
% Found ((((x1 x2) Xx04) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx04) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) Xx04) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))))) as proof of ((K Xx04) Xx)
% Found x2:(Xx02 Xx000)
% Found x2 as proof of (Xx01 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx01 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx01 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx01 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% Found ((and_rect0 (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% 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)) (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx01 Xx000)
% Found x5:(Xx2 Xx01)
% Instantiate: Xx2:=(K Xx3):(fofType->Prop)
% Found x5 as proof of ((K Xx3) Xx01)
% Found x5:(Xx2 Xx01)
% Instantiate: Xx2:=(K Xx3):(fofType->Prop)
% Found x5 as proof of ((K Xx3) Xx01)
% Found x2:(Xx05 Xx000)
% Found x2 as proof of (Xx04 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx04 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx04 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx04 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx04 Xx000)
% Found ((and_rect0 (Xx04 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx04 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx04 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx04 Xx000)
% 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)) (Xx04 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx04 Xx000)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx02) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect0 ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found x4:(Xx02 Xx000)
% Instantiate: Xx01:=Xx02:(fofType->Prop)
% Found (fun (x4:(Xx02 Xx000))=> x4) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found ((x130 (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx01) Xx)
% Found (((x13 Xx01) (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx01) Xx)
% Found ((((x1 x2) Xx01) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx01) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) Xx01) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))))) as proof of ((K Xx01) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx02) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect0 ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found x4:(Xx02 Xx000)
% Instantiate: Xx01:=Xx02:(fofType->Prop)
% Found (fun (x4:(Xx02 Xx000))=> x4) as proof of (Xx01 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4) as proof of ((Xx02 Xx000)->(Xx01 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx02 Xx00)->(Xx01 Xx00)))
% Found ((x130 (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx01) Xx)
% Found (((x13 Xx01) (fun (Xx000:fofType) (x4:(Xx02 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx01) Xx)
% Found ((((x1 x2) Xx01) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx01) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) Xx01) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))))) as proof of ((K Xx01) Xx)
% Found x2:(Xx02 Xx000)
% Instantiate: Xx02:=(K x3):(fofType->Prop)
% Found x2 as proof of (Xx01 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx01 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx01 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx01 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% Found ((and_rect0 (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% 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)) (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx01 Xx000)
% Found x2:(Xx02 Xx000)
% Instantiate: Xx02:=(K x3):(fofType->Prop)
% Found x2 as proof of (Xx01 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx01 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx01 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx01 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% Found ((and_rect0 (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% 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)) (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx01 Xx000)
% Found x11:(Xx5 Xx04)
% Instantiate: Xx5:=(K Xx6):(fofType->Prop)
% Found x11 as proof of ((K Xx6) Xx04)
% Found x11:(Xx5 Xx04)
% Instantiate: Xx5:=(K Xx6):(fofType->Prop)
% Found x11 as proof of ((K Xx6) Xx04)
% Found x11:(Xx5 Xx04)
% Instantiate: Xx5:=(K Xx6):(fofType->Prop)
% Found x11 as proof of ((K Xx6) Xx04)
% Found x11:(Xx5 Xx04)
% Instantiate: Xx5:=(K Xx6):(fofType->Prop)
% Found x11 as proof of ((K Xx6) Xx04)
% Found x11:(Xx5 Xx04)
% Instantiate: Xx5:=(K Xx6):(fofType->Prop)
% Found x11 as proof of ((K Xx6) Xx04)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx02) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect0 ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx02) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx05) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found ((and_rect0 ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx05) Xx)
% Found x2:(Xx02 Xx000)
% Found x2 as proof of (Xx01 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx01 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx01 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx01 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% Found ((and_rect0 (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% 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)) (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx01 Xx000)
% Found x2:(Xx02 Xx000)
% Found x2 as proof of (Xx01 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx01 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx01 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx01 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% Found ((and_rect0 (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% 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)) (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx01 Xx000)
% Found x5:(Xx2 Xx01)
% Instantiate: Xx2:=(K Xx3):(fofType->Prop)
% Found x5 as proof of ((K Xx3) Xx01)
% Found x5:(Xx2 Xx01)
% Instantiate: Xx2:=(K Xx3):(fofType->Prop)
% Found x5 as proof of ((K Xx3) Xx01)
% Found x5:(Xx2 Xx01)
% Instantiate: Xx2:=(K Xx3):(fofType->Prop)
% Found x5 as proof of ((K Xx3) Xx01)
% Found x5:(Xx2 Xx01)
% Instantiate: Xx2:=(K Xx3):(fofType->Prop)
% Found x5 as proof of ((K Xx3) Xx01)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx02) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect0 ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx02) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx02) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx02) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found ((and_rect0 ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx02) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx02) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx02) Xx)
% Found x2:(Xx03 Xx000)
% Found x2 as proof of (Xx02 Xx000)
% Found (fun (x2:(Xx03 Xx000))=> x2) as proof of (Xx02 Xx000)
% Found (fun (Xx000:fofType) (x2:(Xx03 Xx000))=> x2) as proof of ((Xx03 Xx000)->(Xx02 Xx000))
% Found (fun (Xx000:fofType) (x2:(Xx03 Xx000))=> x2) as proof of (forall (Xx00:fofType), ((Xx03 Xx00)->(Xx02 Xx00)))
% Found x2:(Xx05 Xx000)
% Instantiate: Xx05:=(K x3):(fofType->Prop)
% Found x2 as proof of (Xx04 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx04 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx04 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx04 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx04 Xx000)
% Found ((and_rect0 (Xx04 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx04 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx04 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx04 Xx000)
% 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)) (Xx04 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx04 Xx000)
% Found x11:(Xx5 Xx04)
% Instantiate: Xx5:=(K Xx6):(fofType->Prop)
% Found x11 as proof of ((K Xx6) Xx04)
% Found x11:(Xx5 Xx04)
% Instantiate: Xx5:=(K Xx6):(fofType->Prop)
% Found x11 as proof of ((K Xx6) Xx04)
% Found x11:(Xx5 Xx04)
% Instantiate: Xx5:=(K Xx6):(fofType->Prop)
% Found x11 as proof of ((K Xx6) Xx04)
% Found x11:(Xx5 Xx04)
% Instantiate: Xx5:=(K Xx6):(fofType->Prop)
% Found x11 as proof of ((K Xx6) Xx04)
% Found x11:(Xx5 Xx04)
% Instantiate: Xx5:=(K Xx6):(fofType->Prop)
% Found x11 as proof of ((K Xx6) Xx04)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx05) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found ((and_rect0 ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found x4:(Xx05 Xx000)
% Instantiate: Xx04:=Xx05:(fofType->Prop)
% Found (fun (x4:(Xx05 Xx000))=> x4) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx05 Xx000))=> x4) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx05 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found ((x160 (fun (Xx000:fofType) (x4:(Xx05 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx04) Xx)
% Found (((x16 Xx04) (fun (Xx000:fofType) (x4:(Xx05 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx04) Xx)
% Found ((((x1 x2) Xx04) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx04) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) Xx04) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))))) as proof of ((K Xx04) Xx)
% Found x2:(Xx02 Xx000)
% Instantiate: Xx02:=(K x3):(fofType->Prop)
% Found x2 as proof of (Xx01 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx01 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx01 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx01 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% Found ((and_rect0 (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% 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)) (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx01 Xx000)
% Found x2:(Xx05 Xx000)
% Found x2 as proof of (Xx04 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx04 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx04 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx04 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx04 Xx000)
% Found ((and_rect0 (Xx04 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx04 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx04 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx04 Xx000)
% 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)) (Xx04 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx04 Xx000)
% Found x2:(Xx03 Xx000)
% Found x2 as proof of (Xx02 Xx000)
% Found (fun (x2:(Xx03 Xx000))=> x2) as proof of (Xx02 Xx000)
% Found (fun (Xx000:fofType) (x2:(Xx03 Xx000))=> x2) as proof of ((Xx03 Xx000)->(Xx02 Xx000))
% Found (fun (Xx000:fofType) (x2:(Xx03 Xx000))=> x2) as proof of (forall (Xx00:fofType), ((Xx03 Xx00)->(Xx02 Xx00)))
% Found x2:(Xx03 Xx000)
% Found x2 as proof of (Xx02 Xx000)
% Found (fun (x2:(Xx03 Xx000))=> x2) as proof of (Xx02 Xx000)
% Found (fun (Xx000:fofType) (x2:(Xx03 Xx000))=> x2) as proof of ((Xx03 Xx000)->(Xx02 Xx000))
% Found (fun (Xx000:fofType) (x2:(Xx03 Xx000))=> x2) as proof of (forall (Xx00:fofType), ((Xx03 Xx00)->(Xx02 Xx00)))
% Found x2:(Xx06 Xx000)
% Found x2 as proof of (Xx05 Xx000)
% Found (fun (x2:(Xx06 Xx000))=> x2) as proof of (Xx05 Xx000)
% Found (fun (Xx000:fofType) (x2:(Xx06 Xx000))=> x2) as proof of ((Xx06 Xx000)->(Xx05 Xx000))
% Found (fun (Xx000:fofType) (x2:(Xx06 Xx000))=> x2) as proof of (forall (Xx00:fofType), ((Xx06 Xx00)->(Xx05 Xx00)))
% Found x2:(Xx05 Xx000)
% Instantiate: Xx05:=(K x3):(fofType->Prop)
% Found x2 as proof of (Xx04 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx04 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx04 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx04 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx04 Xx000)
% Found ((and_rect0 (Xx04 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx04 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx04 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx04 Xx000)
% 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)) (Xx04 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx04 Xx000)
% Found x2:(Xx02 Xx000)
% Found x2 as proof of (Xx01 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx01 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx01 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx01 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% Found ((and_rect0 (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% 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)) (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx01 Xx000)
% Found x4:(Xx03 Xx000)
% Found x4 as proof of (Xx02 Xx000)
% Found (fun (x4:(Xx03 Xx000))=> x4) as proof of (Xx02 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4) as proof of ((Xx03 Xx000)->(Xx02 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx03 Xx00)->(Xx02 Xx00)))
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx05) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found ((and_rect0 ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx05) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx05) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found ((and_rect0 ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found x4:(Xx05 Xx000)
% Instantiate: Xx04:=Xx05:(fofType->Prop)
% Found (fun (x4:(Xx05 Xx000))=> x4) as proof of (Xx04 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx05 Xx000))=> x4) as proof of ((Xx05 Xx000)->(Xx04 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx05 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx05 Xx00)->(Xx04 Xx00)))
% Found ((x160 (fun (Xx000:fofType) (x4:(Xx05 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx04) Xx)
% Found (((x16 Xx04) (fun (Xx000:fofType) (x4:(Xx05 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx04) Xx)
% Found ((((x1 x2) Xx04) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx04) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) Xx04) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))))) as proof of ((K Xx04) Xx)
% Found x4:(Xx03 Xx000)
% Found x4 as proof of (Xx02 Xx000)
% Found (fun (x4:(Xx03 Xx000))=> x4) as proof of (Xx02 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4) as proof of ((Xx03 Xx000)->(Xx02 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx03 Xx00)->(Xx02 Xx00)))
% Found x4:(Xx03 Xx000)
% Found x4 as proof of (Xx02 Xx000)
% Found (fun (x4:(Xx03 Xx000))=> x4) as proof of (Xx02 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4) as proof of ((Xx03 Xx000)->(Xx02 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx03 Xx00)->(Xx02 Xx00)))
% Found x2:(Xx02 Xx000)
% Instantiate: Xx02:=(K x3):(fofType->Prop)
% Found x2 as proof of (Xx01 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx01 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx01 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx01 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% Found ((and_rect0 (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% 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)) (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx01 Xx000)
% Found x2:(Xx02 Xx000)
% Instantiate: Xx02:=(K x3):(fofType->Prop)
% Found x2 as proof of (Xx01 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx01 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx01 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx01 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% Found ((and_rect0 (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% 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)) (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx01 Xx000)
% Found x4:(Xx03 Xx000)
% Found x4 as proof of (Xx02 Xx000)
% Found (fun (x4:(Xx03 Xx000))=> x4) as proof of (Xx02 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4) as proof of ((Xx03 Xx000)->(Xx02 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx03 Xx00)->(Xx02 Xx00)))
% Found x4:(Xx03 Xx000)
% Found x4 as proof of (Xx02 Xx000)
% Found (fun (x4:(Xx03 Xx000))=> x4) as proof of (Xx02 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4) as proof of ((Xx03 Xx000)->(Xx02 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx03 Xx00)->(Xx02 Xx00)))
% Found x2:(Xx05 Xx000)
% Found x2 as proof of (Xx04 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx04 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx04 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx04 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx04 Xx000)
% Found ((and_rect0 (Xx04 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx04 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx04 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx04 Xx000)
% 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)) (Xx04 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx04 Xx000)
% Found x2:(Xx06 Xx000)
% Found x2 as proof of (Xx05 Xx000)
% Found (fun (x2:(Xx06 Xx000))=> x2) as proof of (Xx05 Xx000)
% Found (fun (Xx000:fofType) (x2:(Xx06 Xx000))=> x2) as proof of ((Xx06 Xx000)->(Xx05 Xx000))
% Found (fun (Xx000:fofType) (x2:(Xx06 Xx000))=> x2) as proof of (forall (Xx00:fofType), ((Xx06 Xx00)->(Xx05 Xx00)))
% Found x2:(Xx02 Xx000)
% Found x2 as proof of (Xx01 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx01 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx01 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx01 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% Found ((and_rect0 (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% 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)) (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx01 Xx000)
% Found x2:(Xx02 Xx000)
% Found x2 as proof of (Xx01 Xx000)
% Found (fun (x6:(x3 Xx))=> x2) as proof of (Xx01 Xx000)
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((x3 Xx)->(Xx01 Xx000))
% Found (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2) as proof of ((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->(Xx01 Xx000)))
% Found (and_rect00 (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% Found ((and_rect0 (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% Found (((fun (P:Type) (x5:((forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))->((x3 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x3 Xx)) P) x5) x4)) (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2)) as proof of (Xx01 Xx000)
% 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)) (Xx01 Xx000)) (fun (x5:(forall (Xx0:fofType), ((x3 Xx0)->((K x3) Xx0)))) (x6:(x3 Xx))=> x2))) as proof of (Xx01 Xx000)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx)) as proof of ((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->((K Xx03) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found ((and_rect0 ((K Xx03) Xx)) (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx00:fofType), ((x2 Xx00)->((K x2) Xx00))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx03) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found ((and_rect0 ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx03) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found ((and_rect0 ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx03) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found ((and_rect0 ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found x4:(Xx03 Xx000)
% Found x4 as proof of (Xx02 Xx000)
% Found (fun (x4:(Xx03 Xx000))=> x4) as proof of (Xx02 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4) as proof of ((Xx03 Xx000)->(Xx02 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx03 Xx00)->(Xx02 Xx00)))
% Found x4:(Xx03 Xx000)
% Found x4 as proof of (Xx02 Xx000)
% Found (fun (x4:(Xx03 Xx000))=> x4) as proof of (Xx02 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4) as proof of ((Xx03 Xx000)->(Xx02 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx03 Xx00)->(Xx02 Xx00)))
% Found x4:(Xx03 Xx000)
% Found x4 as proof of (Xx02 Xx000)
% Found (fun (x4:(Xx03 Xx000))=> x4) as proof of (Xx02 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4) as proof of ((Xx03 Xx000)->(Xx02 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx03 Xx00)->(Xx02 Xx00)))
% Found x4:(Xx03 Xx000)
% Found x4 as proof of (Xx02 Xx000)
% Found (fun (x4:(Xx03 Xx000))=> x4) as proof of (Xx02 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4) as proof of ((Xx03 Xx000)->(Xx02 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx03 Xx00)->(Xx02 Xx00)))
% Found x4:(Xx03 Xx000)
% Found x4 as proof of (Xx02 Xx000)
% Found (fun (x4:(Xx03 Xx000))=> x4) as proof of (Xx02 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4) as proof of ((Xx03 Xx000)->(Xx02 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx03 Xx00)->(Xx02 Xx00)))
% Found x4:(Xx03 Xx000)
% Found x4 as proof of (Xx02 Xx000)
% Found (fun (x4:(Xx03 Xx000))=> x4) as proof of (Xx02 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4) as proof of ((Xx03 Xx000)->(Xx02 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx03 Xx00)->(Xx02 Xx00)))
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx05) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx05) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found ((and_rect0 ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx05) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx05) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx05) Xx)
% Found x4:(Xx03 Xx000)
% Found x4 as proof of (Xx02 Xx000)
% Found (fun (x4:(Xx03 Xx000))=> x4) as proof of (Xx02 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4) as proof of ((Xx03 Xx000)->(Xx02 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx03 Xx00)->(Xx02 Xx00)))
% Found x4:(Xx03 Xx000)
% Found x4 as proof of (Xx02 Xx000)
% Found (fun (x4:(Xx03 Xx000))=> x4) as proof of (Xx02 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4) as proof of ((Xx03 Xx000)->(Xx02 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx03 Xx00)->(Xx02 Xx00)))
% Found x4:(Xx06 Xx000)
% Found x4 as proof of (Xx05 Xx000)
% Found (fun (x4:(Xx06 Xx000))=> x4) as proof of (Xx05 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx06 Xx000))=> x4) as proof of ((Xx06 Xx000)->(Xx05 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx06 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx06 Xx00)->(Xx05 Xx00)))
% Found x40:=(x4 Xx):((x1 Xx)->((K x1) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((K Xx03) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((K Xx03) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx)) as proof of ((x1 Xx)->((K Xx03) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->((K Xx03) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found ((and_rect0 ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x1 Xx0)->((K x1) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx03) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found ((and_rect0 ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx03) Xx)
% Found x5:(Xx2 Xx01)
% Instantiate: Xx2:=(K Xx3):(fofType->Prop)
% Found x5 as proof of ((K Xx3) Xx01)
% Found x4:(Xx03 Xx000)
% Found x4 as proof of (Xx02 Xx000)
% Found (fun (x4:(Xx03 Xx000))=> x4) as proof of (Xx02 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4) as proof of ((Xx03 Xx000)->(Xx02 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx03 Xx00)->(Xx02 Xx00)))
% Found x4:(Xx03 Xx000)
% Found x4 as proof of (Xx02 Xx000)
% Found (fun (x4:(Xx03 Xx000))=> x4) as proof of (Xx02 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4) as proof of ((Xx03 Xx000)->(Xx02 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx03 Xx00)->(Xx02 Xx00)))
% Found x4:(Xx06 Xx000)
% Found x4 as proof of (Xx05 Xx000)
% Found (fun (x4:(Xx06 Xx000))=> x4) as proof of (Xx05 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx06 Xx000))=> x4) as proof of ((Xx06 Xx000)->(Xx05 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx06 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx06 Xx00)->(Xx05 Xx00)))
% Found x4:(Xx06 Xx000)
% Found x4 as proof of (Xx05 Xx000)
% Found (fun (x4:(Xx06 Xx000))=> x4) as proof of (Xx05 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx06 Xx000))=> x4) as proof of ((Xx06 Xx000)->(Xx05 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx06 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx06 Xx00)->(Xx05 Xx00)))
% Found x6:(Xx03 Xx000)
% Found x6 as proof of (Xx02 Xx000)
% Found (fun (x6:(Xx03 Xx000))=> x6) as proof of (Xx02 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx03 Xx000))=> x6) as proof of ((Xx03 Xx000)->(Xx02 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx03 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx03 Xx00)->(Xx02 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found x4:(Xx06 Xx000)
% Found x4 as proof of (Xx05 Xx000)
% Found (fun (x4:(Xx06 Xx000))=> x4) as proof of (Xx05 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx06 Xx000))=> x4) as proof of ((Xx06 Xx000)->(Xx05 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx06 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx06 Xx00)->(Xx05 Xx00)))
% Found x6:(Xx03 Xx000)
% Found x6 as proof of (Xx02 Xx000)
% Found (fun (x6:(Xx03 Xx000))=> x6) as proof of (Xx02 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx03 Xx000))=> x6) as proof of ((Xx03 Xx000)->(Xx02 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx03 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx03 Xx00)->(Xx02 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found x6:(Xx03 Xx000)
% Found x6 as proof of (Xx02 Xx000)
% Found (fun (x6:(Xx03 Xx000))=> x6) as proof of (Xx02 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx03 Xx000))=> x6) as proof of ((Xx03 Xx000)->(Xx02 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx03 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx03 Xx00)->(Xx02 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found x11:(Xx5 Xx04)
% Instantiate: Xx5:=(K Xx6):(fofType->Prop)
% Found x11 as proof of ((K Xx6) Xx04)
% Found x11:(Xx5 Xx04)
% Instantiate: Xx5:=(K Xx6):(fofType->Prop)
% Found x11 as proof of ((K Xx6) Xx04)
% Found x11:(Xx5 Xx04)
% Instantiate: Xx5:=(K Xx6):(fofType->Prop)
% Found x11 as proof of ((K Xx6) Xx04)
% Found x11:(Xx5 Xx04)
% Instantiate: Xx5:=(K Xx6):(fofType->Prop)
% Found x11 as proof of ((K Xx6) Xx04)
% Found x11:(Xx5 Xx04)
% Instantiate: Xx5:=(K Xx6):(fofType->Prop)
% Found x11 as proof of ((K Xx6) Xx04)
% Found x11:(Xx5 Xx04)
% Instantiate: Xx5:=(K Xx6):(fofType->Prop)
% Found x11 as proof of ((K Xx6) Xx04)
% Found x11:(Xx5 Xx04)
% Instantiate: Xx5:=(K Xx6):(fofType->Prop)
% Found x11 as proof of ((K Xx6) Xx04)
% Found x11:(Xx5 Xx04)
% Instantiate: Xx5:=(K Xx6):(fofType->Prop)
% Found x11 as proof of ((K Xx6) Xx04)
% Found x11:(Xx5 Xx04)
% Instantiate: Xx5:=(K Xx6):(fofType->Prop)
% Found x11 as proof of ((K Xx6) Xx04)
% Found x11:(Xx5 Xx04)
% Instantiate: Xx5:=(K Xx6):(fofType->Prop)
% Found x11 as proof of ((K Xx6) Xx04)
% Found x6:(Xx03 Xx000)
% Found x6 as proof of (Xx02 Xx000)
% Found (fun (x6:(Xx03 Xx000))=> x6) as proof of (Xx02 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx03 Xx000))=> x6) as proof of ((Xx03 Xx000)->(Xx02 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx03 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx03 Xx00)->(Xx02 Xx00)))
% Found x400:=(x40 x5):((K x1) Xx)
% Found (x40 x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found x6:(Xx03 Xx000)
% Found x6 as proof of (Xx02 Xx000)
% Found (fun (x6:(Xx03 Xx000))=> x6) as proof of (Xx02 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx03 Xx000))=> x6) as proof of ((Xx03 Xx000)->(Xx02 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx03 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx03 Xx00)->(Xx02 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found x4:(Xx06 Xx000)
% Found x4 as proof of (Xx05 Xx000)
% Found (fun (x4:(Xx06 Xx000))=> x4) as proof of (Xx05 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx06 Xx000))=> x4) as proof of ((Xx06 Xx000)->(Xx05 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx06 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx06 Xx00)->(Xx05 Xx00)))
% Found x40:=(x4 Xx):((x2 Xx)->((K x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((K Xx03) Xx))
% Found (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->((K Xx03) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found ((and_rect0 ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))) as proof of ((K Xx03) Xx)
% Found x4:(Xx03 Xx000)
% Instantiate: Xx02:=Xx03:(fofType->Prop)
% Found (fun (x4:(Xx03 Xx000))=> x4) as proof of (Xx02 Xx000)
% Found (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4) as proof of ((Xx03 Xx000)->(Xx02 Xx000))
% Found (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4) as proof of (forall (Xx00:fofType), ((Xx03 Xx00)->(Xx02 Xx00)))
% Found ((x140 (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx02) Xx)
% Found (((x14 Xx02) (fun (Xx000:fofType) (x4:(Xx03 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K Xx03) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx02) Xx)
% Found ((((x1 x2) Xx02) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx)))) as proof of ((K Xx02) Xx)
% Found (fun (x3:((and (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)))=> ((((x1 x2) Xx02) (fun (Xx000:fofType) (x4:(x2 Xx000))=> x4)) (((fun (P:Type) (x4:((forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((K x2) Xx)) (fun (x4:(forall (Xx0:fofType), ((x2 Xx0)->((K x2) Xx0))))=> (x4 Xx))))) as proof of ((K Xx02) Xx)
% Found x6:(Xx03 Xx000)
% Found x6 as proof of (Xx02 Xx000)
% Found (fun (x6:(Xx03 Xx000))=> x6) as proof of (Xx02 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx03 Xx000))=> x6) as proof of ((Xx03 Xx000)->(Xx02 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx03 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx03 Xx00)->(Xx02 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found x6:(Xx03 Xx000)
% Found x6 as proof of (Xx02 Xx000)
% Found (fun (x6:(Xx03 Xx000))=> x6) as proof of (Xx02 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx03 Xx000))=> x6) as proof of ((Xx03 Xx000)->(Xx02 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx03 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx03 Xx00)->(Xx02 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found x6:(Xx03 Xx000)
% Found x6 as proof of (Xx02 Xx000)
% Found (fun (x6:(Xx03 Xx000))=> x6) as proof of (Xx02 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx03 Xx000))=> x6) as proof of ((Xx03 Xx000)->(Xx02 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx03 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx03 Xx00)->(Xx02 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found x6:(Xx03 Xx000)
% Found x6 as proof of (Xx02 Xx000)
% Found (fun (x6:(Xx03 Xx000))=> x6) as proof of (Xx02 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx03 Xx000))=> x6) as proof of ((Xx03 Xx000)->(Xx02 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx03 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx03 Xx00)->(Xx02 Xx00)))
% Found x400:=(x40 x5):((K x1) Xx)
% Found (x40 x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found x6:(Xx03 Xx000)
% Found x6 as proof of (Xx02 Xx000)
% Found (fun (x6:(Xx03 Xx000))=> x6) as proof of (Xx02 Xx000)
% Found (fun (Xx000:fofType) (x6:(Xx03 Xx000))=> x6) as proof of ((Xx03 Xx000)->(Xx02 Xx000))
% Found (fun (Xx000:fofType) (x6:(Xx03 Xx000))=> x6) as proof of (forall (Xx00:fofType), ((Xx03 Xx00)->(Xx02 Xx00)))
% Found x400:=(x40 x5):((K x2) Xx)
% Found (x40 x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found ((x4 Xx) x5) as proof of ((K Xx03) Xx)
% Found x4:(Xx06 Xx000)
% Found x4 as proof of (Xx05 Xx000)
% Found (fun (x4:(Xx06 Xx000))=> x4) as proof of (Xx05 Xx000)
% Found (fun (Xx000:fofType
% EOF
%------------------------------------------------------------------------------