%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SEV251^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n183.star.cs.uiowa.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory   : 32286.75MB
% OS       : Linux 2.6.32-431.20.3.el6.x86_64
% CPULimit : 300s
% DateTime : Thu Jul 17 13:33:57 EDT 2014

% Result   : Timeout 300.11s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SEV251^5 : TPTP v6.1.0. Released v4.0.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n183.star.cs.uiowa.edu
% % Model    : x86_64 x86_64
% % CPU      : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% % Memory   : 32286.75MB
% % OS       : Linux 2.6.32-431.20.3.el6.x86_64
% % CPULimit : 300
% % DateTime : Thu Jul 17 08:37:36 CDT 2014
% % CPUTime  : 300.11 
% Python 2.7.5
% Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% FOF formula (<kernel.Constant object at 0x2a4cc68>, <kernel.DependentProduct object at 0x27f5638>) of role type named cC
% Using role type
% Declaring cC:((fofType->Prop)->Prop)
% FOF formula (<kernel.Constant object at 0x2a4c908>, <kernel.DependentProduct object at 0x27f3bd8>) of role type named cL
% Using role type
% Declaring cL:((fofType->Prop)->Prop)
% FOF formula (((and ((and (forall (X:(fofType->Prop)) (Y:(fofType->Prop)), (((and (cL X)) (cL Y))->((or (forall (Xx:fofType), ((X Xx)->(Y Xx)))) (forall (Xx:fofType), ((Y Xx)->(X Xx))))))) (forall (Xx:(fofType->Prop)), ((cC Xx)->(cL Xx))))) (forall (Xw:(((fofType->Prop)->Prop)->Prop)), (((and (Xw (fun (Xx:(fofType->Prop))=> False))) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xw Xr)->(Xw (fun (Xt:(fofType->Prop))=> ((or (Xr Xt)) (((eq (fofType->Prop)) Xt) Xx)))))))->(Xw cC))))->((ex (fofType->Prop)) (fun (U:(fofType->Prop))=> ((and (cC U)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((U Xx)->(V Xx))))))))) of role conjecture named cTHM629_pme
% Conjecture to prove = (((and ((and (forall (X:(fofType->Prop)) (Y:(fofType->Prop)), (((and (cL X)) (cL Y))->((or (forall (Xx:fofType), ((X Xx)->(Y Xx)))) (forall (Xx:fofType), ((Y Xx)->(X Xx))))))) (forall (Xx:(fofType->Prop)), ((cC Xx)->(cL Xx))))) (forall (Xw:(((fofType->Prop)->Prop)->Prop)), (((and (Xw (fun (Xx:(fofType->Prop))=> False))) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xw Xr)->(Xw (fun (Xt:(fofType->Prop))=> ((or (Xr Xt)) (((eq (fofType->Prop)) Xt) Xx)))))))->(Xw cC))))->((ex (fofType->Prop)) (fun (U:(fofType->Prop))=> ((and (cC U)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((U Xx)->(V Xx))))))))):Prop
% Parameter fofType_DUMMY:fofType.
% We need to prove ['(((and ((and (forall (X:(fofType->Prop)) (Y:(fofType->Prop)), (((and (cL X)) (cL Y))->((or (forall (Xx:fofType), ((X Xx)->(Y Xx)))) (forall (Xx:fofType), ((Y Xx)->(X Xx))))))) (forall (Xx:(fofType->Prop)), ((cC Xx)->(cL Xx))))) (forall (Xw:(((fofType->Prop)->Prop)->Prop)), (((and (Xw (fun (Xx:(fofType->Prop))=> False))) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xw Xr)->(Xw (fun (Xt:(fofType->Prop))=> ((or (Xr Xt)) (((eq (fofType->Prop)) Xt) Xx)))))))->(Xw cC))))->((ex (fofType->Prop)) (fun (U:(fofType->Prop))=> ((and (cC U)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((U Xx)->(V Xx)))))))))']
% Parameter fofType:Type.
% Parameter cC:((fofType->Prop)->Prop).
% Parameter cL:((fofType->Prop)->Prop).
% Trying to prove (((and ((and (forall (X:(fofType->Prop)) (Y:(fofType->Prop)), (((and (cL X)) (cL Y))->((or (forall (Xx:fofType), ((X Xx)->(Y Xx)))) (forall (Xx:fofType), ((Y Xx)->(X Xx))))))) (forall (Xx:(fofType->Prop)), ((cC Xx)->(cL Xx))))) (forall (Xw:(((fofType->Prop)->Prop)->Prop)), (((and (Xw (fun (Xx:(fofType->Prop))=> False))) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xw Xr)->(Xw (fun (Xt:(fofType->Prop))=> ((or (Xr Xt)) (((eq (fofType->Prop)) Xt) Xx)))))))->(Xw cC))))->((ex (fofType->Prop)) (fun (U:(fofType->Prop))=> ((and (cC U)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((U Xx)->(V Xx)))))))))
% Found eq_ref000:=(eq_ref00 x0):((x0 Xx)->(x0 Xx))
% Found (eq_ref00 x0) as proof of ((x0 Xx)->(V Xx))
% Found ((eq_ref0 Xx) x0) as proof of ((x0 Xx)->(V Xx))
% Found (((eq_ref fofType) Xx) x0) as proof of ((x0 Xx)->(V Xx))
% Found (((eq_ref fofType) Xx) x0) as proof of ((x0 Xx)->(V Xx))
% Found (fun (Xx:fofType)=> (((eq_ref fofType) Xx) x0)) as proof of ((x0 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType)=> (((eq_ref fofType) Xx) x0)) as proof of (forall (Xx:fofType), ((x0 Xx)->(V Xx)))
% Found x000:(x0 Xx)
% Instantiate: x0:=V:(fofType->Prop)
% Found x000 as proof of (V Xx)
% Found (fun (x000:(x0 Xx))=> x000) as proof of (V Xx)
% Found (fun (Xx:fofType) (x000:(x0 Xx))=> x000) as proof of ((x0 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType) (x000:(x0 Xx))=> x000) as proof of (forall (Xx:fofType), ((x0 Xx)->(V Xx)))
% Found x000:(x0 Xx)
% Instantiate: x0:=V:(fofType->Prop)
% Found x000 as proof of (V Xx)
% Found (fun (x000:(x0 Xx))=> x000) as proof of (V Xx)
% Found (fun (Xx:fofType) (x000:(x0 Xx))=> x000) as proof of ((x0 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType) (x000:(x0 Xx))=> x000) as proof of (forall (Xx:fofType), ((x0 Xx)->(V Xx)))
% Found x000:(x0 Xx)
% Instantiate: x0:=V:(fofType->Prop)
% Found x000 as proof of (V Xx)
% Found (fun (x000:(x0 Xx))=> x000) as proof of (V Xx)
% Found (fun (Xx:fofType) (x000:(x0 Xx))=> x000) as proof of ((x0 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType) (x000:(x0 Xx))=> x000) as proof of (forall (Xx:fofType), ((x0 Xx)->(V Xx)))
% Found eq_ref000:=(eq_ref00 x2):((x2 Xx)->(x2 Xx))
% Found (eq_ref00 x2) as proof of ((x2 Xx)->(V Xx))
% Found ((eq_ref0 Xx) x2) as proof of ((x2 Xx)->(V Xx))
% Found (((eq_ref fofType) Xx) x2) as proof of ((x2 Xx)->(V Xx))
% Found (((eq_ref fofType) Xx) x2) as proof of ((x2 Xx)->(V Xx))
% Found (fun (Xx:fofType)=> (((eq_ref fofType) Xx) x2)) as proof of ((x2 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType)=> (((eq_ref fofType) Xx) x2)) as proof of (forall (Xx:fofType), ((x2 Xx)->(V Xx)))
% Found x00000:=(x0000 x00):(V Xx)
% Found (x0000 x00) as proof of (V Xx)
% Found ((x000 V) x00) as proof of (V Xx)
% Found ((x000 V) x00) as proof of (V Xx)
% Found (fun (x000:(x0 Xx))=> ((x000 V) x00)) as proof of (V Xx)
% Found (fun (Xx:fofType) (x000:(x0 Xx))=> ((x000 V) x00)) as proof of ((x0 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType) (x000:(x0 Xx))=> ((x000 V) x00)) as proof of (forall (Xx:fofType), ((x0 Xx)->(V Xx)))
% Found (fun (V:(fofType->Prop)) (x00:(cC V)) (Xx:fofType) (x000:(x0 Xx))=> ((x000 V) x00)) as proof of ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))
% Found (fun (V:(fofType->Prop)) (x00:(cC V)) (Xx:fofType) (x000:(x0 Xx))=> ((x000 V) x00)) as proof of (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))
% Found eq_ref000:=(eq_ref00 x0):((x0 Xx)->(x0 Xx))
% Found (eq_ref00 x0) as proof of ((x0 Xx)->(V Xx))
% Found ((eq_ref0 Xx) x0) as proof of ((x0 Xx)->(V Xx))
% Found (((eq_ref fofType) Xx) x0) as proof of ((x0 Xx)->(V Xx))
% Found (((eq_ref fofType) Xx) x0) as proof of ((x0 Xx)->(V Xx))
% Found (fun (Xx:fofType)=> (((eq_ref fofType) Xx) x0)) as proof of ((x0 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType)=> (((eq_ref fofType) Xx) x0)) as proof of (forall (Xx:fofType), ((x0 Xx)->(V Xx)))
% Found x01:(x2 Xx)
% Instantiate: x2:=V:(fofType->Prop)
% Found x01 as proof of (V Xx)
% Found (fun (x01:(x2 Xx))=> x01) as proof of (V Xx)
% Found (fun (Xx:fofType) (x01:(x2 Xx))=> x01) as proof of ((x2 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType) (x01:(x2 Xx))=> x01) as proof of (forall (Xx:fofType), ((x2 Xx)->(V Xx)))
% Found x000:(x0 Xx)
% Instantiate: x0:=V:(fofType->Prop)
% Found x000 as proof of (V Xx)
% Found (fun (x000:(x0 Xx))=> x000) as proof of (V Xx)
% Found (fun (Xx:fofType) (x000:(x0 Xx))=> x000) as proof of ((x0 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType) (x000:(x0 Xx))=> x000) as proof of (forall (Xx:fofType), ((x0 Xx)->(V Xx)))
% Found x01:(x2 Xx)
% Instantiate: x2:=V:(fofType->Prop)
% Found x01 as proof of (V Xx)
% Found (fun (x01:(x2 Xx))=> x01) as proof of (V Xx)
% Found (fun (Xx:fofType) (x01:(x2 Xx))=> x01) as proof of ((x2 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType) (x01:(x2 Xx))=> x01) as proof of (forall (Xx:fofType), ((x2 Xx)->(V Xx)))
% Found x01:(x2 Xx)
% Instantiate: x2:=V:(fofType->Prop)
% Found x01 as proof of (V Xx)
% Found (fun (x01:(x2 Xx))=> x01) as proof of (V Xx)
% Found (fun (Xx:fofType) (x01:(x2 Xx))=> x01) as proof of ((x2 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType) (x01:(x2 Xx))=> x01) as proof of (forall (Xx:fofType), ((x2 Xx)->(V Xx)))
% Found x01:(x2 Xx)
% Instantiate: x2:=V:(fofType->Prop)
% Found x01 as proof of (V Xx)
% Found (fun (x01:(x2 Xx))=> x01) as proof of (V Xx)
% Found (fun (Xx:fofType) (x01:(x2 Xx))=> x01) as proof of ((x2 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType) (x01:(x2 Xx))=> x01) as proof of (forall (Xx:fofType), ((x2 Xx)->(V Xx)))
% Found x000:(x0 Xx)
% Instantiate: x0:=V:(fofType->Prop)
% Found x000 as proof of (V Xx)
% Found (fun (x000:(x0 Xx))=> x000) as proof of (V Xx)
% Found (fun (Xx:fofType) (x000:(x0 Xx))=> x000) as proof of ((x0 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType) (x000:(x0 Xx))=> x000) as proof of (forall (Xx:fofType), ((x0 Xx)->(V Xx)))
% Found x000:(x0 Xx)
% Instantiate: x0:=V:(fofType->Prop)
% Found x000 as proof of (V Xx)
% Found (fun (x000:(x0 Xx))=> x000) as proof of (V Xx)
% Found (fun (Xx:fofType) (x000:(x0 Xx))=> x000) as proof of ((x0 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType) (x000:(x0 Xx))=> x000) as proof of (forall (Xx:fofType), ((x0 Xx)->(V Xx)))
% Found x000:(x0 Xx)
% Instantiate: x0:=V:(fofType->Prop)
% Found x000 as proof of (V Xx)
% Found (fun (x000:(x0 Xx))=> x000) as proof of (V Xx)
% Found (fun (Xx:fofType) (x000:(x0 Xx))=> x000) as proof of ((x0 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType) (x000:(x0 Xx))=> x000) as proof of (forall (Xx:fofType), ((x0 Xx)->(V Xx)))
% Found eq_ref000:=(eq_ref00 x4):((x4 Xx)->(x4 Xx))
% Found (eq_ref00 x4) as proof of ((x4 Xx)->(V Xx))
% Found ((eq_ref0 Xx) x4) as proof of ((x4 Xx)->(V Xx))
% Found (((eq_ref fofType) Xx) x4) as proof of ((x4 Xx)->(V Xx))
% Found (((eq_ref fofType) Xx) x4) as proof of ((x4 Xx)->(V Xx))
% Found (fun (Xx:fofType)=> (((eq_ref fofType) Xx) x4)) as proof of ((x4 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType)=> (((eq_ref fofType) Xx) x4)) as proof of (forall (Xx:fofType), ((x4 Xx)->(V Xx)))
% Found x0100:=(x010 x00):(V Xx)
% Found (x010 x00) as proof of (V Xx)
% Found ((x01 V) x00) as proof of (V Xx)
% Found ((x01 V) x00) as proof of (V Xx)
% Found (fun (x01:(x2 Xx))=> ((x01 V) x00)) as proof of (V Xx)
% Found (fun (Xx:fofType) (x01:(x2 Xx))=> ((x01 V) x00)) as proof of ((x2 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType) (x01:(x2 Xx))=> ((x01 V) x00)) as proof of (forall (Xx:fofType), ((x2 Xx)->(V Xx)))
% Found (fun (V:(fofType->Prop)) (x00:(cC V)) (Xx:fofType) (x01:(x2 Xx))=> ((x01 V) x00)) as proof of ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))
% Found (fun (V:(fofType->Prop)) (x00:(cC V)) (Xx:fofType) (x01:(x2 Xx))=> ((x01 V) x00)) as proof of (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x2) Xx)):((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x2) Xx)) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx)) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x2) Xx)):((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x2) Xx)) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx)) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))
% Found x000:(x0 Xx)
% Instantiate: x0:=V:(fofType->Prop)
% Found x000 as proof of (V Xx)
% Found (fun (x000:(x0 Xx))=> x000) as proof of (V Xx)
% Found (fun (Xx:fofType) (x000:(x0 Xx))=> x000) as proof of ((x0 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType) (x000:(x0 Xx))=> x000) as proof of (forall (Xx:fofType), ((x0 Xx)->(V Xx)))
% Found eq_ref00:=(eq_ref0 (fun (U:(fofType->Prop))=> ((and (cC U)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((U Xx)->(V Xx)))))))):(((eq ((fofType->Prop)->Prop)) (fun (U:(fofType->Prop))=> ((and (cC U)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((U Xx)->(V Xx)))))))) (fun (U:(fofType->Prop))=> ((and (cC U)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((U Xx)->(V Xx))))))))
% Found (eq_ref0 (fun (U:(fofType->Prop))=> ((and (cC U)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((U Xx)->(V Xx)))))))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (U:(fofType->Prop))=> ((and (cC U)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((U Xx)->(V Xx)))))))) b)
% Found ((eq_ref ((fofType->Prop)->Prop)) (fun (U:(fofType->Prop))=> ((and (cC U)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((U Xx)->(V Xx)))))))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (U:(fofType->Prop))=> ((and (cC U)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((U Xx)->(V Xx)))))))) b)
% Found ((eq_ref ((fofType->Prop)->Prop)) (fun (U:(fofType->Prop))=> ((and (cC U)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((U Xx)->(V Xx)))))))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (U:(fofType->Prop))=> ((and (cC U)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((U Xx)->(V Xx)))))))) b)
% Found ((eq_ref ((fofType->Prop)->Prop)) (fun (U:(fofType->Prop))=> ((and (cC U)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((U Xx)->(V Xx)))))))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (U:(fofType->Prop))=> ((and (cC U)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((U Xx)->(V Xx)))))))) b)
% Found eq_ref000:=(eq_ref00 x0):((x0 Xx)->(x0 Xx))
% Found (eq_ref00 x0) as proof of ((x0 Xx)->(V Xx))
% Found ((eq_ref0 Xx) x0) as proof of ((x0 Xx)->(V Xx))
% Found (((eq_ref fofType) Xx) x0) as proof of ((x0 Xx)->(V Xx))
% Found (((eq_ref fofType) Xx) x0) as proof of ((x0 Xx)->(V Xx))
% Found (fun (Xx:fofType)=> (((eq_ref fofType) Xx) x0)) as proof of ((x0 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType)=> (((eq_ref fofType) Xx) x0)) as proof of (forall (Xx:fofType), ((x0 Xx)->(V Xx)))
% Found eq_ref000:=(eq_ref00 x2):((x2 Xx)->(x2 Xx))
% Found (eq_ref00 x2) as proof of ((x2 Xx)->(V Xx))
% Found ((eq_ref0 Xx) x2) as proof of ((x2 Xx)->(V Xx))
% Found (((eq_ref fofType) Xx) x2) as proof of ((x2 Xx)->(V Xx))
% Found (((eq_ref fofType) Xx) x2) as proof of ((x2 Xx)->(V Xx))
% Found (fun (Xx:fofType)=> (((eq_ref fofType) Xx) x2)) as proof of ((x2 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType)=> (((eq_ref fofType) Xx) x2)) as proof of (forall (Xx:fofType), ((x2 Xx)->(V Xx)))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x0) Xx)):((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found x01:(x4 Xx)
% Instantiate: x4:=V:(fofType->Prop)
% Found x01 as proof of (V Xx)
% Found (fun (x01:(x4 Xx))=> x01) as proof of (V Xx)
% Found (fun (Xx:fofType) (x01:(x4 Xx))=> x01) as proof of ((x4 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType) (x01:(x4 Xx))=> x01) as proof of (forall (Xx:fofType), ((x4 Xx)->(V Xx)))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x0) Xx)):((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found x000:(x0 Xx)
% Instantiate: x0:=V:(fofType->Prop)
% Found x000 as proof of (V Xx)
% Found (fun (x000:(x0 Xx))=> x000) as proof of (V Xx)
% Found (fun (Xx:fofType) (x000:(x0 Xx))=> x000) as proof of ((x0 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType) (x000:(x0 Xx))=> x000) as proof of (forall (Xx:fofType), ((x0 Xx)->(V Xx)))
% Found x01:(x2 Xx)
% Instantiate: x2:=V:(fofType->Prop)
% Found x01 as proof of (V Xx)
% Found (fun (x01:(x2 Xx))=> x01) as proof of (V Xx)
% Found (fun (Xx:fofType) (x01:(x2 Xx))=> x01) as proof of ((x2 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType) (x01:(x2 Xx))=> x01) as proof of (forall (Xx:fofType), ((x2 Xx)->(V Xx)))
% Found x01:(x4 Xx)
% Instantiate: x4:=V:(fofType->Prop)
% Found x01 as proof of (V Xx)
% Found (fun (x01:(x4 Xx))=> x01) as proof of (V Xx)
% Found (fun (Xx:fofType) (x01:(x4 Xx))=> x01) as proof of ((x4 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType) (x01:(x4 Xx))=> x01) as proof of (forall (Xx:fofType), ((x4 Xx)->(V Xx)))
% Found x01:(x4 Xx)
% Instantiate: x4:=V:(fofType->Prop)
% Found x01 as proof of (V Xx)
% Found (fun (x01:(x4 Xx))=> x01) as proof of (V Xx)
% Found (fun (Xx:fofType) (x01:(x4 Xx))=> x01) as proof of ((x4 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType) (x01:(x4 Xx))=> x01) as proof of (forall (Xx:fofType), ((x4 Xx)->(V Xx)))
% Found x01:(x4 Xx)
% Instantiate: x4:=V:(fofType->Prop)
% Found x01 as proof of (V Xx)
% Found (fun (x01:(x4 Xx))=> x01) as proof of (V Xx)
% Found (fun (Xx:fofType) (x01:(x4 Xx))=> x01) as proof of ((x4 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType) (x01:(x4 Xx))=> x01) as proof of (forall (Xx:fofType), ((x4 Xx)->(V Xx)))
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (U:(fofType->Prop))=> ((and (cC U)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((U Xx)->(V Xx)))))))):(((eq ((fofType->Prop)->Prop)) (fun (U:(fofType->Prop))=> ((and (cC U)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((U Xx)->(V Xx)))))))) (fun (x:(fofType->Prop))=> ((and (cC x)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x Xx)->(V Xx))))))))
% Found (eta_expansion_dep00 (fun (U:(fofType->Prop))=> ((and (cC U)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((U Xx)->(V Xx)))))))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (U:(fofType->Prop))=> ((and (cC U)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((U Xx)->(V Xx)))))))) b)
% Found ((eta_expansion_dep0 (fun (x3:(fofType->Prop))=> Prop)) (fun (U:(fofType->Prop))=> ((and (cC U)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((U Xx)->(V Xx)))))))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (U:(fofType->Prop))=> ((and (cC U)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((U Xx)->(V Xx)))))))) b)
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x3:(fofType->Prop))=> Prop)) (fun (U:(fofType->Prop))=> ((and (cC U)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((U Xx)->(V Xx)))))))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (U:(fofType->Prop))=> ((and (cC U)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((U Xx)->(V Xx)))))))) b)
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x3:(fofType->Prop))=> Prop)) (fun (U:(fofType->Prop))=> ((and (cC U)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((U Xx)->(V Xx)))))))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (U:(fofType->Prop))=> ((and (cC U)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((U Xx)->(V Xx)))))))) b)
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x3:(fofType->Prop))=> Prop)) (fun (U:(fofType->Prop))=> ((and (cC U)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((U Xx)->(V Xx)))))))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (U:(fofType->Prop))=> ((and (cC U)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((U Xx)->(V Xx)))))))) b)
% Found x000:(x0 Xx)
% Instantiate: x0:=V:(fofType->Prop)
% Found x000 as proof of (V Xx)
% Found (fun (x000:(x0 Xx))=> x000) as proof of (V Xx)
% Found (fun (Xx:fofType) (x000:(x0 Xx))=> x000) as proof of ((x0 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType) (x000:(x0 Xx))=> x000) as proof of (forall (Xx:fofType), ((x0 Xx)->(V Xx)))
% Found x000:(x0 Xx)
% Instantiate: x0:=V:(fofType->Prop)
% Found x000 as proof of (V Xx)
% Found (fun (x000:(x0 Xx))=> x000) as proof of (V Xx)
% Found (fun (Xx:fofType) (x000:(x0 Xx))=> x000) as proof of ((x0 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType) (x000:(x0 Xx))=> x000) as proof of (forall (Xx:fofType), ((x0 Xx)->(V Xx)))
% Found x000:(x0 Xx)
% Instantiate: x0:=V:(fofType->Prop)
% Found x000 as proof of (V Xx)
% Found (fun (x000:(x0 Xx))=> x000) as proof of (V Xx)
% Found (fun (Xx:fofType) (x000:(x0 Xx))=> x000) as proof of ((x0 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType) (x000:(x0 Xx))=> x000) as proof of (forall (Xx:fofType), ((x0 Xx)->(V Xx)))
% Found x01:(x2 Xx)
% Instantiate: x2:=V:(fofType->Prop)
% Found x01 as proof of (V Xx)
% Found (fun (x01:(x2 Xx))=> x01) as proof of (V Xx)
% Found (fun (Xx:fofType) (x01:(x2 Xx))=> x01) as proof of ((x2 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType) (x01:(x2 Xx))=> x01) as proof of (forall (Xx:fofType), ((x2 Xx)->(V Xx)))
% Found x01:(x2 Xx)
% Instantiate: x2:=V:(fofType->Prop)
% Found x01 as proof of (V Xx)
% Found (fun (x01:(x2 Xx))=> x01) as proof of (V Xx)
% Found (fun (Xx:fofType) (x01:(x2 Xx))=> x01) as proof of ((x2 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType) (x01:(x2 Xx))=> x01) as proof of (forall (Xx:fofType), ((x2 Xx)->(V Xx)))
% Found x01:(x2 Xx)
% Instantiate: x2:=V:(fofType->Prop)
% Found x01 as proof of (V Xx)
% Found (fun (x01:(x2 Xx))=> x01) as proof of (V Xx)
% Found (fun (Xx:fofType) (x01:(x2 Xx))=> x01) as proof of ((x2 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType) (x01:(x2 Xx))=> x01) as proof of (forall (Xx:fofType), ((x2 Xx)->(V Xx)))
% Found x0000000:=(x000000 x00):(V Xx)
% Found (x000000 x00) as proof of (V Xx)
% Found ((x00000 V) x00) as proof of (V Xx)
% Found (((fun (V0:(fofType->Prop)) (x001:(cC V0))=> (((x0000 V0) x001) x1)) V) x00) as proof of (V Xx)
% Found (((fun (V0:(fofType->Prop)) (x001:(cC V0))=> ((((fun (V0:(fofType->Prop)) (x001:(cC V0))=> (((x000 V0) x001) x2)) V0) x001) x1)) V) x00) as proof of (V Xx)
% Found (((fun (V0:(fofType->Prop)) (x001:(cC V0))=> ((((fun (V0:(fofType->Prop)) (x001:(cC V0))=> (((x000 V0) x001) x2)) V0) x001) x1)) V) x00) as proof of (V Xx)
% Found (fun (x000:(x0 Xx))=> (((fun (V0:(fofType->Prop)) (x001:(cC V0))=> ((((fun (V0:(fofType->Prop)) (x001:(cC V0))=> (((x000 V0) x001) x2)) V0) x001) x1)) V) x00)) as proof of (V Xx)
% Found (fun (Xx:fofType) (x000:(x0 Xx))=> (((fun (V0:(fofType->Prop)) (x001:(cC V0))=> ((((fun (V0:(fofType->Prop)) (x001:(cC V0))=> (((x000 V0) x001) x2)) V0) x001) x1)) V) x00)) as proof of ((x0 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType) (x000:(x0 Xx))=> (((fun (V0:(fofType->Prop)) (x001:(cC V0))=> ((((fun (V0:(fofType->Prop)) (x001:(cC V0))=> (((x000 V0) x001) x2)) V0) x001) x1)) V) x00)) as proof of (forall (Xx:fofType), ((x0 Xx)->(V Xx)))
% Found (fun (V:(fofType->Prop)) (x00:(cC V)) (Xx:fofType) (x000:(x0 Xx))=> (((fun (V0:(fofType->Prop)) (x001:(cC V0))=> ((((fun (V0:(fofType->Prop)) (x001:(cC V0))=> (((x000 V0) x001) x2)) V0) x001) x1)) V) x00)) as proof of ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))
% Found (fun (V:(fofType->Prop)) (x00:(cC V)) (Xx:fofType) (x000:(x0 Xx))=> (((fun (V0:(fofType->Prop)) (x001:(cC V0))=> ((((fun (V0:(fofType->Prop)) (x001:(cC V0))=> (((x000 V0) x001) x2)) V0) x001) x1)) V) x00)) as proof of (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x0) Xx)):((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x0) Xx)):((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found x0100:=(x010 x00):(V Xx)
% Found (x010 x00) as proof of (V Xx)
% Found ((x01 V) x00) as proof of (V Xx)
% Found ((x01 V) x00) as proof of (V Xx)
% Found (fun (x01:(x4 Xx))=> ((x01 V) x00)) as proof of (V Xx)
% Found (fun (Xx:fofType) (x01:(x4 Xx))=> ((x01 V) x00)) as proof of ((x4 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType) (x01:(x4 Xx))=> ((x01 V) x00)) as proof of (forall (Xx:fofType), ((x4 Xx)->(V Xx)))
% Found (fun (V:(fofType->Prop)) (x00:(cC V)) (Xx:fofType) (x01:(x4 Xx))=> ((x01 V) x00)) as proof of ((cC V)->(forall (Xx:fofType), ((x4 Xx)->(V Xx))))
% Found (fun (V:(fofType->Prop)) (x00:(cC V)) (Xx:fofType) (x01:(x4 Xx))=> ((x01 V) x00)) as proof of (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x4 Xx)->(V Xx)))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x4) Xx)):((Xr x4)->((or (Xr x4)) (((eq (fofType->Prop)) x4) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x4) Xx)) as proof of ((Xr x4)->((or (Xr x4)) (((eq (fofType->Prop)) x4) Xx)))
% Found ((or_introl (Xr x4)) (((eq (fofType->Prop)) x4) Xx)) as proof of ((Xr x4)->((or (Xr x4)) (((eq (fofType->Prop)) x4) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x4)) (((eq (fofType->Prop)) x4) Xx))) as proof of ((Xr x4)->((or (Xr x4)) (((eq (fofType->Prop)) x4) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x4)) (((eq (fofType->Prop)) x4) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x4)->((or (Xr x4)) (((eq (fofType->Prop)) x4) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x4)) (((eq (fofType->Prop)) x4) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x4)->((or (Xr x4)) (((eq (fofType->Prop)) x4) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x4) Xx)):((Xr x4)->((or (Xr x4)) (((eq (fofType->Prop)) x4) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x4) Xx)) as proof of ((Xr x4)->((or (Xr x4)) (((eq (fofType->Prop)) x4) Xx)))
% Found ((or_introl (Xr x4)) (((eq (fofType->Prop)) x4) Xx)) as proof of ((Xr x4)->((or (Xr x4)) (((eq (fofType->Prop)) x4) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x4)) (((eq (fofType->Prop)) x4) Xx))) as proof of ((Xr x4)->((or (Xr x4)) (((eq (fofType->Prop)) x4) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x4)) (((eq (fofType->Prop)) x4) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x4)->((or (Xr x4)) (((eq (fofType->Prop)) x4) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x4)) (((eq (fofType->Prop)) x4) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x4)->((or (Xr x4)) (((eq (fofType->Prop)) x4) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x0) Xx)):((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x0) Xx)):((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x2) Xx)):((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x2) Xx)) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx)) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))
% Found eta_expansion000:=(eta_expansion00 (fun (U:(fofType->Prop))=> ((and (cC U)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((U Xx)->(V Xx)))))))):(((eq ((fofType->Prop)->Prop)) (fun (U:(fofType->Prop))=> ((and (cC U)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((U Xx)->(V Xx)))))))) (fun (x:(fofType->Prop))=> ((and (cC x)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x Xx)->(V Xx))))))))
% Found (eta_expansion00 (fun (U:(fofType->Prop))=> ((and (cC U)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((U Xx)->(V Xx)))))))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (U:(fofType->Prop))=> ((and (cC U)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((U Xx)->(V Xx)))))))) b)
% Found ((eta_expansion0 Prop) (fun (U:(fofType->Prop))=> ((and (cC U)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((U Xx)->(V Xx)))))))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (U:(fofType->Prop))=> ((and (cC U)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((U Xx)->(V Xx)))))))) b)
% Found (((eta_expansion (fofType->Prop)) Prop) (fun (U:(fofType->Prop))=> ((and (cC U)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((U Xx)->(V Xx)))))))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (U:(fofType->Prop))=> ((and (cC U)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((U Xx)->(V Xx)))))))) b)
% Found (((eta_expansion (fofType->Prop)) Prop) (fun (U:(fofType->Prop))=> ((and (cC U)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((U Xx)->(V Xx)))))))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (U:(fofType->Prop))=> ((and (cC U)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((U Xx)->(V Xx)))))))) b)
% Found (((eta_expansion (fofType->Prop)) Prop) (fun (U:(fofType->Prop))=> ((and (cC U)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((U Xx)->(V Xx)))))))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (U:(fofType->Prop))=> ((and (cC U)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((U Xx)->(V Xx)))))))) b)
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x0) Xx)):((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x2) Xx)):((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x2) Xx)) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx)) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x0) Xx)):((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x0) Xx)):((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x0) Xx)):((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x2) Xx)):((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x2) Xx)) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx)) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x0) Xx)):((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x2) Xx)):((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x2) Xx)) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx)) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x0) Xx)):((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found x010000:=(x01000 x00):(V Xx)
% Found (x01000 x00) as proof of (V Xx)
% Found ((x0100 V) x00) as proof of (V Xx)
% Found (((fun (V0:(fofType->Prop)) (x000:(cC V0))=> (((x010 V0) x000) x3)) V) x00) as proof of (V Xx)
% Found (((fun (V0:(fofType->Prop)) (x000:(cC V0))=> ((((fun (V0:(fofType->Prop)) (x000:(cC V0))=> (((x01 V0) x000) x4)) V0) x000) x3)) V) x00) as proof of (V Xx)
% Found (((fun (V0:(fofType->Prop)) (x000:(cC V0))=> ((((fun (V0:(fofType->Prop)) (x000:(cC V0))=> (((x01 V0) x000) x4)) V0) x000) x3)) V) x00) as proof of (V Xx)
% Found (fun (x01:(x2 Xx))=> (((fun (V0:(fofType->Prop)) (x000:(cC V0))=> ((((fun (V0:(fofType->Prop)) (x000:(cC V0))=> (((x01 V0) x000) x4)) V0) x000) x3)) V) x00)) as proof of (V Xx)
% Found (fun (Xx:fofType) (x01:(x2 Xx))=> (((fun (V0:(fofType->Prop)) (x000:(cC V0))=> ((((fun (V0:(fofType->Prop)) (x000:(cC V0))=> (((x01 V0) x000) x4)) V0) x000) x3)) V) x00)) as proof of ((x2 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType) (x01:(x2 Xx))=> (((fun (V0:(fofType->Prop)) (x000:(cC V0))=> ((((fun (V0:(fofType->Prop)) (x000:(cC V0))=> (((x01 V0) x000) x4)) V0) x000) x3)) V) x00)) as proof of (forall (Xx:fofType), ((x2 Xx)->(V Xx)))
% Found (fun (V:(fofType->Prop)) (x00:(cC V)) (Xx:fofType) (x01:(x2 Xx))=> (((fun (V0:(fofType->Prop)) (x000:(cC V0))=> ((((fun (V0:(fofType->Prop)) (x000:(cC V0))=> (((x01 V0) x000) x4)) V0) x000) x3)) V) x00)) as proof of ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))
% Found (fun (V:(fofType->Prop)) (x00:(cC V)) (Xx:fofType) (x01:(x2 Xx))=> (((fun (V0:(fofType->Prop)) (x000:(cC V0))=> ((((fun (V0:(fofType->Prop)) (x000:(cC V0))=> (((x01 V0) x000) x4)) V0) x000) x3)) V) x00)) as proof of (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x2) Xx)):((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x2) Xx)) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx)) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x2) Xx)):((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x2) Xx)) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx)) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))
% Found x2:(forall (Xw:(((fofType->Prop)->Prop)->Prop)), (((and (Xw (fun (Xx:(fofType->Prop))=> False))) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xw Xr)->(Xw (fun (Xt:(fofType->Prop))=> ((or (Xr Xt)) (((eq (fofType->Prop)) Xt) Xx)))))))->(Xw cC)))
% Found x2 as proof of (forall (Xw:(((fofType->Prop)->Prop)->Prop)), (((and (Xw (fun (Xx0:(fofType->Prop))=> False))) (forall (Xr:((fofType->Prop)->Prop)) (Xx0:(fofType->Prop)), ((Xw Xr)->(Xw (fun (Xt:(fofType->Prop))=> ((or (Xr Xt)) (((eq (fofType->Prop)) Xt) Xx0)))))))->(Xw cC)))
% Found x4:(forall (Xx:(fofType->Prop)), ((cC Xx)->(cL Xx)))
% Found x4 as proof of (forall (Xx0:(fofType->Prop)), ((cC Xx0)->(cL Xx0)))
% Found x3:(forall (X:(fofType->Prop)) (Y:(fofType->Prop)), (((and (cL X)) (cL Y))->((or (forall (Xx:fofType), ((X Xx)->(Y Xx)))) (forall (Xx:fofType), ((Y Xx)->(X Xx))))))
% Found x3 as proof of (forall (X:(fofType->Prop)) (Y:(fofType->Prop)), (((and (cL X)) (cL Y))->((or (forall (Xx0:fofType), ((X Xx0)->(Y Xx0)))) (forall (Xx0:fofType), ((Y Xx0)->(X Xx0))))))
% Found x1:((and (forall (X:(fofType->Prop)) (Y:(fofType->Prop)), (((and (cL X)) (cL Y))->((or (forall (Xx:fofType), ((X Xx)->(Y Xx)))) (forall (Xx:fofType), ((Y Xx)->(X Xx))))))) (forall (Xx:(fofType->Prop)), ((cC Xx)->(cL Xx))))
% Found x1 as proof of ((and (forall (X:(fofType->Prop)) (Y:(fofType->Prop)), (((and (cL X)) (cL Y))->((or (forall (Xx0:fofType), ((X Xx0)->(Y Xx0)))) (forall (Xx0:fofType), ((Y Xx0)->(X Xx0))))))) (forall (Xx0:(fofType->Prop)), ((cC Xx0)->(cL Xx0))))
% Found x00:(cC V)
% Found x00 as proof of (cC V)
% Found (((((x0000 x00) x4) x3) x2) x1) as proof of (V Xx)
% Found ((((((x000 V) x00) x4) x3) x2) x1) as proof of (V Xx)
% Found ((((((x000 V) x00) x4) x3) x2) x1) as proof of (V Xx)
% Found (fun (x000:(x0 Xx))=> ((((((x000 V) x00) x4) x3) x2) x1)) as proof of (V Xx)
% Found (fun (Xx:fofType) (x000:(x0 Xx))=> ((((((x000 V) x00) x4) x3) x2) x1)) as proof of ((x0 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType) (x000:(x0 Xx))=> ((((((x000 V) x00) x4) x3) x2) x1)) as proof of (forall (Xx:fofType), ((x0 Xx)->(V Xx)))
% Found (fun (V:(fofType->Prop)) (x00:(cC V)) (Xx:fofType) (x000:(x0 Xx))=> ((((((x000 V) x00) x4) x3) x2) x1)) as proof of ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))
% Found (fun (V:(fofType->Prop)) (x00:(cC V)) (Xx:fofType) (x000:(x0 Xx))=> ((((((x000 V) x00) x4) x3) x2) x1)) as proof of (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x0) Xx)):((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x0) Xx)):((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->Prop)->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (U:(fofType->Prop))=> ((and (cC U)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((U Xx)->(V Xx))))))))
% Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (U:(fofType->Prop))=> ((and (cC U)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((U Xx)->(V Xx))))))))
% Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (U:(fofType->Prop))=> ((and (cC U)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((U Xx)->(V Xx))))))))
% Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (U:(fofType->Prop))=> ((and (cC U)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((U Xx)->(V Xx))))))))
% Found eta_expansion000:=(eta_expansion00 a):(((eq ((fofType->Prop)->Prop)) a) (fun (x:(fofType->Prop))=> (a x)))
% Found (eta_expansion00 a) as proof of (((eq ((fofType->Prop)->Prop)) a) b)
% Found ((eta_expansion0 Prop) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b)
% Found (((eta_expansion (fofType->Prop)) Prop) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b)
% Found (((eta_expansion (fofType->Prop)) Prop) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b)
% Found (((eta_expansion (fofType->Prop)) Prop) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b)
% Found eq_ref00:=(eq_ref0 a):(((eq ((fofType->Prop)->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq ((fofType->Prop)->Prop)) a) b)
% Found ((eq_ref ((fofType->Prop)->Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b)
% Found ((eq_ref ((fofType->Prop)->Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b)
% Found ((eq_ref ((fofType->Prop)->Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b)
% Found eq_ref00:=(eq_ref0 (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))):(((eq Prop) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))
% Found (eq_ref0 (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))) as proof of (((eq Prop) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))) b)
% Found ((eq_ref Prop) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))) as proof of (((eq Prop) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))) b)
% Found ((eq_ref Prop) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))) as proof of (((eq Prop) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))) b)
% Found ((eq_ref Prop) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))) as proof of (((eq Prop) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->Prop)->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (U:(fofType->Prop))=> ((and (cC U)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((U Xx)->(V Xx))))))))
% Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (U:(fofType->Prop))=> ((and (cC U)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((U Xx)->(V Xx))))))))
% Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (U:(fofType->Prop))=> ((and (cC U)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((U Xx)->(V Xx))))))))
% Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (U:(fofType->Prop))=> ((and (cC U)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((U Xx)->(V Xx))))))))
% Found eta_expansion_dep000:=(eta_expansion_dep00 a):(((eq ((fofType->Prop)->Prop)) a) (fun (x:(fofType->Prop))=> (a x)))
% Found (eta_expansion_dep00 a) as proof of (((eq ((fofType->Prop)->Prop)) a) b)
% Found ((eta_expansion_dep0 (fun (x3:(fofType->Prop))=> Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b)
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x3:(fofType->Prop))=> Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b)
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x3:(fofType->Prop))=> Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b)
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x3:(fofType->Prop))=> Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b)
% Found eq_ref00:=(eq_ref0 a):(((eq ((fofType->Prop)->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq ((fofType->Prop)->Prop)) a) b)
% Found ((eq_ref ((fofType->Prop)->Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b)
% Found ((eq_ref ((fofType->Prop)->Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b)
% Found ((eq_ref ((fofType->Prop)->Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b)
% Found iff_sym:=(fun (A:Prop) (B:Prop) (H:((iff A) B))=> ((((conj (B->A)) (A->B)) (((proj2 (A->B)) (B->A)) H)) (((proj1 (A->B)) (B->A)) H))):(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% Instantiate: b:=(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A))):Prop
% Found iff_sym as proof of b
% Found eq_ref00:=(eq_ref0 (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))):(((eq Prop) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))
% Found (eq_ref0 (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))) as proof of (((eq Prop) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))) b)
% Found ((eq_ref Prop) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))) as proof of (((eq Prop) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))) b)
% Found ((eq_ref Prop) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))) as proof of (((eq Prop) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))) b)
% Found ((eq_ref Prop) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))) as proof of (((eq Prop) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))) b)
% Found eq_ref00:=(eq_ref0 x0):(((eq (fofType->Prop)) x0) x0)
% Found (eq_ref0 x0) as proof of (((eq (fofType->Prop)) x0) b)
% Found ((eq_ref (fofType->Prop)) x0) as proof of (((eq (fofType->Prop)) x0) b)
% Found ((eq_ref (fofType->Prop)) x0) as proof of (((eq (fofType->Prop)) x0) b)
% Found ((eq_ref (fofType->Prop)) x0) as proof of (((eq (fofType->Prop)) x0) b)
% Found eta_expansion000:=(eta_expansion00 x0):(((eq (fofType->Prop)) x0) (fun (x:fofType)=> (x0 x)))
% Found (eta_expansion00 x0) as proof of (((eq (fofType->Prop)) x0) b)
% Found ((eta_expansion0 Prop) x0) as proof of (((eq (fofType->Prop)) x0) b)
% Found (((eta_expansion fofType) Prop) x0) as proof of (((eq (fofType->Prop)) x0) b)
% Found (((eta_expansion fofType) Prop) x0) as proof of (((eq (fofType->Prop)) x0) b)
% Found (((eta_expansion fofType) Prop) x0) as proof of (((eq (fofType->Prop)) x0) b)
% Found eq_ref00:=(eq_ref0 (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))):(((eq Prop) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))
% Found (eq_ref0 (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))) as proof of (((eq Prop) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))) b)
% Found ((eq_ref Prop) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))) as proof of (((eq Prop) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))) b)
% Found ((eq_ref Prop) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))) as proof of (((eq Prop) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))) b)
% Found ((eq_ref Prop) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))) as proof of (((eq Prop) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->Prop)->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (U:(fofType->Prop))=> ((and (cC U)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((U Xx)->(V Xx))))))))
% Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (U:(fofType->Prop))=> ((and (cC U)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((U Xx)->(V Xx))))))))
% Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (U:(fofType->Prop))=> ((and (cC U)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((U Xx)->(V Xx))))))))
% Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (U:(fofType->Prop))=> ((and (cC U)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((U Xx)->(V Xx))))))))
% Found eta_expansion_dep000:=(eta_expansion_dep00 a):(((eq ((fofType->Prop)->Prop)) a) (fun (x:(fofType->Prop))=> (a x)))
% Found (eta_expansion_dep00 a) as proof of (((eq ((fofType->Prop)->Prop)) a) b)
% Found ((eta_expansion_dep0 (fun (x5:(fofType->Prop))=> Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b)
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x5:(fofType->Prop))=> Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b)
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x5:(fofType->Prop))=> Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b)
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x5:(fofType->Prop))=> Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b)
% Found eq_ref00:=(eq_ref0 a):(((eq ((fofType->Prop)->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq ((fofType->Prop)->Prop)) a) b)
% Found ((eq_ref ((fofType->Prop)->Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b)
% Found ((eq_ref ((fofType->Prop)->Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b)
% Found ((eq_ref ((fofType->Prop)->Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b)
% Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (x0 x1))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (x0 x1))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (x0 x1))
% Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (x0 x1))
% Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (x0 x)))
% Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (x0 x1))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (x0 x1))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (x0 x1))
% Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (x0 x1))
% Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (x0 x)))
% Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (x0 x1))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (x0 x1))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (x0 x1))
% Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (x0 x1))
% Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (x0 x)))
% Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (x0 x1))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (x0 x1))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (x0 x1))
% Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (x0 x1))
% Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (x0 x)))
% Found x:((and ((and (forall (X:(fofType->Prop)) (Y:(fofType->Prop)), (((and (cL X)) (cL Y))->((or (forall (Xx:fofType), ((X Xx)->(Y Xx)))) (forall (Xx:fofType), ((Y Xx)->(X Xx))))))) (forall (Xx:(fofType->Prop)), ((cC Xx)->(cL Xx))))) (forall (Xw:(((fofType->Prop)->Prop)->Prop)), (((and (Xw (fun (Xx:(fofType->Prop))=> False))) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xw Xr)->(Xw (fun (Xt:(fofType->Prop))=> ((or (Xr Xt)) (((eq (fofType->Prop)) Xt) Xx)))))))->(Xw cC))))
% Instantiate: b:=((and ((and (forall (X:(fofType->Prop)) (Y:(fofType->Prop)), (((and (cL X)) (cL Y))->((or (forall (Xx:fofType), ((X Xx)->(Y Xx)))) (forall (Xx:fofType), ((Y Xx)->(X Xx))))))) (forall (Xx:(fofType->Prop)), ((cC Xx)->(cL Xx))))) (forall (Xw:(((fofType->Prop)->Prop)->Prop)), (((and (Xw (fun (Xx:(fofType->Prop))=> False))) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xw Xr)->(Xw (fun (Xt:(fofType->Prop))=> ((or (Xr Xt)) (((eq (fofType->Prop)) Xt) Xx)))))))->(Xw cC)))):Prop
% Found x as proof of b
% Found x:((and ((and (forall (X:(fofType->Prop)) (Y:(fofType->Prop)), (((and (cL X)) (cL Y))->((or (forall (Xx:fofType), ((X Xx)->(Y Xx)))) (forall (Xx:fofType), ((Y Xx)->(X Xx))))))) (forall (Xx:(fofType->Prop)), ((cC Xx)->(cL Xx))))) (forall (Xw:(((fofType->Prop)->Prop)->Prop)), (((and (Xw (fun (Xx:(fofType->Prop))=> False))) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xw Xr)->(Xw (fun (Xt:(fofType->Prop))=> ((or (Xr Xt)) (((eq (fofType->Prop)) Xt) Xx)))))))->(Xw cC))))
% Instantiate: b:=((and ((and (forall (X:(fofType->Prop)) (Y:(fofType->Prop)), (((and (cL X)) (cL Y))->((or (forall (Xx:fofType), ((X Xx)->(Y Xx)))) (forall (Xx:fofType), ((Y Xx)->(X Xx))))))) (forall (Xx:(fofType->Prop)), ((cC Xx)->(cL Xx))))) (forall (Xw:(((fofType->Prop)->Prop)->Prop)), (((and (Xw (fun (Xx:(fofType->Prop))=> False))) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xw Xr)->(Xw (fun (Xt:(fofType->Prop))=> ((or (Xr Xt)) (((eq (fofType->Prop)) Xt) Xx)))))))->(Xw cC)))):Prop
% Found x as proof of b
% Found eq_ref00:=(eq_ref0 (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x4 Xx)->(V Xx)))))):(((eq Prop) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x4 Xx)->(V Xx)))))) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x4 Xx)->(V Xx))))))
% Found (eq_ref0 (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x4 Xx)->(V Xx)))))) as proof of (((eq Prop) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x4 Xx)->(V Xx)))))) b)
% Found ((eq_ref Prop) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x4 Xx)->(V Xx)))))) as proof of (((eq Prop) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x4 Xx)->(V Xx)))))) b)
% Found ((eq_ref Prop) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x4 Xx)->(V Xx)))))) as proof of (((eq Prop) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x4 Xx)->(V Xx)))))) b)
% Found ((eq_ref Prop) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x4 Xx)->(V Xx)))))) as proof of (((eq Prop) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x4 Xx)->(V Xx)))))) b)
% Found eta_expansion_dep000:=(eta_expansion_dep00 x2):(((eq (fofType->Prop)) x2) (fun (x:fofType)=> (x2 x)))
% Found (eta_expansion_dep00 x2) as proof of (((eq (fofType->Prop)) x2) b)
% Found ((eta_expansion_dep0 (fun (x4:fofType)=> Prop)) x2) as proof of (((eq (fofType->Prop)) x2) b)
% Found (((eta_expansion_dep fofType) (fun (x4:fofType)=> Prop)) x2) as proof of (((eq (fofType->Prop)) x2) b)
% Found (((eta_expansion_dep fofType) (fun (x4:fofType)=> Prop)) x2) as proof of (((eq (fofType->Prop)) x2) b)
% Found (((eta_expansion_dep fofType) (fun (x4:fofType)=> Prop)) x2) as proof of (((eq (fofType->Prop)) x2) b)
% Found eq_ref000:=(eq_ref00 x0):((x0 Xx)->(x0 Xx))
% Found (eq_ref00 x0) as proof of ((x0 Xx)->(V Xx))
% Found ((eq_ref0 Xx) x0) as proof of ((x0 Xx)->(V Xx))
% Found (((eq_ref fofType) Xx) x0) as proof of ((x0 Xx)->(V Xx))
% Found (((eq_ref fofType) Xx) x0) as proof of ((x0 Xx)->(V Xx))
% Found (fun (Xx:fofType)=> (((eq_ref fofType) Xx) x0)) as proof of ((x0 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType)=> (((eq_ref fofType) Xx) x0)) as proof of (forall (Xx:fofType), ((x0 Xx)->(V Xx)))
% Found eta_expansion_dep000:=(eta_expansion_dep00 x2):(((eq (fofType->Prop)) x2) (fun (x:fofType)=> (x2 x)))
% Found (eta_expansion_dep00 x2) as proof of (((eq (fofType->Prop)) x2) b)
% Found ((eta_expansion_dep0 (fun (x4:fofType)=> Prop)) x2) as proof of (((eq (fofType->Prop)) x2) b)
% Found (((eta_expansion_dep fofType) (fun (x4:fofType)=> Prop)) x2) as proof of (((eq (fofType->Prop)) x2) b)
% Found (((eta_expansion_dep fofType) (fun (x4:fofType)=> Prop)) x2) as proof of (((eq (fofType->Prop)) x2) b)
% Found (((eta_expansion_dep fofType) (fun (x4:fofType)=> Prop)) x2) as proof of (((eq (fofType->Prop)) x2) b)
% Found eq_ref00:=(eq_ref0 (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))):(((eq Prop) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))
% Found (eq_ref0 (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))) as proof of (((eq Prop) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))) b)
% Found ((eq_ref Prop) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))) as proof of (((eq Prop) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))) b)
% Found ((eq_ref Prop) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))) as proof of (((eq Prop) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))) b)
% Found ((eq_ref Prop) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))) as proof of (((eq Prop) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))) b)
% Found eq_ref00:=(eq_ref0 (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))):(((eq Prop) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))
% Found (eq_ref0 (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))) as proof of (((eq Prop) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))) b)
% Found ((eq_ref Prop) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))) as proof of (((eq Prop) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))) b)
% Found ((eq_ref Prop) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))) as proof of (((eq Prop) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))) b)
% Found ((eq_ref Prop) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))) as proof of (((eq Prop) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))) b)
% Found eta_expansion000:=(eta_expansion00 x0):(((eq (fofType->Prop)) x0) (fun (x:fofType)=> (x0 x)))
% Found (eta_expansion00 x0) as proof of (((eq (fofType->Prop)) x0) b)
% Found ((eta_expansion0 Prop) x0) as proof of (((eq (fofType->Prop)) x0) b)
% Found (((eta_expansion fofType) Prop) x0) as proof of (((eq (fofType->Prop)) x0) b)
% Found (((eta_expansion fofType) Prop) x0) as proof of (((eq (fofType->Prop)) x0) b)
% Found (((eta_expansion fofType) Prop) x0) as proof of (((eq (fofType->Prop)) x0) b)
% Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b)
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))
% Found ((eq_trans0000 ((eq_ref Prop) (f x0))) ((eq_ref Prop) b)) as proof of (((eq Prop) (f x0)) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))
% Found (((eq_trans000 ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) ((eq_ref Prop) (f x0))) ((eq_ref Prop) b)) as proof of (((eq Prop) (f x0)) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))
% Found ((((eq_trans00 ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) ((eq_ref Prop) (f x0))) ((eq_ref Prop) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))) as proof of (((eq Prop) (f x0)) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))
% Found (((((eq_trans0 (f x0)) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) ((eq_ref Prop) (f x0))) ((eq_ref Prop) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))) as proof of (((eq Prop) (f x0)) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))
% Found ((((((eq_trans Prop) (f x0)) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) ((eq_ref Prop) (f x0))) ((eq_ref Prop) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))) as proof of (((eq Prop) (f x0)) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))
% Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b)
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))
% Found ((eq_trans0000 ((eq_ref Prop) (f x0))) ((eq_ref Prop) b)) as proof of (((eq Prop) (f x0)) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))
% Found (((eq_trans000 ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) ((eq_ref Prop) (f x0))) ((eq_ref Prop) b)) as proof of (((eq Prop) (f x0)) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))
% Found ((((eq_trans00 ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) ((eq_ref Prop) (f x0))) ((eq_ref Prop) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))) as proof of (((eq Prop) (f x0)) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))
% Found (((((eq_trans0 (f x0)) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) ((eq_ref Prop) (f x0))) ((eq_ref Prop) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))) as proof of (((eq Prop) (f x0)) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))
% Found ((((((eq_trans Prop) (f x0)) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) ((eq_ref Prop) (f x0))) ((eq_ref Prop) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))) as proof of (((eq Prop) (f x0)) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))
% Found x:((and ((and (forall (X:(fofType->Prop)) (Y:(fofType->Prop)), (((and (cL X)) (cL Y))->((or (forall (Xx:fofType), ((X Xx)->(Y Xx)))) (forall (Xx:fofType), ((Y Xx)->(X Xx))))))) (forall (Xx:(fofType->Prop)), ((cC Xx)->(cL Xx))))) (forall (Xw:(((fofType->Prop)->Prop)->Prop)), (((and (Xw (fun (Xx:(fofType->Prop))=> False))) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xw Xr)->(Xw (fun (Xt:(fofType->Prop))=> ((or (Xr Xt)) (((eq (fofType->Prop)) Xt) Xx)))))))->(Xw cC))))
% Instantiate: b:=((and ((and (forall (X:(fofType->Prop)) (Y:(fofType->Prop)), (((and (cL X)) (cL Y))->((or (forall (Xx:fofType), ((X Xx)->(Y Xx)))) (forall (Xx:fofType), ((Y Xx)->(X Xx))))))) (forall (Xx:(fofType->Prop)), ((cC Xx)->(cL Xx))))) (forall (Xw:(((fofType->Prop)->Prop)->Prop)), (((and (Xw (fun (Xx:(fofType->Prop))=> False))) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xw Xr)->(Xw (fun (Xt:(fofType->Prop))=> ((or (Xr Xt)) (((eq (fofType->Prop)) Xt) Xx)))))))->(Xw cC)))):Prop
% Found x as proof of b
% Found eq_ref000:=(eq_ref00 P0):((P0 (f x0))->(P0 (f x0)))
% Found (eq_ref00 P0) as proof of (P1 (f x0))
% Found ((eq_ref0 (f x0)) P0) as proof of (P1 (f x0))
% Found (((eq_ref Prop) (f x0)) P0) as proof of (P1 (f x0))
% Found (((eq_ref Prop) (f x0)) P0) as proof of (P1 (f x0))
% Found eq_ref000:=(eq_ref00 P0):((P0 (f x0))->(P0 (f x0)))
% Found (eq_ref00 P0) as proof of (P1 (f x0))
% Found ((eq_ref0 (f x0)) P0) as proof of (P1 (f x0))
% Found (((eq_ref Prop) (f x0)) P0) as proof of (P1 (f x0))
% Found (((eq_ref Prop) (f x0)) P0) as proof of (P1 (f x0))
% Found eta_expansion000:=(eta_expansion00 x0):(((eq (fofType->Prop)) x0) (fun (x:fofType)=> (x0 x)))
% Found (eta_expansion00 x0) as proof of (((eq (fofType->Prop)) x0) b)
% Found ((eta_expansion0 Prop) x0) as proof of (((eq (fofType->Prop)) x0) b)
% Found (((eta_expansion fofType) Prop) x0) as proof of (((eq (fofType->Prop)) x0) b)
% Found (((eta_expansion fofType) Prop) x0) as proof of (((eq (fofType->Prop)) x0) b)
% Found (((eta_expansion fofType) Prop) x0) as proof of (((eq (fofType->Prop)) x0) b)
% Found eta_expansion_dep000:=(eta_expansion_dep00 x0):(((eq (fofType->Prop)) x0) (fun (x:fofType)=> (x0 x)))
% Found (eta_expansion_dep00 x0) as proof of (((eq (fofType->Prop)) x0) b)
% Found ((eta_expansion_dep0 (fun (x4:fofType)=> Prop)) x0) as proof of (((eq (fofType->Prop)) x0) b)
% Found (((eta_expansion_dep fofType) (fun (x4:fofType)=> Prop)) x0) as proof of (((eq (fofType->Prop)) x0) b)
% Found (((eta_expansion_dep fofType) (fun (x4:fofType)=> Prop)) x0) as proof of (((eq (fofType->Prop)) x0) b)
% Found (((eta_expansion_dep fofType) (fun (x4:fofType)=> Prop)) x0) as proof of (((eq (fofType->Prop)) x0) b)
% Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) (x2 x3))
% Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (x2 x3))
% Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (x2 x3))
% Found (fun (x3:fofType)=> ((eq_ref Prop) (f x3))) as proof of (((eq Prop) (f x3)) (x2 x3))
% Found (fun (x3:fofType)=> ((eq_ref Prop) (f x3))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (x2 x)))
% Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) (x2 x3))
% Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (x2 x3))
% Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (x2 x3))
% Found (fun (x3:fofType)=> ((eq_ref Prop) (f x3))) as proof of (((eq Prop) (f x3)) (x2 x3))
% Found (fun (x3:fofType)=> ((eq_ref Prop) (f x3))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (x2 x)))
% Found eq_ref00:=(eq_ref0 (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))):(((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))))
% Found (eq_ref0 (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))) b)
% Found ((eq_ref Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))) b)
% Found ((eq_ref Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))) b)
% Found ((eq_ref Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))) b)
% Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) (x2 x3))
% Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (x2 x3))
% Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (x2 x3))
% Found (fun (x3:fofType)=> ((eq_ref Prop) (f x3))) as proof of (((eq Prop) (f x3)) (x2 x3))
% Found (fun (x3:fofType)=> ((eq_ref Prop) (f x3))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (x2 x)))
% Found eq_ref00:=(eq_ref0 x0):(((eq (fofType->Prop)) x0) x0)
% Found (eq_ref0 x0) as proof of (((eq (fofType->Prop)) x0) b)
% Found ((eq_ref (fofType->Prop)) x0) as proof of (((eq (fofType->Prop)) x0) b)
% Found ((eq_ref (fofType->Prop)) x0) as proof of (((eq (fofType->Prop)) x0) b)
% Found ((eq_ref (fofType->Prop)) x0) as proof of (((eq (fofType->Prop)) x0) b)
% Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) (x2 x3))
% Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (x2 x3))
% Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (x2 x3))
% Found (fun (x3:fofType)=> ((eq_ref Prop) (f x3))) as proof of (((eq Prop) (f x3)) (x2 x3))
% Found (fun (x3:fofType)=> ((eq_ref Prop) (f x3))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (x2 x)))
% Found eq_ref00:=(eq_ref0 (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))):(((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))))
% Found (eq_ref0 (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))) b)
% Found ((eq_ref Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))) b)
% Found ((eq_ref Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))) b)
% Found ((eq_ref Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))) b)
% Found x000:(x0 Xx)
% Instantiate: x0:=V:(fofType->Prop)
% Found x000 as proof of (V Xx)
% Found (fun (x000:(x0 Xx))=> x000) as proof of (V Xx)
% Found (fun (Xx:fofType) (x000:(x0 Xx))=> x000) as proof of ((x0 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType) (x000:(x0 Xx))=> x000) as proof of (forall (Xx:fofType), ((x0 Xx)->(V Xx)))
% Found x000:(x0 Xx)
% Instantiate: x0:=V:(fofType->Prop)
% Found x000 as proof of (V Xx)
% Found (fun (x000:(x0 Xx))=> x000) as proof of (V Xx)
% Found (fun (Xx:fofType) (x000:(x0 Xx))=> x000) as proof of ((x0 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType) (x000:(x0 Xx))=> x000) as proof of (forall (Xx:fofType), ((x0 Xx)->(V Xx)))
% Found x000:(x0 Xx)
% Instantiate: x0:=V:(fofType->Prop)
% Found x000 as proof of (V Xx)
% Found (fun (x000:(x0 Xx))=> x000) as proof of (V Xx)
% Found (fun (Xx:fofType) (x000:(x0 Xx))=> x000) as proof of ((x0 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType) (x000:(x0 Xx))=> x000) as proof of (forall (Xx:fofType), ((x0 Xx)->(V Xx)))
% Found eq_substitution:=(fun (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq U) (f a)) (f x)))) ((eq_ref U) (f a)))):(forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b))))
% Instantiate: b:=(forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b)))):Prop
% Found eq_substitution as proof of b
% Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) (x0 x3))
% Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (x0 x3))
% Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (x0 x3))
% Found (fun (x3:fofType)=> ((eq_ref Prop) (f x3))) as proof of (((eq Prop) (f x3)) (x0 x3))
% Found (fun (x3:fofType)=> ((eq_ref Prop) (f x3))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (x0 x)))
% Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) (x0 x3))
% Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (x0 x3))
% Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (x0 x3))
% Found (fun (x3:fofType)=> ((eq_ref Prop) (f x3))) as proof of (((eq Prop) (f x3)) (x0 x3))
% Found (fun (x3:fofType)=> ((eq_ref Prop) (f x3))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (x0 x)))
% Found eq_ref00:=(eq_ref0 (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))):(((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))))
% Found (eq_ref0 (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) b)
% Found ((eq_ref Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) b)
% Found ((eq_ref Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) b)
% Found ((eq_ref Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) b)
% Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) (x0 x3))
% Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (x0 x3))
% Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (x0 x3))
% Found (fun (x3:fofType)=> ((eq_ref Prop) (f x3))) as proof of (((eq Prop) (f x3)) (x0 x3))
% Found (fun (x3:fofType)=> ((eq_ref Prop) (f x3))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (x0 x)))
% Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) (x0 x3))
% Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (x0 x3))
% Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (x0 x3))
% Found (fun (x3:fofType)=> ((eq_ref Prop) (f x3))) as proof of (((eq Prop) (f x3)) (x0 x3))
% Found (fun (x3:fofType)=> ((eq_ref Prop) (f x3))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (x0 x)))
% Found eq_ref00:=(eq_ref0 (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))):(((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))))
% Found (eq_ref0 (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) b)
% Found ((eq_ref Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) b)
% Found ((eq_ref Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) b)
% Found ((eq_ref Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) b)
% Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) (x0 x3))
% Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (x0 x3))
% Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (x0 x3))
% Found (fun (x3:fofType)=> ((eq_ref Prop) (f x3))) as proof of (((eq Prop) (f x3)) (x0 x3))
% Found (fun (x3:fofType)=> ((eq_ref Prop) (f x3))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (x0 x)))
% Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) (x0 x3))
% Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (x0 x3))
% Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (x0 x3))
% Found (fun (x3:fofType)=> ((eq_ref Prop) (f x3))) as proof of (((eq Prop) (f x3)) (x0 x3))
% Found (fun (x3:fofType)=> ((eq_ref Prop) (f x3))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (x0 x)))
% Found eq_ref00:=(eq_ref0 (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))):(((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))))
% Found (eq_ref0 (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) b)
% Found ((eq_ref Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) b)
% Found ((eq_ref Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) b)
% Found ((eq_ref Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) b)
% Found eq_substitution:=(fun (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq U) (f a)) (f x)))) ((eq_ref U) (f a)))):(forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b))))
% Instantiate: b:=(forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b)))):Prop
% Found eq_substitution as proof of b
% Found eq_substitution:=(fun (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq U) (f a)) (f x)))) ((eq_ref U) (f a)))):(forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b))))
% Instantiate: b:=(forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b)))):Prop
% Found eq_substitution as proof of b
% Found eq_ref000:=(eq_ref00 x2):((x2 Xx)->(x2 Xx))
% Found (eq_ref00 x2) as proof of ((x2 Xx)->(V Xx))
% Found ((eq_ref0 Xx) x2) as proof of ((x2 Xx)->(V Xx))
% Found (((eq_ref fofType) Xx) x2) as proof of ((x2 Xx)->(V Xx))
% Found (((eq_ref fofType) Xx) x2) as proof of ((x2 Xx)->(V Xx))
% Found (fun (Xx:fofType)=> (((eq_ref fofType) Xx) x2)) as proof of ((x2 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType)=> (((eq_ref fofType) Xx) x2)) as proof of (forall (Xx:fofType), ((x2 Xx)->(V Xx)))
% Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) (x0 x3))
% Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (x0 x3))
% Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (x0 x3))
% Found (fun (x3:fofType)=> ((eq_ref Prop) (f x3))) as proof of (((eq Prop) (f x3)) (x0 x3))
% Found (fun (x3:fofType)=> ((eq_ref Prop) (f x3))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (x0 x)))
% Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) (x0 x3))
% Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (x0 x3))
% Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (x0 x3))
% Found (fun (x3:fofType)=> ((eq_ref Prop) (f x3))) as proof of (((eq Prop) (f x3)) (x0 x3))
% Found (fun (x3:fofType)=> ((eq_ref Prop) (f x3))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (x0 x)))
% Found eq_ref00:=(eq_ref0 (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))):(((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))))
% Found (eq_ref0 (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) b)
% Found ((eq_ref Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) b)
% Found ((eq_ref Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) b)
% Found ((eq_ref Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) b)
% Found x00000:=(x0000 x00):(V Xx)
% Found (x0000 x00) as proof of (V Xx)
% Found ((x000 V) x00) as proof of (V Xx)
% Found ((x000 V) x00) as proof of (V Xx)
% Found (fun (x000:(x0 Xx))=> ((x000 V) x00)) as proof of (V Xx)
% Found (fun (Xx:fofType) (x000:(x0 Xx))=> ((x000 V) x00)) as proof of ((x0 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType) (x000:(x0 Xx))=> ((x000 V) x00)) as proof of (forall (Xx:fofType), ((x0 Xx)->(V Xx)))
% Found (fun (V:(fofType->Prop)) (x00:(cC V)) (Xx:fofType) (x000:(x0 Xx))=> ((x000 V) x00)) as proof of ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))
% Found (fun (V:(fofType->Prop)) (x00:(cC V)) (Xx:fofType) (x000:(x0 Xx))=> ((x000 V) x00)) as proof of b
% Found eq_ref00:=(eq_ref0 x4):(((eq (fofType->Prop)) x4) x4)
% Found (eq_ref0 x4) as proof of (((eq (fofType->Prop)) x4) b)
% Found ((eq_ref (fofType->Prop)) x4) as proof of (((eq (fofType->Prop)) x4) b)
% Found ((eq_ref (fofType->Prop)) x4) as proof of (((eq (fofType->Prop)) x4) b)
% Found ((eq_ref (fofType->Prop)) x4) as proof of (((eq (fofType->Prop)) x4) b)
% Found eq_ref00:=(eq_ref0 (f x2)):(((eq Prop) (f x2)) (f x2))
% Found (eq_ref0 (f x2)) as proof of (((eq Prop) (f x2)) b)
% Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) b)
% Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) b)
% Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))))
% Found ((eq_trans0000 ((eq_ref Prop) (f x2))) ((eq_ref Prop) b)) as proof of (((eq Prop) (f x2)) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))))
% Found (((eq_trans000 ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))) ((eq_ref Prop) (f x2))) ((eq_ref Prop) b)) as proof of (((eq Prop) (f x2)) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))))
% Found ((((eq_trans00 ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))) ((eq_ref Prop) (f x2))) ((eq_ref Prop) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))))) as proof of (((eq Prop) (f x2)) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))))
% Found (((((eq_trans0 (f x2)) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))) ((eq_ref Prop) (f x2))) ((eq_ref Prop) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))))) as proof of (((eq Prop) (f x2)) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))))
% Found ((((((eq_trans Prop) (f x2)) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))) ((eq_ref Prop) (f x2))) ((eq_ref Prop) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))))) as proof of (((eq Prop) (f x2)) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))))
% Found eq_ref00:=(eq_ref0 (f x2)):(((eq Prop) (f x2)) (f x2))
% Found (eq_ref0 (f x2)) as proof of (((eq Prop) (f x2)) b)
% Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) b)
% Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) b)
% Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))))
% Found ((eq_trans0000 ((eq_ref Prop) (f x2))) ((eq_ref Prop) b)) as proof of (((eq Prop) (f x2)) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))))
% Found (((eq_trans000 ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))) ((eq_ref Prop) (f x2))) ((eq_ref Prop) b)) as proof of (((eq Prop) (f x2)) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))))
% Found ((((eq_trans00 ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))) ((eq_ref Prop) (f x2))) ((eq_ref Prop) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))))) as proof of (((eq Prop) (f x2)) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))))
% Found (((((eq_trans0 (f x2)) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))) ((eq_ref Prop) (f x2))) ((eq_ref Prop) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))))) as proof of (((eq Prop) (f x2)) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))))
% Found ((((((eq_trans Prop) (f x2)) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))) ((eq_ref Prop) (f x2))) ((eq_ref Prop) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))))) as proof of (((eq Prop) (f x2)) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))))
% Found eq_ref000:=(eq_ref00 P0):((P0 (f x2))->(P0 (f x2)))
% Found (eq_ref00 P0) as proof of (P1 (f x2))
% Found ((eq_ref0 (f x2)) P0) as proof of (P1 (f x2))
% Found (((eq_ref Prop) (f x2)) P0) as proof of (P1 (f x2))
% Found (((eq_ref Prop) (f x2)) P0) as proof of (P1 (f x2))
% Found eq_ref000:=(eq_ref00 P0):((P0 (f x2))->(P0 (f x2)))
% Found (eq_ref00 P0) as proof of (P1 (f x2))
% Found ((eq_ref0 (f x2)) P0) as proof of (P1 (f x2))
% Found (((eq_ref Prop) (f x2)) P0) as proof of (P1 (f x2))
% Found (((eq_ref Prop) (f x2)) P0) as proof of (P1 (f x2))
% Found eta_expansion000:=(eta_expansion00 x4):(((eq (fofType->Prop)) x4) (fun (x:fofType)=> (x4 x)))
% Found (eta_expansion00 x4) as proof of (((eq (fofType->Prop)) x4) b)
% Found ((eta_expansion0 Prop) x4) as proof of (((eq (fofType->Prop)) x4) b)
% Found (((eta_expansion fofType) Prop) x4) as proof of (((eq (fofType->Prop)) x4) b)
% Found (((eta_expansion fofType) Prop) x4) as proof of (((eq (fofType->Prop)) x4) b)
% Found (((eta_expansion fofType) Prop) x4) as proof of (((eq (fofType->Prop)) x4) b)
% Found conj1:=(conj False):(forall (B:Prop), (False->(B->((and False) B))))
% Instantiate: b:=(forall (B:Prop), (False->(B->((and False) B)))):Prop
% Found conj1 as proof of b
% Found eq_ref000:=(eq_ref00 x0):((x0 Xx)->(x0 Xx))
% Found (eq_ref00 x0) as proof of ((x0 Xx)->(V Xx))
% Found ((eq_ref0 Xx) x0) as proof of ((x0 Xx)->(V Xx))
% Found (((eq_ref fofType) Xx) x0) as proof of ((x0 Xx)->(V Xx))
% Found (((eq_ref fofType) Xx) x0) as proof of ((x0 Xx)->(V Xx))
% Found (fun (Xx:fofType)=> (((eq_ref fofType) Xx) x0)) as proof of ((x0 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType)=> (((eq_ref fofType) Xx) x0)) as proof of (forall (Xx:fofType), ((x0 Xx)->(V Xx)))
% Found eq_ref00:=(eq_ref0 x0):(((eq (fofType->Prop)) x0) x0)
% Found (eq_ref0 x0) as proof of (((eq (fofType->Prop)) x0) b)
% Found ((eq_ref (fofType->Prop)) x0) as proof of (((eq (fofType->Prop)) x0) b)
% Found ((eq_ref (fofType->Prop)) x0) as proof of (((eq (fofType->Prop)) x0) b)
% Found ((eq_ref (fofType->Prop)) x0) as proof of (((eq (fofType->Prop)) x0) b)
% Found eta_expansion_dep000:=(eta_expansion_dep00 x2):(((eq (fofType->Prop)) x2) (fun (x:fofType)=> (x2 x)))
% Found (eta_expansion_dep00 x2) as proof of (((eq (fofType->Prop)) x2) b)
% Found ((eta_expansion_dep0 (fun (x6:fofType)=> Prop)) x2) as proof of (((eq (fofType->Prop)) x2) b)
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) x2) as proof of (((eq (fofType->Prop)) x2) b)
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) x2) as proof of (((eq (fofType->Prop)) x2) b)
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) x2) as proof of (((eq (fofType->Prop)) x2) b)
% Found conj1:=(conj False):(forall (B:Prop), (False->(B->((and False) B))))
% Instantiate: b:=(forall (B:Prop), (False->(B->((and False) B)))):Prop
% Found conj1 as proof of b
% Found eq_substitution:=(fun (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq U) (f a)) (f x)))) ((eq_ref U) (f a)))):(forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b))))
% Instantiate: b:=(forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b)))):Prop
% Found eq_substitution as proof of b
% Found eq_substitution:=(fun (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq U) (f a)) (f x)))) ((eq_ref U) (f a)))):(forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b))))
% Instantiate: b:=(forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b)))):Prop
% Found eq_substitution as proof of b
% Found eq_substitution:=(fun (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq U) (f a)) (f x)))) ((eq_ref U) (f a)))):(forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b))))
% Instantiate: b:=(forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b)))):Prop
% Found eq_substitution as proof of b
% Found x01:(x2 Xx)
% Instantiate: x2:=V:(fofType->Prop)
% Found x01 as proof of (V Xx)
% Found (fun (x01:(x2 Xx))=> x01) as proof of (V Xx)
% Found (fun (Xx:fofType) (x01:(x2 Xx))=> x01) as proof of ((x2 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType) (x01:(x2 Xx))=> x01) as proof of (forall (Xx:fofType), ((x2 Xx)->(V Xx)))
% Found eta_expansion_dep000:=(eta_expansion_dep00 x0):(((eq (fofType->Prop)) x0) (fun (x:fofType)=> (x0 x)))
% Found (eta_expansion_dep00 x0) as proof of (((eq (fofType->Prop)) x0) b)
% Found ((eta_expansion_dep0 (fun (x6:fofType)=> Prop)) x0) as proof of (((eq (fofType->Prop)) x0) b)
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) x0) as proof of (((eq (fofType->Prop)) x0) b)
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) x0) as proof of (((eq (fofType->Prop)) x0) b)
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) x0) as proof of (((eq (fofType->Prop)) x0) b)
% Found eq_ref00:=(eq_ref0 x2):(((eq (fofType->Prop)) x2) x2)
% Found (eq_ref0 x2) as proof of (((eq (fofType->Prop)) x2) b)
% Found ((eq_ref (fofType->Prop)) x2) as proof of (((eq (fofType->Prop)) x2) b)
% Found ((eq_ref (fofType->Prop)) x2) as proof of (((eq (fofType->Prop)) x2) b)
% Found ((eq_ref (fofType->Prop)) x2) as proof of (((eq (fofType->Prop)) x2) b)
% Found conj1:=(conj False):(forall (B:Prop), (False->(B->((and False) B))))
% Instantiate: b:=(forall (B:Prop), (False->(B->((and False) B)))):Prop
% Found conj1 as proof of b
% Found eta_expansion000:=(eta_expansion00 x0):(((eq (fofType->Prop)) x0) (fun (x:fofType)=> (x0 x)))
% Found (eta_expansion00 x0) as proof of (((eq (fofType->Prop)) x0) b)
% Found ((eta_expansion0 Prop) x0) as proof of (((eq (fofType->Prop)) x0) b)
% Found (((eta_expansion fofType) Prop) x0) as proof of (((eq (fofType->Prop)) x0) b)
% Found (((eta_expansion fofType) Prop) x0) as proof of (((eq (fofType->Prop)) x0) b)
% Found (((eta_expansion fofType) Prop) x0) as proof of (((eq (fofType->Prop)) x0) b)
% Found eta_expansion_dep000:=(eta_expansion_dep00 x0):(((eq (fofType->Prop)) x0) (fun (x:fofType)=> (x0 x)))
% Found (eta_expansion_dep00 x0) as proof of (((eq (fofType->Prop)) x0) b)
% Found ((eta_expansion_dep0 (fun (x6:fofType)=> Prop)) x0) as proof of (((eq (fofType->Prop)) x0) b)
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) x0) as proof of (((eq (fofType->Prop)) x0) b)
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) x0) as proof of (((eq (fofType->Prop)) x0) b)
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) x0) as proof of (((eq (fofType->Prop)) x0) b)
% Found eq_ref00:=(eq_ref0 x2):(((eq (fofType->Prop)) x2) x2)
% Found (eq_ref0 x2) as proof of (((eq (fofType->Prop)) x2) b)
% Found ((eq_ref (fofType->Prop)) x2) as proof of (((eq (fofType->Prop)) x2) b)
% Found ((eq_ref (fofType->Prop)) x2) as proof of (((eq (fofType->Prop)) x2) b)
% Found ((eq_ref (fofType->Prop)) x2) as proof of (((eq (fofType->Prop)) x2) b)
% Found conj1:=(conj False):(forall (B:Prop), (False->(B->((and False) B))))
% Instantiate: b:=(forall (B:Prop), (False->(B->((and False) B)))):Prop
% Found conj1 as proof of b
% Found eq_ref000:=(eq_ref00 x0):((x0 Xx)->(x0 Xx))
% Found (eq_ref00 x0) as proof of ((x0 Xx)->(V Xx))
% Found ((eq_ref0 Xx) x0) as proof of ((x0 Xx)->(V Xx))
% Found (((eq_ref fofType) Xx) x0) as proof of ((x0 Xx)->(V Xx))
% Found (((eq_ref fofType) Xx) x0) as proof of ((x0 Xx)->(V Xx))
% Found (fun (Xx:fofType)=> (((eq_ref fofType) Xx) x0)) as proof of ((x0 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType)=> (((eq_ref fofType) Xx) x0)) as proof of (forall (Xx:fofType), ((x0 Xx)->(V Xx)))
% Found eq_ref00:=(eq_ref0 (f x5)):(((eq Prop) (f x5)) (f x5))
% Found (eq_ref0 (f x5)) as proof of (((eq Prop) (f x5)) (x4 x5))
% Found ((eq_ref Prop) (f x5)) as proof of (((eq Prop) (f x5)) (x4 x5))
% Found ((eq_ref Prop) (f x5)) as proof of (((eq Prop) (f x5)) (x4 x5))
% Found (fun (x5:fofType)=> ((eq_ref Prop) (f x5))) as proof of (((eq Prop) (f x5)) (x4 x5))
% Found (fun (x5:fofType)=> ((eq_ref Prop) (f x5))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (x4 x)))
% Found eq_ref00:=(eq_ref0 (f x5)):(((eq Prop) (f x5)) (f x5))
% Found (eq_ref0 (f x5)) as proof of (((eq Prop) (f x5)) (x4 x5))
% Found ((eq_ref Prop) (f x5)) as proof of (((eq Prop) (f x5)) (x4 x5))
% Found ((eq_ref Prop) (f x5)) as proof of (((eq Prop) (f x5)) (x4 x5))
% Found (fun (x5:fofType)=> ((eq_ref Prop) (f x5))) as proof of (((eq Prop) (f x5)) (x4 x5))
% Found (fun (x5:fofType)=> ((eq_ref Prop) (f x5))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (x4 x)))
% Found x000:(x0 Xx)
% Instantiate: x0:=V:(fofType->Prop)
% Found x000 as proof of (V Xx)
% Found (fun (x000:(x0 Xx))=> x000) as proof of (V Xx)
% Found (fun (Xx:fofType) (x000:(x0 Xx))=> x000) as proof of ((x0 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType) (x000:(x0 Xx))=> x000) as proof of (forall (Xx:fofType), ((x0 Xx)->(V Xx)))
% Found eq_ref00:=(eq_ref0 (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x4)->((or (Xr x4)) (((eq (fofType->Prop)) x4) Xx))))):(((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x4)->((or (Xr x4)) (((eq (fofType->Prop)) x4) Xx))))) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x4)->((or (Xr x4)) (((eq (fofType->Prop)) x4) Xx)))))
% Found (eq_ref0 (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x4)->((or (Xr x4)) (((eq (fofType->Prop)) x4) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x4)->((or (Xr x4)) (((eq (fofType->Prop)) x4) Xx))))) b)
% Found ((eq_ref Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x4)->((or (Xr x4)) (((eq (fofType->Prop)) x4) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x4)->((or (Xr x4)) (((eq (fofType->Prop)) x4) Xx))))) b)
% Found ((eq_ref Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x4)->((or (Xr x4)) (((eq (fofType->Prop)) x4) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x4)->((or (Xr x4)) (((eq (fofType->Prop)) x4) Xx))))) b)
% Found ((eq_ref Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x4)->((or (Xr x4)) (((eq (fofType->Prop)) x4) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x4)->((or (Xr x4)) (((eq (fofType->Prop)) x4) Xx))))) b)
% Found eta_expansion_dep000:=(eta_expansion_dep00 x0):(((eq (fofType->Prop)) x0) (fun (x:fofType)=> (x0 x)))
% Found (eta_expansion_dep00 x0) as proof of (((eq (fofType->Prop)) x0) b)
% Found ((eta_expansion_dep0 (fun (x6:fofType)=> Prop)) x0) as proof of (((eq (fofType->Prop)) x0) b)
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) x0) as proof of (((eq (fofType->Prop)) x0) b)
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) x0) as proof of (((eq (fofType->Prop)) x0) b)
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) x0) as proof of (((eq (fofType->Prop)) x0) b)
% Found eq_ref00:=(eq_ref0 x0):(((eq (fofType->Prop)) x0) x0)
% Found (eq_ref0 x0) as proof of (((eq (fofType->Prop)) x0) b)
% Found ((eq_ref (fofType->Prop)) x0) as proof of (((eq (fofType->Prop)) x0) b)
% Found ((eq_ref (fofType->Prop)) x0) as proof of (((eq (fofType->Prop)) x0) b)
% Found ((eq_ref (fofType->Prop)) x0) as proof of (((eq (fofType->Prop)) x0) b)
% Found eta_expansion_dep000:=(eta_expansion_dep00 x2):(((eq (fofType->Prop)) x2) (fun (x:fofType)=> (x2 x)))
% Found (eta_expansion_dep00 x2) as proof of (((eq (fofType->Prop)) x2) b)
% Found ((eta_expansion_dep0 (fun (x6:fofType)=> Prop)) x2) as proof of (((eq (fofType->Prop)) x2) b)
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) x2) as proof of (((eq (fofType->Prop)) x2) b)
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) x2) as proof of (((eq (fofType->Prop)) x2) b)
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) x2) as proof of (((eq (fofType->Prop)) x2) b)
% Found conj1:=(conj False):(forall (B:Prop), (False->(B->((and False) B))))
% Instantiate: b:=(forall (B:Prop), (False->(B->((and False) B)))):Prop
% Found conj1 as proof of b
% Found x01:(x2 Xx)
% Instantiate: x2:=V:(fofType->Prop)
% Found x01 as proof of (V Xx)
% Found (fun (x01:(x2 Xx))=> x01) as proof of (V Xx)
% Found (fun (Xx:fofType) (x01:(x2 Xx))=> x01) as proof of ((x2 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType) (x01:(x2 Xx))=> x01) as proof of (forall (Xx:fofType), ((x2 Xx)->(V Xx)))
% Found x01:(x2 Xx)
% Instantiate: x2:=V:(fofType->Prop)
% Found x01 as proof of (V Xx)
% Found (fun (x01:(x2 Xx))=> x01) as proof of (V Xx)
% Found (fun (Xx:fofType) (x01:(x2 Xx))=> x01) as proof of ((x2 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType) (x01:(x2 Xx))=> x01) as proof of (forall (Xx:fofType), ((x2 Xx)->(V Xx)))
% Found x01:(x2 Xx)
% Instantiate: x2:=V:(fofType->Prop)
% Found x01 as proof of (V Xx)
% Found (fun (x01:(x2 Xx))=> x01) as proof of (V Xx)
% Found (fun (Xx:fofType) (x01:(x2 Xx))=> x01) as proof of ((x2 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType) (x01:(x2 Xx))=> x01) as proof of (forall (Xx:fofType), ((x2 Xx)->(V Xx)))
% Found eq_ref00:=(eq_ref0 (f x5)):(((eq Prop) (f x5)) (f x5))
% Found (eq_ref0 (f x5)) as proof of (((eq Prop) (f x5)) (x4 x5))
% Found ((eq_ref Prop) (f x5)) as proof of (((eq Prop) (f x5)) (x4 x5))
% Found ((eq_ref Prop) (f x5)) as proof of (((eq Prop) (f x5)) (x4 x5))
% Found (fun (x5:fofType)=> ((eq_ref Prop) (f x5))) as proof of (((eq Prop) (f x5)) (x4 x5))
% Found (fun (x5:fofType)=> ((eq_ref Prop) (f x5))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (x4 x)))
% Found eq_ref00:=(eq_ref0 (f x5)):(((eq Prop) (f x5)) (f x5))
% Found (eq_ref0 (f x5)) as proof of (((eq Prop) (f x5)) (x4 x5))
% Found ((eq_ref Prop) (f x5)) as proof of (((eq Prop) (f x5)) (x4 x5))
% Found ((eq_ref Prop) (f x5)) as proof of (((eq Prop) (f x5)) (x4 x5))
% Found (fun (x5:fofType)=> ((eq_ref Prop) (f x5))) as proof of (((eq Prop) (f x5)) (x4 x5))
% Found (fun (x5:fofType)=> ((eq_ref Prop) (f x5))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (x4 x)))
% Found eq_ref00:=(eq_ref0 (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x4)->((or (Xr x4)) (((eq (fofType->Prop)) x4) Xx))))):(((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x4)->((or (Xr x4)) (((eq (fofType->Prop)) x4) Xx))))) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x4)->((or (Xr x4)) (((eq (fofType->Prop)) x4) Xx)))))
% Found (eq_ref0 (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x4)->((or (Xr x4)) (((eq (fofType->Prop)) x4) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x4)->((or (Xr x4)) (((eq (fofType->Prop)) x4) Xx))))) b)
% Found ((eq_ref Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x4)->((or (Xr x4)) (((eq (fofType->Prop)) x4) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x4)->((or (Xr x4)) (((eq (fofType->Prop)) x4) Xx))))) b)
% Found ((eq_ref Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x4)->((or (Xr x4)) (((eq (fofType->Prop)) x4) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x4)->((or (Xr x4)) (((eq (fofType->Prop)) x4) Xx))))) b)
% Found ((eq_ref Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x4)->((or (Xr x4)) (((eq (fofType->Prop)) x4) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x4)->((or (Xr x4)) (((eq (fofType->Prop)) x4) Xx))))) b)
% Found conj1:=(conj False):(forall (B:Prop), (False->(B->((and False) B))))
% Instantiate: b:=(forall (B:Prop), (False->(B->((and False) B)))):Prop
% Found conj1 as proof of b
% Found eq_ref00:=(eq_ref0 (f x5)):(((eq Prop) (f x5)) (f x5))
% Found (eq_ref0 (f x5)) as proof of (((eq Prop) (f x5)) (x0 x5))
% Found ((eq_ref Prop) (f x5)) as proof of (((eq Prop) (f x5)) (x0 x5))
% Found ((eq_ref Prop) (f x5)) as proof of (((eq Prop) (f x5)) (x0 x5))
% Found (fun (x5:fofType)=> ((eq_ref Prop) (f x5))) as proof of (((eq Prop) (f x5)) (x0 x5))
% Found (fun (x5:fofType)=> ((eq_ref Prop) (f x5))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (x0 x)))
% Found eq_ref00:=(eq_ref0 (f x5)):(((eq Prop) (f x5)) (f x5))
% Found (eq_ref0 (f x5)) as proof of (((eq Prop) (f x5)) (x0 x5))
% Found ((eq_ref Prop) (f x5)) as proof of (((eq Prop) (f x5)) (x0 x5))
% Found ((eq_ref Prop) (f x5)) as proof of (((eq Prop) (f x5)) (x0 x5))
% Found (fun (x5:fofType)=> ((eq_ref Prop) (f x5))) as proof of (((eq Prop) (f x5)) (x0 x5))
% Found (fun (x5:fofType)=> ((eq_ref Prop) (f x5))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (x0 x)))
% Found eq_ref00:=(eq_ref0 (f x5)):(((eq Prop) (f x5)) (f x5))
% Found (eq_ref0 (f x5)) as proof of (((eq Prop) (f x5)) (x2 x5))
% Found ((eq_ref Prop) (f x5)) as proof of (((eq Prop) (f x5)) (x2 x5))
% Found ((eq_ref Prop) (f x5)) as proof of (((eq Prop) (f x5)) (x2 x5))
% Found (fun (x5:fofType)=> ((eq_ref Prop) (f x5))) as proof of (((eq Prop) (f x5)) (x2 x5))
% Found (fun (x5:fofType)=> ((eq_ref Prop) (f x5))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (x2 x)))
% Found eq_ref00:=(eq_ref0 (f x5)):(((eq Prop) (f x5)) (f x5))
% Found (eq_ref0 (f x5)) as proof of (((eq Prop) (f x5)) (x2 x5))
% Found ((eq_ref Prop) (f x5)) as proof of (((eq Prop) (f x5)) (x2 x5))
% Found ((eq_ref Prop) (f x5)) as proof of (((eq Prop) (f x5)) (x2 x5))
% Found (fun (x5:fofType)=> ((eq_ref Prop) (f x5))) as proof of (((eq Prop) (f x5)) (x2 x5))
% Found (fun (x5:fofType)=> ((eq_ref Prop) (f x5))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (x2 x)))
% Found eq_ref00:=(eq_ref0 (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))):(((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))))
% Found (eq_ref0 (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) b)
% Found ((eq_ref Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) b)
% Found ((eq_ref Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) b)
% Found ((eq_ref Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) b)
% Found eq_ref00:=(eq_ref0 (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))):(((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))))
% Found (eq_ref0 (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))) b)
% Found ((eq_ref Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))) b)
% Found ((eq_ref Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))) b)
% Found ((eq_ref Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))) b)
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x2) Xx)):((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x2) Xx)) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx)) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) b) Xx)):((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found eq_ref00:=(eq_ref0 (f x5)):(((eq Prop) (f x5)) (f x5))
% Found (eq_ref0 (f x5)) as proof of (((eq Prop) (f x5)) (x0 x5))
% Found ((eq_ref Prop) (f x5)) as proof of (((eq Prop) (f x5)) (x0 x5))
% Found ((eq_ref Prop) (f x5)) as proof of (((eq Prop) (f x5)) (x0 x5))
% Found (fun (x5:fofType)=> ((eq_ref Prop) (f x5))) as proof of (((eq Prop) (f x5)) (x0 x5))
% Found (fun (x5:fofType)=> ((eq_ref Prop) (f x5))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (x0 x)))
% Found eq_ref00:=(eq_ref0 (f x5)):(((eq Prop) (f x5)) (f x5))
% Found (eq_ref0 (f x5)) as proof of (((eq Prop) (f x5)) (x0 x5))
% Found ((eq_ref Prop) (f x5)) as proof of (((eq Prop) (f x5)) (x0 x5))
% Found ((eq_ref Prop) (f x5)) as proof of (((eq Prop) (f x5)) (x0 x5))
% Found (fun (x5:fofType)=> ((eq_ref Prop) (f x5))) as proof of (((eq Prop) (f x5)) (x0 x5))
% Found (fun (x5:fofType)=> ((eq_ref Prop) (f x5))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (x0 x)))
% Found x000:(x0 Xx)
% Instantiate: x0:=V:(fofType->Prop)
% Found x000 as proof of (V Xx)
% Found (fun (x000:(x0 Xx))=> x000) as proof of (V Xx)
% Found (fun (Xx:fofType) (x000:(x0 Xx))=> x000) as proof of ((x0 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType) (x000:(x0 Xx))=> x000) as proof of (forall (Xx:fofType), ((x0 Xx)->(V Xx)))
% Found x000:(x0 Xx)
% Instantiate: x0:=V:(fofType->Prop)
% Found x000 as proof of (V Xx)
% Found (fun (x000:(x0 Xx))=> x000) as proof of (V Xx)
% Found (fun (Xx:fofType) (x000:(x0 Xx))=> x000) as proof of ((x0 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType) (x000:(x0 Xx))=> x000) as proof of (forall (Xx:fofType), ((x0 Xx)->(V Xx)))
% Found x000:(x0 Xx)
% Instantiate: x0:=V:(fofType->Prop)
% Found x000 as proof of (V Xx)
% Found (fun (x000:(x0 Xx))=> x000) as proof of (V Xx)
% Found (fun (Xx:fofType) (x000:(x0 Xx))=> x000) as proof of ((x0 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType) (x000:(x0 Xx))=> x000) as proof of (forall (Xx:fofType), ((x0 Xx)->(V Xx)))
% Found eq_ref00:=(eq_ref0 (f x5)):(((eq Prop) (f x5)) (f x5))
% Found (eq_ref0 (f x5)) as proof of (((eq Prop) (f x5)) (x2 x5))
% Found ((eq_ref Prop) (f x5)) as proof of (((eq Prop) (f x5)) (x2 x5))
% Found ((eq_ref Prop) (f x5)) as proof of (((eq Prop) (f x5)) (x2 x5))
% Found (fun (x5:fofType)=> ((eq_ref Prop) (f x5))) as proof of (((eq Prop) (f x5)) (x2 x5))
% Found (fun (x5:fofType)=> ((eq_ref Prop) (f x5))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (x2 x)))
% Found eq_ref00:=(eq_ref0 (f x5)):(((eq Prop) (f x5)) (f x5))
% Found (eq_ref0 (f x5)) as proof of (((eq Prop) (f x5)) (x2 x5))
% Found ((eq_ref Prop) (f x5)) as proof of (((eq Prop) (f x5)) (x2 x5))
% Found ((eq_ref Prop) (f x5)) as proof of (((eq Prop) (f x5)) (x2 x5))
% Found (fun (x5:fofType)=> ((eq_ref Prop) (f x5))) as proof of (((eq Prop) (f x5)) (x2 x5))
% Found (fun (x5:fofType)=> ((eq_ref Prop) (f x5))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (x2 x)))
% Found eq_ref00:=(eq_ref0 (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))):(((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))))
% Found (eq_ref0 (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) b)
% Found ((eq_ref Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) b)
% Found ((eq_ref Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) b)
% Found ((eq_ref Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) b)
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x2) Xx)):((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x2) Xx)) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx)) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of b
% Found eq_ref00:=(eq_ref0 (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))):(((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))))
% Found (eq_ref0 (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))) b)
% Found ((eq_ref Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))) b)
% Found ((eq_ref Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))) b)
% Found ((eq_ref Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))) b)
% Found x000:(x0 Xx)
% Instantiate: x0:=V:(fofType->Prop)
% Found x000 as proof of (V Xx)
% Found (fun (x000:(x0 Xx))=> x000) as proof of (V Xx)
% Found (fun (Xx:fofType) (x000:(x0 Xx))=> x000) as proof of ((x0 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType) (x000:(x0 Xx))=> x000) as proof of (forall (Xx:fofType), ((x0 Xx)->(V Xx)))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x2) Xx)):((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x2) Xx)) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx)) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) b) Xx)):((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) b) Xx)):((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found eq_ref00:=(eq_ref0 (f x5)):(((eq Prop) (f x5)) (f x5))
% Found (eq_ref0 (f x5)) as proof of (((eq Prop) (f x5)) (x0 x5))
% Found ((eq_ref Prop) (f x5)) as proof of (((eq Prop) (f x5)) (x0 x5))
% Found ((eq_ref Prop) (f x5)) as proof of (((eq Prop) (f x5)) (x0 x5))
% Found (fun (x5:fofType)=> ((eq_ref Prop) (f x5))) as proof of (((eq Prop) (f x5)) (x0 x5))
% Found (fun (x5:fofType)=> ((eq_ref Prop) (f x5))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (x0 x)))
% Found eq_ref00:=(eq_ref0 (f x5)):(((eq Prop) (f x5)) (f x5))
% Found (eq_ref0 (f x5)) as proof of (((eq Prop) (f x5)) (x0 x5))
% Found ((eq_ref Prop) (f x5)) as proof of (((eq Prop) (f x5)) (x0 x5))
% Found ((eq_ref Prop) (f x5)) as proof of (((eq Prop) (f x5)) (x0 x5))
% Found (fun (x5:fofType)=> ((eq_ref Prop) (f x5))) as proof of (((eq Prop) (f x5)) (x0 x5))
% Found (fun (x5:fofType)=> ((eq_ref Prop) (f x5))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (x0 x)))
% Found eq_ref00:=(eq_ref0 (f x5)):(((eq Prop) (f x5)) (f x5))
% Found (eq_ref0 (f x5)) as proof of (((eq Prop) (f x5)) (x0 x5))
% Found ((eq_ref Prop) (f x5)) as proof of (((eq Prop) (f x5)) (x0 x5))
% Found ((eq_ref Prop) (f x5)) as proof of (((eq Prop) (f x5)) (x0 x5))
% Found (fun (x5:fofType)=> ((eq_ref Prop) (f x5))) as proof of (((eq Prop) (f x5)) (x0 x5))
% Found (fun (x5:fofType)=> ((eq_ref Prop) (f x5))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (x0 x)))
% Found eq_ref00:=(eq_ref0 (f x5)):(((eq Prop) (f x5)) (f x5))
% Found (eq_ref0 (f x5)) as proof of (((eq Prop) (f x5)) (x0 x5))
% Found ((eq_ref Prop) (f x5)) as proof of (((eq Prop) (f x5)) (x0 x5))
% Found ((eq_ref Prop) (f x5)) as proof of (((eq Prop) (f x5)) (x0 x5))
% Found (fun (x5:fofType)=> ((eq_ref Prop) (f x5))) as proof of (((eq Prop) (f x5)) (x0 x5))
% Found (fun (x5:fofType)=> ((eq_ref Prop) (f x5))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (x0 x)))
% Found eq_ref00:=(eq_ref0 (f x5)):(((eq Prop) (f x5)) (f x5))
% Found (eq_ref0 (f x5)) as proof of (((eq Prop) (f x5)) (x2 x5))
% Found ((eq_ref Prop) (f x5)) as proof of (((eq Prop) (f x5)) (x2 x5))
% Found ((eq_ref Prop) (f x5)) as proof of (((eq Prop) (f x5)) (x2 x5))
% Found (fun (x5:fofType)=> ((eq_ref Prop) (f x5))) as proof of (((eq Prop) (f x5)) (x2 x5))
% Found (fun (x5:fofType)=> ((eq_ref Prop) (f x5))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (x2 x)))
% Found eq_ref00:=(eq_ref0 (f x5)):(((eq Prop) (f x5)) (f x5))
% Found (eq_ref0 (f x5)) as proof of (((eq Prop) (f x5)) (x2 x5))
% Found ((eq_ref Prop) (f x5)) as proof of (((eq Prop) (f x5)) (x2 x5))
% Found ((eq_ref Prop) (f x5)) as proof of (((eq Prop) (f x5)) (x2 x5))
% Found (fun (x5:fofType)=> ((eq_ref Prop) (f x5))) as proof of (((eq Prop) (f x5)) (x2 x5))
% Found (fun (x5:fofType)=> ((eq_ref Prop) (f x5))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (x2 x)))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x2) Xx)):((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x2) Xx)) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx)) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of b
% Found eq_ref00:=(eq_ref0 (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))):(((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))))
% Found (eq_ref0 (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) b)
% Found ((eq_ref Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) b)
% Found ((eq_ref Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) b)
% Found ((eq_ref Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) b)
% Found eq_ref00:=(eq_ref0 (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))):(((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))))
% Found (eq_ref0 (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) b)
% Found ((eq_ref Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) b)
% Found ((eq_ref Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) b)
% Found ((eq_ref Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (cC x4)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x4 Xx)->(V Xx)))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (cC x4)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x4 Xx)->(V Xx)))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (cC x4)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x4 Xx)->(V Xx)))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (cC x4)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x4 Xx)->(V Xx)))))))
% Found eq_ref00:=(eq_ref0 (f x4)):(((eq Prop) (f x4)) (f x4))
% Found (eq_ref0 (f x4)) as proof of (((eq Prop) (f x4)) b)
% Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) b)
% Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) b)
% Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) b)
% Found ((eq_trans0000 ((eq_ref Prop) (f x4))) ((eq_ref Prop) b)) as proof of (((eq Prop) (f x4)) ((and (cC x4)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x4 Xx)->(V Xx)))))))
% Found (((eq_trans000 ((and (cC x4)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x4 Xx)->(V Xx))))))) ((eq_ref Prop) (f x4))) ((eq_ref Prop) b)) as proof of (((eq Prop) (f x4)) ((and (cC x4)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x4 Xx)->(V Xx)))))))
% Found ((((eq_trans00 ((and (cC x4)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x4 Xx)->(V Xx))))))) ((and (cC x4)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x4 Xx)->(V Xx))))))) ((eq_ref Prop) (f x4))) ((eq_ref Prop) ((and (cC x4)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x4 Xx)->(V Xx)))))))) as proof of (((eq Prop) (f x4)) ((and (cC x4)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x4 Xx)->(V Xx)))))))
% Found (((((eq_trans0 (f x4)) ((and (cC x4)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x4 Xx)->(V Xx))))))) ((and (cC x4)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x4 Xx)->(V Xx))))))) ((eq_ref Prop) (f x4))) ((eq_ref Prop) ((and (cC x4)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x4 Xx)->(V Xx)))))))) as proof of (((eq Prop) (f x4)) ((and (cC x4)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x4 Xx)->(V Xx)))))))
% Found ((((((eq_trans Prop) (f x4)) ((and (cC x4)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x4 Xx)->(V Xx))))))) ((and (cC x4)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x4 Xx)->(V Xx))))))) ((eq_ref Prop) (f x4))) ((eq_ref Prop) ((and (cC x4)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x4 Xx)->(V Xx)))))))) as proof of (((eq Prop) (f x4)) ((and (cC x4)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x4 Xx)->(V Xx)))))))
% Found eq_ref00:=(eq_ref0 (f x4)):(((eq Prop) (f x4)) (f x4))
% Found (eq_ref0 (f x4)) as proof of (((eq Prop) (f x4)) b)
% Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) b)
% Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) b)
% Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (cC x4)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x4 Xx)->(V Xx)))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (cC x4)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x4 Xx)->(V Xx)))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (cC x4)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x4 Xx)->(V Xx)))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (cC x4)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x4 Xx)->(V Xx)))))))
% Found ((eq_trans0000 ((eq_ref Prop) (f x4))) ((eq_ref Prop) b)) as proof of (((eq Prop) (f x4)) ((and (cC x4)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x4 Xx)->(V Xx)))))))
% Found (((eq_trans000 ((and (cC x4)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x4 Xx)->(V Xx))))))) ((eq_ref Prop) (f x4))) ((eq_ref Prop) b)) as proof of (((eq Prop) (f x4)) ((and (cC x4)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x4 Xx)->(V Xx)))))))
% Found ((((eq_trans00 ((and (cC x4)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x4 Xx)->(V Xx))))))) ((and (cC x4)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x4 Xx)->(V Xx))))))) ((eq_ref Prop) (f x4))) ((eq_ref Prop) ((and (cC x4)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x4 Xx)->(V Xx)))))))) as proof of (((eq Prop) (f x4)) ((and (cC x4)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x4 Xx)->(V Xx)))))))
% Found (((((eq_trans0 (f x4)) ((and (cC x4)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x4 Xx)->(V Xx))))))) ((and (cC x4)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x4 Xx)->(V Xx))))))) ((eq_ref Prop) (f x4))) ((eq_ref Prop) ((and (cC x4)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x4 Xx)->(V Xx)))))))) as proof of (((eq Prop) (f x4)) ((and (cC x4)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x4 Xx)->(V Xx)))))))
% Found ((((((eq_trans Prop) (f x4)) ((and (cC x4)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x4 Xx)->(V Xx))))))) ((and (cC x4)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x4 Xx)->(V Xx))))))) ((eq_ref Prop) (f x4))) ((eq_ref Prop) ((and (cC x4)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x4 Xx)->(V Xx)))))))) as proof of (((eq Prop) (f x4)) ((and (cC x4)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x4 Xx)->(V Xx)))))))
% Found eq_ref00:=(eq_ref0 (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))):(((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))))
% Found (eq_ref0 (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))) b)
% Found ((eq_ref Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))) b)
% Found ((eq_ref Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))) b)
% Found ((eq_ref Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (f x0))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% Found eq_ref00:=(eq_ref0 ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))):(((eq Prop) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))
% Found (eq_ref0 ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) as proof of (((eq Prop) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) b)
% Found ((eq_ref Prop) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) as proof of (((eq Prop) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) b)
% Found ((eq_ref Prop) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) as proof of (((eq Prop) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) b)
% Found ((eq_ref Prop) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) as proof of (((eq Prop) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) b)
% Found eq_ref00:=(eq_ref0 ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))):(((eq Prop) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))
% Found (eq_ref0 ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) as proof of (((eq Prop) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) b)
% Found ((eq_ref Prop) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) as proof of (((eq Prop) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) b)
% Found ((eq_ref Prop) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) as proof of (((eq Prop) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) b)
% Found ((eq_ref Prop) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) as proof of (((eq Prop) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (f x0))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% Found x0100:=(x010 x00):(V Xx)
% Found (x010 x00) as proof of (V Xx)
% Found ((x01 V) x00) as proof of (V Xx)
% Found ((x01 V) x00) as proof of (V Xx)
% Found (fun (x01:(x2 Xx))=> ((x01 V) x00)) as proof of (V Xx)
% Found (fun (Xx:fofType) (x01:(x2 Xx))=> ((x01 V) x00)) as proof of ((x2 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType) (x01:(x2 Xx))=> ((x01 V) x00)) as proof of (forall (Xx:fofType), ((x2 Xx)->(V Xx)))
% Found (fun (V:(fofType->Prop)) (x00:(cC V)) (Xx:fofType) (x01:(x2 Xx))=> ((x01 V) x00)) as proof of ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))
% Found (fun (V:(fofType->Prop)) (x00:(cC V)) (Xx:fofType) (x01:(x2 Xx))=> ((x01 V) x00)) as proof of b
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x2) Xx)):((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x2) Xx)) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx)) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x2) Xx)):((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x2) Xx)) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx)) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) b) Xx)):((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x0) Xx)):((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found eq_ref000:=(eq_ref00 x4):((x4 Xx)->(x4 Xx))
% Found (eq_ref00 x4) as proof of ((x4 Xx)->(V Xx))
% Found ((eq_ref0 Xx) x4) as proof of ((x4 Xx)->(V Xx))
% Found (((eq_ref fofType) Xx) x4) as proof of ((x4 Xx)->(V Xx))
% Found (((eq_ref fofType) Xx) x4) as proof of ((x4 Xx)->(V Xx))
% Found (fun (Xx:fofType)=> (((eq_ref fofType) Xx) x4)) as proof of ((x4 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType)=> (((eq_ref fofType) Xx) x4)) as proof of (forall (Xx:fofType), ((x4 Xx)->(V Xx)))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) f) Xx)):((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) f) Xx)):((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found eq_ref00:=(eq_ref0 (f x5)):(((eq Prop) (f x5)) (f x5))
% Found (eq_ref0 (f x5)) as proof of (((eq Prop) (f x5)) (x0 x5))
% Found ((eq_ref Prop) (f x5)) as proof of (((eq Prop) (f x5)) (x0 x5))
% Found ((eq_ref Prop) (f x5)) as proof of (((eq Prop) (f x5)) (x0 x5))
% Found (fun (x5:fofType)=> ((eq_ref Prop) (f x5))) as proof of (((eq Prop) (f x5)) (x0 x5))
% Found (fun (x5:fofType)=> ((eq_ref Prop) (f x5))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (x0 x)))
% Found eq_ref00:=(eq_ref0 (f x5)):(((eq Prop) (f x5)) (f x5))
% Found (eq_ref0 (f x5)) as proof of (((eq Prop) (f x5)) (x0 x5))
% Found ((eq_ref Prop) (f x5)) as proof of (((eq Prop) (f x5)) (x0 x5))
% Found ((eq_ref Prop) (f x5)) as proof of (((eq Prop) (f x5)) (x0 x5))
% Found (fun (x5:fofType)=> ((eq_ref Prop) (f x5))) as proof of (((eq Prop) (f x5)) (x0 x5))
% Found (fun (x5:fofType)=> ((eq_ref Prop) (f x5))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (x0 x)))
% Found eq_ref00:=(eq_ref0 (f x5)):(((eq Prop) (f x5)) (f x5))
% Found (eq_ref0 (f x5)) as proof of (((eq Prop) (f x5)) (x0 x5))
% Found ((eq_ref Prop) (f x5)) as proof of (((eq Prop) (f x5)) (x0 x5))
% Found ((eq_ref Prop) (f x5)) as proof of (((eq Prop) (f x5)) (x0 x5))
% Found (fun (x5:fofType)=> ((eq_ref Prop) (f x5))) as proof of (((eq Prop) (f x5)) (x0 x5))
% Found (fun (x5:fofType)=> ((eq_ref Prop) (f x5))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (x0 x)))
% Found eq_ref00:=(eq_ref0 (f x5)):(((eq Prop) (f x5)) (f x5))
% Found (eq_ref0 (f x5)) as proof of (((eq Prop) (f x5)) (x0 x5))
% Found ((eq_ref Prop) (f x5)) as proof of (((eq Prop) (f x5)) (x0 x5))
% Found ((eq_ref Prop) (f x5)) as proof of (((eq Prop) (f x5)) (x0 x5))
% Found (fun (x5:fofType)=> ((eq_ref Prop) (f x5))) as proof of (((eq Prop) (f x5)) (x0 x5))
% Found (fun (x5:fofType)=> ((eq_ref Prop) (f x5))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (x0 x)))
% Found eq_ref00:=(eq_ref0 (f x5)):(((eq Prop) (f x5)) (f x5))
% Found (eq_ref0 (f x5)) as proof of (((eq Prop) (f x5)) (x2 x5))
% Found ((eq_ref Prop) (f x5)) as proof of (((eq Prop) (f x5)) (x2 x5))
% Found ((eq_ref Prop) (f x5)) as proof of (((eq Prop) (f x5)) (x2 x5))
% Found (fun (x5:fofType)=> ((eq_ref Prop) (f x5))) as proof of (((eq Prop) (f x5)) (x2 x5))
% Found (fun (x5:fofType)=> ((eq_ref Prop) (f x5))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (x2 x)))
% Found eq_ref00:=(eq_ref0 (f x5)):(((eq Prop) (f x5)) (f x5))
% Found (eq_ref0 (f x5)) as proof of (((eq Prop) (f x5)) (x2 x5))
% Found ((eq_ref Prop) (f x5)) as proof of (((eq Prop) (f x5)) (x2 x5))
% Found ((eq_ref Prop) (f x5)) as proof of (((eq Prop) (f x5)) (x2 x5))
% Found (fun (x5:fofType)=> ((eq_ref Prop) (f x5))) as proof of (((eq Prop) (f x5)) (x2 x5))
% Found (fun (x5:fofType)=> ((eq_ref Prop) (f x5))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (x2 x)))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) b) Xx)):((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found eq_ref00:=(eq_ref0 (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))):(((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))))
% Found (eq_ref0 (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) b)
% Found ((eq_ref Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) b)
% Found ((eq_ref Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) b)
% Found ((eq_ref Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) b)
% Found eq_ref00:=(eq_ref0 (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))):(((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))))
% Found (eq_ref0 (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) b)
% Found ((eq_ref Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) b)
% Found ((eq_ref Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) b)
% Found ((eq_ref Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) b)
% Found eq_ref00:=(eq_ref0 (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))):(((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))))
% Found (eq_ref0 (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))) b)
% Found ((eq_ref Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))) b)
% Found ((eq_ref Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))) b)
% Found ((eq_ref Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))) b)
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x0) Xx)):((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of b
% Found eq_ref00:=(eq_ref0 (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))):(((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))))
% Found (eq_ref0 (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) b)
% Found ((eq_ref Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) b)
% Found ((eq_ref Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) b)
% Found ((eq_ref Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) b)
% Found eq_ref000:=(eq_ref00 P0):((P0 (f x4))->(P0 (f x4)))
% Found (eq_ref00 P0) as proof of (P1 (f x4))
% Found ((eq_ref0 (f x4)) P0) as proof of (P1 (f x4))
% Found (((eq_ref Prop) (f x4)) P0) as proof of (P1 (f x4))
% Found (((eq_ref Prop) (f x4)) P0) as proof of (P1 (f x4))
% Found eq_ref000:=(eq_ref00 P0):((P0 (f x4))->(P0 (f x4)))
% Found (eq_ref00 P0) as proof of (P1 (f x4))
% Found ((eq_ref0 (f x4)) P0) as proof of (P1 (f x4))
% Found (((eq_ref Prop) (f x4)) P0) as proof of (P1 (f x4))
% Found (((eq_ref Prop) (f x4)) P0) as proof of (P1 (f x4))
% Found eq_ref00:=(eq_ref0 (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))):(((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))))
% Found (eq_ref0 (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) b)
% Found ((eq_ref Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) b)
% Found ((eq_ref Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) b)
% Found ((eq_ref Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) b)
% Found eq_ref00:=(eq_ref0 (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))):(((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))))
% Found (eq_ref0 (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))) b)
% Found ((eq_ref Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))) b)
% Found ((eq_ref Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))) b)
% Found ((eq_ref Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))) b)
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) f) Xx)):((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) f) Xx)):((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) f) Xx)):((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) f) Xx)):((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x0) Xx)):((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) b) Xx)):((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) b) Xx)):((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found x000:(x0 Xx)
% Instantiate: x0:=V:(fofType->Prop)
% Found x000 as proof of (V Xx)
% Found (fun (x000:(x0 Xx))=> x000) as proof of (V Xx)
% Found (fun (Xx:fofType) (x000:(x0 Xx))=> x000) as proof of ((x0 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType) (x000:(x0 Xx))=> x000) as proof of (forall (Xx:fofType), ((x0 Xx)->(V Xx)))
% Found x000:(x0 Xx)
% Instantiate: x0:=V:(fofType->Prop)
% Found x000 as proof of (V Xx)
% Found (fun (x000:(x0 Xx))=> x000) as proof of (V Xx)
% Found (fun (Xx:fofType) (x000:(x0 Xx))=> x000) as proof of ((x0 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType) (x000:(x0 Xx))=> x000) as proof of (forall (Xx:fofType), ((x0 Xx)->(V Xx)))
% Found x000:(x0 Xx)
% Instantiate: x0:=V:(fofType->Prop)
% Found x000 as proof of (V Xx)
% Found (fun (x000:(x0 Xx))=> x000) as proof of (V Xx)
% Found (fun (Xx:fofType) (x000:(x0 Xx))=> x000) as proof of ((x0 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType) (x000:(x0 Xx))=> x000) as proof of (forall (Xx:fofType), ((x0 Xx)->(V Xx)))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x0) Xx)):((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of b
% Found eq_ref00:=(eq_ref0 (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))):(((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))))
% Found (eq_ref0 (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) b)
% Found ((eq_ref Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) b)
% Found ((eq_ref Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) b)
% Found ((eq_ref Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) b)
% Found eq_ref00:=(eq_ref0 (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))):(((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))))
% Found (eq_ref0 (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) b)
% Found ((eq_ref Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) b)
% Found ((eq_ref Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) b)
% Found ((eq_ref Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))) b)
% Found eq_ref00:=(eq_ref0 (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))):(((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))))
% Found (eq_ref0 (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))) b)
% Found ((eq_ref Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))) b)
% Found ((eq_ref Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))) b)
% Found ((eq_ref Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))) as proof of (((eq Prop) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))) b)
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) f) Xx)):((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) f) Xx)):((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) b) Xx)):((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) b) Xx)):((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found eq_ref000:=(eq_ref00 x0):((x0 Xx)->(x0 Xx))
% Found (eq_ref00 x0) as proof of ((x0 Xx)->(V Xx))
% Found ((eq_ref0 Xx) x0) as proof of ((x0 Xx)->(V Xx))
% Found (((eq_ref fofType) Xx) x0) as proof of ((x0 Xx)->(V Xx))
% Found (((eq_ref fofType) Xx) x0) as proof of ((x0 Xx)->(V Xx))
% Found (fun (Xx:fofType)=> (((eq_ref fofType) Xx) x0)) as proof of ((x0 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType)=> (((eq_ref fofType) Xx) x0)) as proof of (forall (Xx:fofType), ((x0 Xx)->(V Xx)))
% Found eq_ref000:=(eq_ref00 x2):((x2 Xx)->(x2 Xx))
% Found (eq_ref00 x2) as proof of ((x2 Xx)->(V Xx))
% Found ((eq_ref0 Xx) x2) as proof of ((x2 Xx)->(V Xx))
% Found (((eq_ref fofType) Xx) x2) as proof of ((x2 Xx)->(V Xx))
% Found (((eq_ref fofType) Xx) x2) as proof of ((x2 Xx)->(V Xx))
% Found (fun (Xx:fofType)=> (((eq_ref fofType) Xx) x2)) as proof of ((x2 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType)=> (((eq_ref fofType) Xx) x2)) as proof of (forall (Xx:fofType), ((x2 Xx)->(V Xx)))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) f) Xx)):((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) f) Xx)):((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x0) Xx)):((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of b
% Found x000:(x0 Xx)
% Instantiate: x0:=V:(fofType->Prop)
% Found x000 as proof of (V Xx)
% Found (fun (x000:(x0 Xx))=> x000) as proof of (V Xx)
% Found (fun (Xx:fofType) (x000:(x0 Xx))=> x000) as proof of ((x0 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType) (x000:(x0 Xx))=> x000) as proof of (forall (Xx:fofType), ((x0 Xx)->(V Xx)))
% Found x000:(x0 Xx)
% Instantiate: x0:=V:(fofType->Prop)
% Found x000 as proof of (V Xx)
% Found (fun (x000:(x0 Xx))=> x000) as proof of (V Xx)
% Found (fun (Xx:fofType) (x000:(x0 Xx))=> x000) as proof of ((x0 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType) (x000:(x0 Xx))=> x000) as proof of (forall (Xx:fofType), ((x0 Xx)->(V Xx)))
% Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Instantiate: b:=(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C)))):Prop
% Found iff_trans as proof of b
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))
% Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b)
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% Found ((eq_trans0000 ((eq_ref Prop) (f x0))) ((eq_ref Prop) b)) as proof of (((eq Prop) (f x0)) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))
% Found (((eq_trans000 ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) ((eq_ref Prop) (f x0))) ((eq_ref Prop) b)) as proof of (((eq Prop) (f x0)) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))
% Found ((((eq_trans00 ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) ((eq_ref Prop) (f x0))) ((eq_ref Prop) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))) as proof of (((eq Prop) (f x0)) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))
% Found (((((eq_trans0 (f x0)) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) ((eq_ref Prop) (f x0))) ((eq_ref Prop) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))) as proof of (((eq Prop) (f x0)) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))
% Found ((((((eq_trans Prop) (f x0)) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) ((eq_ref Prop) (f x0))) ((eq_ref Prop) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))) as proof of (((eq Prop) (f x0)) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))
% Found (fun (x2:(forall (Xw:(((fofType->Prop)->Prop)->Prop)), (((and (Xw (fun (Xx:(fofType->Prop))=> False))) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xw Xr)->(Xw (fun (Xt:(fofType->Prop))=> ((or (Xr Xt)) (((eq (fofType->Prop)) Xt) Xx)))))))->(Xw cC))))=> ((((((eq_trans Prop) (f x0)) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) ((eq_ref Prop) (f x0))) ((eq_ref Prop) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))))) as proof of (((eq Prop) (f x0)) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))
% Found (fun (x1:((and (forall (X:(fofType->Prop)) (Y:(fofType->Prop)), (((and (cL X)) (cL Y))->((or (forall (Xx:fofType), ((X Xx)->(Y Xx)))) (forall (Xx:fofType), ((Y Xx)->(X Xx))))))) (forall (Xx:(fofType->Prop)), ((cC Xx)->(cL Xx))))) (x2:(forall (Xw:(((fofType->Prop)->Prop)->Prop)), (((and (Xw (fun (Xx:(fofType->Prop))=> False))) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xw Xr)->(Xw (fun (Xt:(fofType->Prop))=> ((or (Xr Xt)) (((eq (fofType->Prop)) Xt) Xx)))))))->(Xw cC))))=> ((((((eq_trans Prop) (f x0)) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) ((eq_ref Prop) (f x0))) ((eq_ref Prop) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))))) as proof of ((forall (Xw:(((fofType->Prop)->Prop)->Prop)), (((and (Xw (fun (Xx:(fofType->Prop))=> False))) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xw Xr)->(Xw (fun (Xt:(fofType->Prop))=> ((or (Xr Xt)) (((eq (fofType->Prop)) Xt) Xx)))))))->(Xw cC)))->(((eq Prop) (f x0)) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))))
% Found (fun (x1:((and (forall (X:(fofType->Prop)) (Y:(fofType->Prop)), (((and (cL X)) (cL Y))->((or (forall (Xx:fofType), ((X Xx)->(Y Xx)))) (forall (Xx:fofType), ((Y Xx)->(X Xx))))))) (forall (Xx:(fofType->Prop)), ((cC Xx)->(cL Xx))))) (x2:(forall (Xw:(((fofType->Prop)->Prop)->Prop)), (((and (Xw (fun (Xx:(fofType->Prop))=> False))) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xw Xr)->(Xw (fun (Xt:(fofType->Prop))=> ((or (Xr Xt)) (((eq (fofType->Prop)) Xt) Xx)))))))->(Xw cC))))=> ((((((eq_trans Prop) (f x0)) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) ((eq_ref Prop) (f x0))) ((eq_ref Prop) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))))) as proof of (((and (forall (X:(fofType->Prop)) (Y:(fofType->Prop)), (((and (cL X)) (cL Y))->((or (forall (Xx:fofType), ((X Xx)->(Y Xx)))) (forall (Xx:fofType), ((Y Xx)->(X Xx))))))) (forall (Xx:(fofType->Prop)), ((cC Xx)->(cL Xx))))->((forall (Xw:(((fofType->Prop)->Prop)->Prop)), (((and (Xw (fun (Xx:(fofType->Prop))=> False))) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xw Xr)->(Xw (fun (Xt:(fofType->Prop))=> ((or (Xr Xt)) (((eq (fofType->Prop)) Xt) Xx)))))))->(Xw cC)))->(((eq Prop) (f x0)) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))))
% Found (and_rect00 (fun (x1:((and (forall (X:(fofType->Prop)) (Y:(fofType->Prop)), (((and (cL X)) (cL Y))->((or (forall (Xx:fofType), ((X Xx)->(Y Xx)))) (forall (Xx:fofType), ((Y Xx)->(X Xx))))))) (forall (Xx:(fofType->Prop)), ((cC Xx)->(cL Xx))))) (x2:(forall (Xw:(((fofType->Prop)->Prop)->Prop)), (((and (Xw (fun (Xx:(fofType->Prop))=> False))) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xw Xr)->(Xw (fun (Xt:(fofType->Prop))=> ((or (Xr Xt)) (((eq (fofType->Prop)) Xt) Xx)))))))->(Xw cC))))=> ((((((eq_trans Prop) (f x0)) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) ((eq_ref Prop) (f x0))) ((eq_ref Prop) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))))) as proof of (((eq Prop) (f x0)) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))
% Found ((and_rect0 (((eq Prop) (f x0)) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))) (fun (x1:((and (forall (X:(fofType->Prop)) (Y:(fofType->Prop)), (((and (cL X)) (cL Y))->((or (forall (Xx:fofType), ((X Xx)->(Y Xx)))) (forall (Xx:fofType), ((Y Xx)->(X Xx))))))) (forall (Xx:(fofType->Prop)), ((cC Xx)->(cL Xx))))) (x2:(forall (Xw:(((fofType->Prop)->Prop)->Prop)), (((and (Xw (fun (Xx:(fofType->Prop))=> False))) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xw Xr)->(Xw (fun (Xt:(fofType->Prop))=> ((or (Xr Xt)) (((eq (fofType->Prop)) Xt) Xx)))))))->(Xw cC))))=> ((((((eq_trans Prop) (f x0)) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) ((eq_ref Prop) (f x0))) ((eq_ref Prop) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))))) as proof of (((eq Prop) (f x0)) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))
% Found (((fun (P0:Type) (x1:(((and (forall (X:(fofType->Prop)) (Y:(fofType->Prop)), (((and (cL X)) (cL Y))->((or (forall (Xx:fofType), ((X Xx)->(Y Xx)))) (forall (Xx:fofType), ((Y Xx)->(X Xx))))))) (forall (Xx:(fofType->Prop)), ((cC Xx)->(cL Xx))))->((forall (Xw:(((fofType->Prop)->Prop)->Prop)), (((and (Xw (fun (Xx:(fofType->Prop))=> False))) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xw Xr)->(Xw (fun (Xt:(fofType->Prop))=> ((or (Xr Xt)) (((eq (fofType->Prop)) Xt) Xx)))))))->(Xw cC)))->P0)))=> (((((and_rect ((and (forall (X:(fofType->Prop)) (Y:(fofType->Prop)), (((and (cL X)) (cL Y))->((or (forall (Xx:fofType), ((X Xx)->(Y Xx)))) (forall (Xx:fofType), ((Y Xx)->(X Xx))))))) (forall (Xx:(fofType->Prop)), ((cC Xx)->(cL Xx))))) (forall (Xw:(((fofType->Prop)->Prop)->Prop)), (((and (Xw (fun (Xx:(fofType->Prop))=> False))) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xw Xr)->(Xw (fun (Xt:(fofType->Prop))=> ((or (Xr Xt)) (((eq (fofType->Prop)) Xt) Xx)))))))->(Xw cC)))) P0) x1) x)) (((eq Prop) (f x0)) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))) (fun (x1:((and (forall (X:(fofType->Prop)) (Y:(fofType->Prop)), (((and (cL X)) (cL Y))->((or (forall (Xx:fofType), ((X Xx)->(Y Xx)))) (forall (Xx:fofType), ((Y Xx)->(X Xx))))))) (forall (Xx:(fofType->Prop)), ((cC Xx)->(cL Xx))))) (x2:(forall (Xw:(((fofType->Prop)->Prop)->Prop)), (((and (Xw (fun (Xx:(fofType->Prop))=> False))) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xw Xr)->(Xw (fun (Xt:(fofType->Prop))=> ((or (Xr Xt)) (((eq (fofType->Prop)) Xt) Xx)))))))->(Xw cC))))=> ((((((eq_trans Prop) (f x0)) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) ((eq_ref Prop) (f x0))) ((eq_ref Prop) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))))) as proof of (((eq Prop) (f x0)) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))
% Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b)
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))
% Found ((eq_trans0000 ((eq_ref Prop) (f x0))) ((eq_ref Prop) b)) as proof of (((eq Prop) (f x0)) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))
% Found (((eq_trans000 ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) ((eq_ref Prop) (f x0))) ((eq_ref Prop) b)) as proof of (((eq Prop) (f x0)) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))
% Found ((((eq_trans00 ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) ((eq_ref Prop) (f x0))) ((eq_ref Prop) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))) as proof of (((eq Prop) (f x0)) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))
% Found (((((eq_trans0 (f x0)) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) ((eq_ref Prop) (f x0))) ((eq_ref Prop) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))) as proof of (((eq Prop) (f x0)) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))
% Found ((((((eq_trans Prop) (f x0)) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) ((eq_ref Prop) (f x0))) ((eq_ref Prop) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))) as proof of (((eq Prop) (f x0)) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))
% Found (fun (x2:(forall (Xw:(((fofType->Prop)->Prop)->Prop)), (((and (Xw (fun (Xx:(fofType->Prop))=> False))) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xw Xr)->(Xw (fun (Xt:(fofType->Prop))=> ((or (Xr Xt)) (((eq (fofType->Prop)) Xt) Xx)))))))->(Xw cC))))=> ((((((eq_trans Prop) (f x0)) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) ((eq_ref Prop) (f x0))) ((eq_ref Prop) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))))) as proof of (((eq Prop) (f x0)) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))
% Found (fun (x1:((and (forall (X:(fofType->Prop)) (Y:(fofType->Prop)), (((and (cL X)) (cL Y))->((or (forall (Xx:fofType), ((X Xx)->(Y Xx)))) (forall (Xx:fofType), ((Y Xx)->(X Xx))))))) (forall (Xx:(fofType->Prop)), ((cC Xx)->(cL Xx))))) (x2:(forall (Xw:(((fofType->Prop)->Prop)->Prop)), (((and (Xw (fun (Xx:(fofType->Prop))=> False))) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xw Xr)->(Xw (fun (Xt:(fofType->Prop))=> ((or (Xr Xt)) (((eq (fofType->Prop)) Xt) Xx)))))))->(Xw cC))))=> ((((((eq_trans Prop) (f x0)) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) ((eq_ref Prop) (f x0))) ((eq_ref Prop) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))))) as proof of ((forall (Xw:(((fofType->Prop)->Prop)->Prop)), (((and (Xw (fun (Xx:(fofType->Prop))=> False))) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xw Xr)->(Xw (fun (Xt:(fofType->Prop))=> ((or (Xr Xt)) (((eq (fofType->Prop)) Xt) Xx)))))))->(Xw cC)))->(((eq Prop) (f x0)) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))))
% Found (fun (x1:((and (forall (X:(fofType->Prop)) (Y:(fofType->Prop)), (((and (cL X)) (cL Y))->((or (forall (Xx:fofType), ((X Xx)->(Y Xx)))) (forall (Xx:fofType), ((Y Xx)->(X Xx))))))) (forall (Xx:(fofType->Prop)), ((cC Xx)->(cL Xx))))) (x2:(forall (Xw:(((fofType->Prop)->Prop)->Prop)), (((and (Xw (fun (Xx:(fofType->Prop))=> False))) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xw Xr)->(Xw (fun (Xt:(fofType->Prop))=> ((or (Xr Xt)) (((eq (fofType->Prop)) Xt) Xx)))))))->(Xw cC))))=> ((((((eq_trans Prop) (f x0)) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) ((eq_ref Prop) (f x0))) ((eq_ref Prop) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))))) as proof of (((and (forall (X:(fofType->Prop)) (Y:(fofType->Prop)), (((and (cL X)) (cL Y))->((or (forall (Xx:fofType), ((X Xx)->(Y Xx)))) (forall (Xx:fofType), ((Y Xx)->(X Xx))))))) (forall (Xx:(fofType->Prop)), ((cC Xx)->(cL Xx))))->((forall (Xw:(((fofType->Prop)->Prop)->Prop)), (((and (Xw (fun (Xx:(fofType->Prop))=> False))) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xw Xr)->(Xw (fun (Xt:(fofType->Prop))=> ((or (Xr Xt)) (((eq (fofType->Prop)) Xt) Xx)))))))->(Xw cC)))->(((eq Prop) (f x0)) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))))
% Found (and_rect00 (fun (x1:((and (forall (X:(fofType->Prop)) (Y:(fofType->Prop)), (((and (cL X)) (cL Y))->((or (forall (Xx:fofType), ((X Xx)->(Y Xx)))) (forall (Xx:fofType), ((Y Xx)->(X Xx))))))) (forall (Xx:(fofType->Prop)), ((cC Xx)->(cL Xx))))) (x2:(forall (Xw:(((fofType->Prop)->Prop)->Prop)), (((and (Xw (fun (Xx:(fofType->Prop))=> False))) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xw Xr)->(Xw (fun (Xt:(fofType->Prop))=> ((or (Xr Xt)) (((eq (fofType->Prop)) Xt) Xx)))))))->(Xw cC))))=> ((((((eq_trans Prop) (f x0)) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) ((eq_ref Prop) (f x0))) ((eq_ref Prop) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))))) as proof of (((eq Prop) (f x0)) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))
% Found ((and_rect0 (((eq Prop) (f x0)) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))) (fun (x1:((and (forall (X:(fofType->Prop)) (Y:(fofType->Prop)), (((and (cL X)) (cL Y))->((or (forall (Xx:fofType), ((X Xx)->(Y Xx)))) (forall (Xx:fofType), ((Y Xx)->(X Xx))))))) (forall (Xx:(fofType->Prop)), ((cC Xx)->(cL Xx))))) (x2:(forall (Xw:(((fofType->Prop)->Prop)->Prop)), (((and (Xw (fun (Xx:(fofType->Prop))=> False))) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xw Xr)->(Xw (fun (Xt:(fofType->Prop))=> ((or (Xr Xt)) (((eq (fofType->Prop)) Xt) Xx)))))))->(Xw cC))))=> ((((((eq_trans Prop) (f x0)) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) ((eq_ref Prop) (f x0))) ((eq_ref Prop) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))))) as proof of (((eq Prop) (f x0)) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))
% Found (((fun (P0:Type) (x1:(((and (forall (X:(fofType->Prop)) (Y:(fofType->Prop)), (((and (cL X)) (cL Y))->((or (forall (Xx:fofType), ((X Xx)->(Y Xx)))) (forall (Xx:fofType), ((Y Xx)->(X Xx))))))) (forall (Xx:(fofType->Prop)), ((cC Xx)->(cL Xx))))->((forall (Xw:(((fofType->Prop)->Prop)->Prop)), (((and (Xw (fun (Xx:(fofType->Prop))=> False))) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xw Xr)->(Xw (fun (Xt:(fofType->Prop))=> ((or (Xr Xt)) (((eq (fofType->Prop)) Xt) Xx)))))))->(Xw cC)))->P0)))=> (((((and_rect ((and (forall (X:(fofType->Prop)) (Y:(fofType->Prop)), (((and (cL X)) (cL Y))->((or (forall (Xx:fofType), ((X Xx)->(Y Xx)))) (forall (Xx:fofType), ((Y Xx)->(X Xx))))))) (forall (Xx:(fofType->Prop)), ((cC Xx)->(cL Xx))))) (forall (Xw:(((fofType->Prop)->Prop)->Prop)), (((and (Xw (fun (Xx:(fofType->Prop))=> False))) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xw Xr)->(Xw (fun (Xt:(fofType->Prop))=> ((or (Xr Xt)) (((eq (fofType->Prop)) Xt) Xx)))))))->(Xw cC)))) P0) x1) x)) (((eq Prop) (f x0)) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))) (fun (x1:((and (forall (X:(fofType->Prop)) (Y:(fofType->Prop)), (((and (cL X)) (cL Y))->((or (forall (Xx:fofType), ((X Xx)->(Y Xx)))) (forall (Xx:fofType), ((Y Xx)->(X Xx))))))) (forall (Xx:(fofType->Prop)), ((cC Xx)->(cL Xx))))) (x2:(forall (Xw:(((fofType->Prop)->Prop)->Prop)), (((and (Xw (fun (Xx:(fofType->Prop))=> False))) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xw Xr)->(Xw (fun (Xt:(fofType->Prop))=> ((or (Xr Xt)) (((eq (fofType->Prop)) Xt) Xx)))))))->(Xw cC))))=> ((((((eq_trans Prop) (f x0)) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) ((eq_ref Prop) (f x0))) ((eq_ref Prop) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))))) as proof of (((eq Prop) (f x0)) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) b) Xx)):((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) b) Xx)):((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) f) Xx)):((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) f) Xx)):((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) f) Xx)):((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) f) Xx)):((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x0) Xx)):((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x0) Xx)):((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of b
% Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Instantiate: b:=(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C)))):Prop
% Found iff_trans as proof of b
% Found x01:(x4 Xx)
% Instantiate: x4:=V:(fofType->Prop)
% Found x01 as proof of (V Xx)
% Found (fun (x01:(x4 Xx))=> x01) as proof of (V Xx)
% Found (fun (Xx:fofType) (x01:(x4 Xx))=> x01) as proof of ((x4 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType) (x01:(x4 Xx))=> x01) as proof of (forall (Xx:fofType), ((x4 Xx)->(V Xx)))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) b) Xx)):((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) f) Xx)):((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) f) Xx)):((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) f) Xx)):((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) f) Xx)):((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x0) Xx)):((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Instantiate: b:=(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C)))):Prop
% Found iff_trans as proof of b
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) f) Xx)):((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) f) Xx)):((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) f) Xx)):((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) f) Xx)):((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x0) Xx)):((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Instantiate: b:=(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C)))):Prop
% Found iff_trans as proof of b
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) b) Xx)):((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found eq_ref000:=(eq_ref00 x0):((x0 Xx)->(x0 Xx))
% Found (eq_ref00 x0) as proof of ((x0 Xx)->(V Xx))
% Found ((eq_ref0 Xx) x0) as proof of ((x0 Xx)->(V Xx))
% Found (((eq_ref fofType) Xx) x0) as proof of ((x0 Xx)->(V Xx))
% Found (((eq_ref fofType) Xx) x0) as proof of ((x0 Xx)->(V Xx))
% Found (fun (Xx:fofType)=> (((eq_ref fofType) Xx) x0)) as proof of ((x0 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType)=> (((eq_ref fofType) Xx) x0)) as proof of (forall (Xx:fofType), ((x0 Xx)->(V Xx)))
% Found eq_ref000:=(eq_ref00 x0):((x0 Xx)->(x0 Xx))
% Found (eq_ref00 x0) as proof of ((x0 Xx)->(V Xx))
% Found ((eq_ref0 Xx) x0) as proof of ((x0 Xx)->(V Xx))
% Found (((eq_ref fofType) Xx) x0) as proof of ((x0 Xx)->(V Xx))
% Found (((eq_ref fofType) Xx) x0) as proof of ((x0 Xx)->(V Xx))
% Found (fun (Xx:fofType)=> (((eq_ref fofType) Xx) x0)) as proof of ((x0 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType)=> (((eq_ref fofType) Xx) x0)) as proof of (forall (Xx:fofType), ((x0 Xx)->(V Xx)))
% Found eq_ref000:=(eq_ref00 x2):((x2 Xx)->(x2 Xx))
% Found (eq_ref00 x2) as proof of ((x2 Xx)->(V Xx))
% Found ((eq_ref0 Xx) x2) as proof of ((x2 Xx)->(V Xx))
% Found (((eq_ref fofType) Xx) x2) as proof of ((x2 Xx)->(V Xx))
% Found (((eq_ref fofType) Xx) x2) as proof of ((x2 Xx)->(V Xx))
% Found (fun (Xx:fofType)=> (((eq_ref fofType) Xx) x2)) as proof of ((x2 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType)=> (((eq_ref fofType) Xx) x2)) as proof of (forall (Xx:fofType), ((x2 Xx)->(V Xx)))
% Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Instantiate: b:=(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C)))):Prop
% Found iff_trans as proof of b
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x0) Xx)):((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found x000:(x0 Xx)
% Instantiate: x0:=V:(fofType->Prop)
% Found x000 as proof of (V Xx)
% Found (fun (x000:(x0 Xx))=> x000) as proof of (V Xx)
% Found (fun (Xx:fofType) (x000:(x0 Xx))=> x000) as proof of ((x0 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType) (x000:(x0 Xx))=> x000) as proof of (forall (Xx:fofType), ((x0 Xx)->(V Xx)))
% Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Instantiate: b:=(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C)))):Prop
% Found iff_trans as proof of b
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) f) Xx)):((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) f) Xx)):((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found x01:(x2 Xx)
% Instantiate: x2:=V:(fofType->Prop)
% Found x01 as proof of (V Xx)
% Found (fun (x01:(x2 Xx))=> x01) as proof of (V Xx)
% Found (fun (Xx:fofType) (x01:(x2 Xx))=> x01) as proof of ((x2 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType) (x01:(x2 Xx))=> x01) as proof of (forall (Xx:fofType), ((x2 Xx)->(V Xx)))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x0) Xx)):((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) b) Xx)):((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) b) Xx)):((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found x01:(x4 Xx)
% Instantiate: x4:=V:(fofType->Prop)
% Found x01 as proof of (V Xx)
% Found (fun (x01:(x4 Xx))=> x01) as proof of (V Xx)
% Found (fun (Xx:fofType) (x01:(x4 Xx))=> x01) as proof of ((x4 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType) (x01:(x4 Xx))=> x01) as proof of (forall (Xx:fofType), ((x4 Xx)->(V Xx)))
% Found x01:(x4 Xx)
% Instantiate: x4:=V:(fofType->Prop)
% Found x01 as proof of (V Xx)
% Found (fun (x01:(x4 Xx))=> x01) as proof of (V Xx)
% Found (fun (Xx:fofType) (x01:(x4 Xx))=> x01) as proof of ((x4 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType) (x01:(x4 Xx))=> x01) as proof of (forall (Xx:fofType), ((x4 Xx)->(V Xx)))
% Found x01:(x4 Xx)
% Instantiate: x4:=V:(fofType->Prop)
% Found x01 as proof of (V Xx)
% Found (fun (x01:(x4 Xx))=> x01) as proof of (V Xx)
% Found (fun (Xx:fofType) (x01:(x4 Xx))=> x01) as proof of ((x4 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType) (x01:(x4 Xx))=> x01) as proof of (forall (Xx:fofType), ((x4 Xx)->(V Xx)))
% Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Instantiate: b:=(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C)))):Prop
% Found iff_trans as proof of b
% Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Instantiate: b:=(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C)))):Prop
% Found iff_trans as proof of b
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x0) Xx)):((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Instantiate: b:=(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C)))):Prop
% Found iff_trans as proof of b
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) b) Xx)):((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) f) Xx)):((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) f) Xx)):((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Instantiate: b:=(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C)))):Prop
% Found iff_trans as proof of b
% Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Instantiate: b:=(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C)))):Prop
% Found iff_trans as proof of b
% Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Instantiate: b:=(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C)))):Prop
% Found iff_trans as proof of b
% Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Instantiate: b:=(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C)))):Prop
% Found iff_trans as proof of b
% Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Instantiate: b:=(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C)))):Prop
% Found iff_trans as proof of b
% Found eq_ref00:=(eq_ref0 ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))):(((eq Prop) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))))
% Found (eq_ref0 ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))) as proof of (((eq Prop) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))) b)
% Found ((eq_ref Prop) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))) as proof of (((eq Prop) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))) b)
% Found ((eq_ref Prop) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))) as proof of (((eq Prop) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))) b)
% Found ((eq_ref Prop) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))) as proof of (((eq Prop) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (f x2))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x2))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x2))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x2))
% Found eq_ref00:=(eq_ref0 ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))):(((eq Prop) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))))
% Found (eq_ref0 ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))) as proof of (((eq Prop) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))) b)
% Found ((eq_ref Prop) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))) as proof of (((eq Prop) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))) b)
% Found ((eq_ref Prop) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))) as proof of (((eq Prop) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))) b)
% Found ((eq_ref Prop) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))) as proof of (((eq Prop) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (f x2))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x2))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x2))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x2))
% Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Instantiate: b:=(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C)))):Prop
% Found iff_trans as proof of b
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) f) Xx)):((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) f) Xx)):((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found x000:(x0 Xx)
% Instantiate: x0:=V:(fofType->Prop)
% Found x000 as proof of (V Xx)
% Found (fun (x000:(x0 Xx))=> x000) as proof of (V Xx)
% Found (fun (Xx:fofType) (x000:(x0 Xx))=> x000) as proof of ((x0 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType) (x000:(x0 Xx))=> x000) as proof of (forall (Xx:fofType), ((x0 Xx)->(V Xx)))
% Found x000:(x0 Xx)
% Instantiate: x0:=V:(fofType->Prop)
% Found x000 as proof of (V Xx)
% Found (fun (x000:(x0 Xx))=> x000) as proof of (V Xx)
% Found (fun (Xx:fofType) (x000:(x0 Xx))=> x000) as proof of ((x0 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType) (x000:(x0 Xx))=> x000) as proof of (forall (Xx:fofType), ((x0 Xx)->(V Xx)))
% Found x000:(x0 Xx)
% Instantiate: x0:=V:(fofType->Prop)
% Found x000 as proof of (V Xx)
% Found (fun (x000:(x0 Xx))=> x000) as proof of (V Xx)
% Found (fun (Xx:fofType) (x000:(x0 Xx))=> x000) as proof of ((x0 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType) (x000:(x0 Xx))=> x000) as proof of (forall (Xx:fofType), ((x0 Xx)->(V Xx)))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) f) Xx)):((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) f) Xx)):((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found x01:(x2 Xx)
% Instantiate: x2:=V:(fofType->Prop)
% Found x01 as proof of (V Xx)
% Found (fun (x01:(x2 Xx))=> x01) as proof of (V Xx)
% Found (fun (Xx:fofType) (x01:(x2 Xx))=> x01) as proof of ((x2 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType) (x01:(x2 Xx))=> x01) as proof of (forall (Xx:fofType), ((x2 Xx)->(V Xx)))
% Found x01:(x2 Xx)
% Instantiate: x2:=V:(fofType->Prop)
% Found x01 as proof of (V Xx)
% Found (fun (x01:(x2 Xx))=> x01) as proof of (V Xx)
% Found (fun (Xx:fofType) (x01:(x2 Xx))=> x01) as proof of ((x2 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType) (x01:(x2 Xx))=> x01) as proof of (forall (Xx:fofType), ((x2 Xx)->(V Xx)))
% Found x01:(x2 Xx)
% Instantiate: x2:=V:(fofType->Prop)
% Found x01 as proof of (V Xx)
% Found (fun (x01:(x2 Xx))=> x01) as proof of (V Xx)
% Found (fun (Xx:fofType) (x01:(x2 Xx))=> x01) as proof of ((x2 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType) (x01:(x2 Xx))=> x01) as proof of (forall (Xx:fofType), ((x2 Xx)->(V Xx)))
% Found x0000000:=(x000000 x00):(V Xx)
% Found (x000000 x00) as proof of (V Xx)
% Found ((x00000 V) x00) as proof of (V Xx)
% Found (((fun (V0:(fofType->Prop)) (x001:(cC V0))=> (((x0000 V0) x001) x2)) V) x00) as proof of (V Xx)
% Found (((fun (V0:(fofType->Prop)) (x001:(cC V0))=> ((((fun (V0:(fofType->Prop)) (x001:(cC V0))=> (((x000 V0) x001) x1)) V0) x001) x2)) V) x00) as proof of (V Xx)
% Found (((fun (V0:(fofType->Prop)) (x001:(cC V0))=> ((((fun (V0:(fofType->Prop)) (x001:(cC V0))=> (((x000 V0) x001) x1)) V0) x001) x2)) V) x00) as proof of (V Xx)
% Found (fun (x000:(x0 Xx))=> (((fun (V0:(fofType->Prop)) (x001:(cC V0))=> ((((fun (V0:(fofType->Prop)) (x001:(cC V0))=> (((x000 V0) x001) x1)) V0) x001) x2)) V) x00)) as proof of (V Xx)
% Found (fun (Xx:fofType) (x000:(x0 Xx))=> (((fun (V0:(fofType->Prop)) (x001:(cC V0))=> ((((fun (V0:(fofType->Prop)) (x001:(cC V0))=> (((x000 V0) x001) x1)) V0) x001) x2)) V) x00)) as proof of ((x0 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType) (x000:(x0 Xx))=> (((fun (V0:(fofType->Prop)) (x001:(cC V0))=> ((((fun (V0:(fofType->Prop)) (x001:(cC V0))=> (((x000 V0) x001) x1)) V0) x001) x2)) V) x00)) as proof of (forall (Xx:fofType), ((x0 Xx)->(V Xx)))
% Found (fun (V:(fofType->Prop)) (x00:(cC V)) (Xx:fofType) (x000:(x0 Xx))=> (((fun (V0:(fofType->Prop)) (x001:(cC V0))=> ((((fun (V0:(fofType->Prop)) (x001:(cC V0))=> (((x000 V0) x001) x1)) V0) x001) x2)) V) x00)) as proof of ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))
% Found (fun (V:(fofType->Prop)) (x00:(cC V)) (Xx:fofType) (x000:(x0 Xx))=> (((fun (V0:(fofType->Prop)) (x001:(cC V0))=> ((((fun (V0:(fofType->Prop)) (x001:(cC V0))=> (((x000 V0) x001) x1)) V0) x001) x2)) V) x00)) as proof of b
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x0) Xx)):((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x0) Xx)):((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Instantiate: b:=(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C)))):Prop
% Found iff_trans as proof of b
% Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Instantiate: b:=(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C)))):Prop
% Found iff_trans as proof of b
% Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Instantiate: b:=(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C)))):Prop
% Found iff_trans as proof of b
% Found x000:(x0 Xx)
% Instantiate: x0:=V:(fofType->Prop)
% Found x000 as proof of (V Xx)
% Found (fun (x000:(x0 Xx))=> x000) as proof of (V Xx)
% Found (fun (Xx:fofType) (x000:(x0 Xx))=> x000) as proof of ((x0 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType) (x000:(x0 Xx))=> x000) as proof of (forall (Xx:fofType), ((x0 Xx)->(V Xx)))
% Found x000:(x0 Xx)
% Instantiate: x0:=V:(fofType->Prop)
% Found x000 as proof of (V Xx)
% Found (fun (x000:(x0 Xx))=> x000) as proof of (V Xx)
% Found (fun (Xx:fofType) (x000:(x0 Xx))=> x000) as proof of ((x0 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType) (x000:(x0 Xx))=> x000) as proof of (forall (Xx:fofType), ((x0 Xx)->(V Xx)))
% Found x01:(x2 Xx)
% Instantiate: x2:=V:(fofType->Prop)
% Found x01 as proof of (V Xx)
% Found (fun (x01:(x2 Xx))=> x01) as proof of (V Xx)
% Found (fun (Xx:fofType) (x01:(x2 Xx))=> x01) as proof of ((x2 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType) (x01:(x2 Xx))=> x01) as proof of (forall (Xx:fofType), ((x2 Xx)->(V Xx)))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x4) Xx)):((Xr x4)->((or (Xr x4)) (((eq (fofType->Prop)) x4) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x4) Xx)) as proof of ((Xr x4)->((or (Xr x4)) (((eq (fofType->Prop)) x4) Xx)))
% Found ((or_introl (Xr x4)) (((eq (fofType->Prop)) x4) Xx)) as proof of ((Xr x4)->((or (Xr x4)) (((eq (fofType->Prop)) x4) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x4)) (((eq (fofType->Prop)) x4) Xx))) as proof of ((Xr x4)->((or (Xr x4)) (((eq (fofType->Prop)) x4) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x4)) (((eq (fofType->Prop)) x4) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x4)->((or (Xr x4)) (((eq (fofType->Prop)) x4) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x4)) (((eq (fofType->Prop)) x4) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x4)->((or (Xr x4)) (((eq (fofType->Prop)) x4) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) b) Xx)):((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) f) Xx)):((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) f) Xx)):((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x4) Xx)):((Xr x4)->((or (Xr x4)) (((eq (fofType->Prop)) x4) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x4) Xx)) as proof of ((Xr x4)->((or (Xr x4)) (((eq (fofType->Prop)) x4) Xx)))
% Found ((or_introl (Xr x4)) (((eq (fofType->Prop)) x4) Xx)) as proof of ((Xr x4)->((or (Xr x4)) (((eq (fofType->Prop)) x4) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x4)) (((eq (fofType->Prop)) x4) Xx))) as proof of ((Xr x4)->((or (Xr x4)) (((eq (fofType->Prop)) x4) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x4)) (((eq (fofType->Prop)) x4) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x4)->((or (Xr x4)) (((eq (fofType->Prop)) x4) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x4)) (((eq (fofType->Prop)) x4) Xx))) as proof of b
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x4) Xx)):((Xr x4)->((or (Xr x4)) (((eq (fofType->Prop)) x4) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x4) Xx)) as proof of ((Xr x4)->((or (Xr x4)) (((eq (fofType->Prop)) x4) Xx)))
% Found ((or_introl (Xr x4)) (((eq (fofType->Prop)) x4) Xx)) as proof of ((Xr x4)->((or (Xr x4)) (((eq (fofType->Prop)) x4) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x4)) (((eq (fofType->Prop)) x4) Xx))) as proof of ((Xr x4)->((or (Xr x4)) (((eq (fofType->Prop)) x4) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x4)) (((eq (fofType->Prop)) x4) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x4)->((or (Xr x4)) (((eq (fofType->Prop)) x4) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x4)) (((eq (fofType->Prop)) x4) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x4)->((or (Xr x4)) (((eq (fofType->Prop)) x4) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) b) Xx)):((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) b) Xx)):((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b)
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% Found (eq_sym010 ((eq_ref Prop) (f x0))) as proof of (((eq Prop) b) (f x0))
% Found ((eq_sym01 b) ((eq_ref Prop) (f x0))) as proof of (((eq Prop) b) (f x0))
% Found (((eq_sym0 (f x0)) b) ((eq_ref Prop) (f x0))) as proof of (((eq Prop) b) (f x0))
% Found (((eq_sym0 (f x0)) b) ((eq_ref Prop) (f x0))) as proof of (((eq Prop) b) (f x0))
% Found ((eq_trans0000 ((eq_ref Prop) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))) (((eq_sym0 (f x0)) b) ((eq_ref Prop) (f x0)))) as proof of (((eq Prop) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) (f x0))
% Found (((eq_trans000 (f x0)) ((eq_ref Prop) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))) (((eq_sym0 (f x0)) b) ((eq_ref Prop) (f x0)))) as proof of (((eq Prop) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) (f x0))
% Found ((((eq_trans00 ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) (f x0)) ((eq_ref Prop) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))) (((eq_sym0 (f x0)) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) ((eq_ref Prop) (f x0)))) as proof of (((eq Prop) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) (f x0))
% Found (((((eq_trans0 ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) (f x0)) ((eq_ref Prop) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))) (((eq_sym0 (f x0)) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) ((eq_ref Prop) (f x0)))) as proof of (((eq Prop) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) (f x0))
% Found ((((((eq_trans Prop) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) (f x0)) ((eq_ref Prop) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))) (((eq_sym0 (f x0)) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) ((eq_ref Prop) (f x0)))) as proof of (((eq Prop) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) (f x0))
% Found ((((((eq_trans Prop) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) (f x0)) ((eq_ref Prop) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))) (((eq_sym0 (f x0)) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) ((eq_ref Prop) (f x0)))) as proof of (((eq Prop) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) (f x0))
% Found (eq_sym000 ((((((eq_trans Prop) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) (f x0)) ((eq_ref Prop) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))) (((eq_sym0 (f x0)) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) ((eq_ref Prop) (f x0))))) as proof of (((eq Prop) (f x0)) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))
% Found ((eq_sym00 (f x0)) ((((((eq_trans Prop) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) (f x0)) ((eq_ref Prop) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))) (((eq_sym0 (f x0)) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) ((eq_ref Prop) (f x0))))) as proof of (((eq Prop) (f x0)) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))
% Found (((eq_sym0 ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) (f x0)) ((((((eq_trans Prop) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) (f x0)) ((eq_ref Prop) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))) (((eq_sym0 (f x0)) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) ((eq_ref Prop) (f x0))))) as proof of (((eq Prop) (f x0)) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))
% Found ((((eq_sym Prop) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) (f x0)) ((((((eq_trans Prop) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) (f x0)) ((eq_ref Prop) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))) ((((eq_sym Prop) (f x0)) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))))) ((eq_ref Prop) (f x0))))) as proof of (((eq Prop) (f x0)) ((and (cC x0)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx)))))))
% Found x0100:=(x010 x00):(V Xx)
% Found (x010 x00) as proof of (V Xx)
% Found ((x01 V) x00) as proof of (V Xx)
% Found ((x01 V) x00) as proof of (V Xx)
% Found (fun (x01:(x4 Xx))=> ((x01 V) x00)) as proof of (V Xx)
% Found (fun (Xx:fofType) (x01:(x4 Xx))=> ((x01 V) x00)) as proof of ((x4 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType) (x01:(x4 Xx))=> ((x01 V) x00)) as proof of (forall (Xx:fofType), ((x4 Xx)->(V Xx)))
% Found (fun (V:(fofType->Prop)) (x00:(cC V)) (Xx:fofType) (x01:(x4 Xx))=> ((x01 V) x00)) as proof of ((cC V)->(forall (Xx:fofType), ((x4 Xx)->(V Xx))))
% Found (fun (V:(fofType->Prop)) (x00:(cC V)) (Xx:fofType) (x01:(x4 Xx))=> ((x01 V) x00)) as proof of b
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x4) Xx)):((Xr x4)->((or (Xr x4)) (((eq (fofType->Prop)) x4) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x4) Xx)) as proof of ((Xr x4)->((or (Xr x4)) (((eq (fofType->Prop)) x4) Xx)))
% Found ((or_introl (Xr x4)) (((eq (fofType->Prop)) x4) Xx)) as proof of ((Xr x4)->((or (Xr x4)) (((eq (fofType->Prop)) x4) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x4)) (((eq (fofType->Prop)) x4) Xx))) as proof of ((Xr x4)->((or (Xr x4)) (((eq (fofType->Prop)) x4) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x4)) (((eq (fofType->Prop)) x4) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x4)->((or (Xr x4)) (((eq (fofType->Prop)) x4) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x4)) (((eq (fofType->Prop)) x4) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x4)->((or (Xr x4)) (((eq (fofType->Prop)) x4) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x4) Xx)):((Xr x4)->((or (Xr x4)) (((eq (fofType->Prop)) x4) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x4) Xx)) as proof of ((Xr x4)->((or (Xr x4)) (((eq (fofType->Prop)) x4) Xx)))
% Found ((or_introl (Xr x4)) (((eq (fofType->Prop)) x4) Xx)) as proof of ((Xr x4)->((or (Xr x4)) (((eq (fofType->Prop)) x4) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x4)) (((eq (fofType->Prop)) x4) Xx))) as proof of ((Xr x4)->((or (Xr x4)) (((eq (fofType->Prop)) x4) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x4)) (((eq (fofType->Prop)) x4) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x4)->((or (Xr x4)) (((eq (fofType->Prop)) x4) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x4)) (((eq (fofType->Prop)) x4) Xx))) as proof of b
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x4) Xx)):((Xr x4)->((or (Xr x4)) (((eq (fofType->Prop)) x4) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x4) Xx)) as proof of ((Xr x4)->((or (Xr x4)) (((eq (fofType->Prop)) x4) Xx)))
% Found ((or_introl (Xr x4)) (((eq (fofType->Prop)) x4) Xx)) as proof of ((Xr x4)->((or (Xr x4)) (((eq (fofType->Prop)) x4) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x4)) (((eq (fofType->Prop)) x4) Xx))) as proof of ((Xr x4)->((or (Xr x4)) (((eq (fofType->Prop)) x4) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x4)) (((eq (fofType->Prop)) x4) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x4)->((or (Xr x4)) (((eq (fofType->Prop)) x4) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x4)) (((eq (fofType->Prop)) x4) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x4)->((or (Xr x4)) (((eq (fofType->Prop)) x4) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) b) Xx)):((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x0) Xx)):((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Instantiate: b:=(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C)))):Prop
% Found iff_trans as proof of b
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x2) Xx)):((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x2) Xx)) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx)) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))
% Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Instantiate: b:=(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C)))):Prop
% Found iff_trans as proof of b
% Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Instantiate: b:=(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C)))):Prop
% Found iff_trans as proof of b
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) b) Xx)):((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) b) Xx)):((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) f) Xx)):((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) f) Xx)):((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found x000:(x0 Xx)
% Instantiate: x0:=V:(fofType->Prop)
% Found x000 as proof of (V Xx)
% Found (fun (x000:(x0 Xx))=> x000) as proof of (V Xx)
% Found (fun (Xx:fofType) (x000:(x0 Xx))=> x000) as proof of ((x0 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType) (x000:(x0 Xx))=> x000) as proof of (forall (Xx:fofType), ((x0 Xx)->(V Xx)))
% Found x000:(x0 Xx)
% Instantiate: x0:=V:(fofType->Prop)
% Found x000 as proof of (V Xx)
% Found (fun (x000:(x0 Xx))=> x000) as proof of (V Xx)
% Found (fun (Xx:fofType) (x000:(x0 Xx))=> x000) as proof of ((x0 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType) (x000:(x0 Xx))=> x000) as proof of (forall (Xx:fofType), ((x0 Xx)->(V Xx)))
% Found x000:(x0 Xx)
% Instantiate: x0:=V:(fofType->Prop)
% Found x000 as proof of (V Xx)
% Found (fun (x000:(x0 Xx))=> x000) as proof of (V Xx)
% Found (fun (Xx:fofType) (x000:(x0 Xx))=> x000) as proof of ((x0 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType) (x000:(x0 Xx))=> x000) as proof of (forall (Xx:fofType), ((x0 Xx)->(V Xx)))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))))
% Found eq_ref00:=(eq_ref0 (f x2)):(((eq Prop) (f x2)) (f x2))
% Found (eq_ref0 (f x2)) as proof of (((eq Prop) (f x2)) b)
% Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) b)
% Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) b)
% Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) b)
% Found ((eq_trans0000 ((eq_ref Prop) (f x2))) ((eq_ref Prop) b)) as proof of (((eq Prop) (f x2)) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))))
% Found (((eq_trans000 ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))) ((eq_ref Prop) (f x2))) ((eq_ref Prop) b)) as proof of (((eq Prop) (f x2)) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))))
% Found ((((eq_trans00 ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))) ((eq_ref Prop) (f x2))) ((eq_ref Prop) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))))) as proof of (((eq Prop) (f x2)) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))))
% Found (((((eq_trans0 (f x2)) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))) ((eq_ref Prop) (f x2))) ((eq_ref Prop) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))))) as proof of (((eq Prop) (f x2)) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))))
% Found ((((((eq_trans Prop) (f x2)) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))) ((eq_ref Prop) (f x2))) ((eq_ref Prop) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))))) as proof of (((eq Prop) (f x2)) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))))
% Found (fun (x4:(forall (Xx:(fofType->Prop)), ((cC Xx)->(cL Xx))))=> ((((((eq_trans Prop) (f x2)) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))) ((eq_ref Prop) (f x2))) ((eq_ref Prop) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))))) as proof of (((eq Prop) (f x2)) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))))
% Found (fun (x3:(forall (X:(fofType->Prop)) (Y:(fofType->Prop)), (((and (cL X)) (cL Y))->((or (forall (Xx:fofType), ((X Xx)->(Y Xx)))) (forall (Xx:fofType), ((Y Xx)->(X Xx))))))) (x4:(forall (Xx:(fofType->Prop)), ((cC Xx)->(cL Xx))))=> ((((((eq_trans Prop) (f x2)) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))) ((eq_ref Prop) (f x2))) ((eq_ref Prop) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))))) as proof of ((forall (Xx:(fofType->Prop)), ((cC Xx)->(cL Xx)))->(((eq Prop) (f x2)) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))))
% Found (fun (x3:(forall (X:(fofType->Prop)) (Y:(fofType->Prop)), (((and (cL X)) (cL Y))->((or (forall (Xx:fofType), ((X Xx)->(Y Xx)))) (forall (Xx:fofType), ((Y Xx)->(X Xx))))))) (x4:(forall (Xx:(fofType->Prop)), ((cC Xx)->(cL Xx))))=> ((((((eq_trans Prop) (f x2)) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))) ((eq_ref Prop) (f x2))) ((eq_ref Prop) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))))) as proof of ((forall (X:(fofType->Prop)) (Y:(fofType->Prop)), (((and (cL X)) (cL Y))->((or (forall (Xx:fofType), ((X Xx)->(Y Xx)))) (forall (Xx:fofType), ((Y Xx)->(X Xx))))))->((forall (Xx:(fofType->Prop)), ((cC Xx)->(cL Xx)))->(((eq Prop) (f x2)) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))))))
% Found (and_rect10 (fun (x3:(forall (X:(fofType->Prop)) (Y:(fofType->Prop)), (((and (cL X)) (cL Y))->((or (forall (Xx:fofType), ((X Xx)->(Y Xx)))) (forall (Xx:fofType), ((Y Xx)->(X Xx))))))) (x4:(forall (Xx:(fofType->Prop)), ((cC Xx)->(cL Xx))))=> ((((((eq_trans Prop) (f x2)) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))) ((eq_ref Prop) (f x2))) ((eq_ref Prop) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))))))) as proof of (((eq Prop) (f x2)) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))))
% Found ((and_rect1 (((eq Prop) (f x2)) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))))) (fun (x3:(forall (X:(fofType->Prop)) (Y:(fofType->Prop)), (((and (cL X)) (cL Y))->((or (forall (Xx:fofType), ((X Xx)->(Y Xx)))) (forall (Xx:fofType), ((Y Xx)->(X Xx))))))) (x4:(forall (Xx:(fofType->Prop)), ((cC Xx)->(cL Xx))))=> ((((((eq_trans Prop) (f x2)) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))) ((eq_ref Prop) (f x2))) ((eq_ref Prop) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))))))) as proof of (((eq Prop) (f x2)) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))))
% Found (((fun (P0:Type) (x3:((forall (X:(fofType->Prop)) (Y:(fofType->Prop)), (((and (cL X)) (cL Y))->((or (forall (Xx:fofType), ((X Xx)->(Y Xx)))) (forall (Xx:fofType), ((Y Xx)->(X Xx))))))->((forall (Xx:(fofType->Prop)), ((cC Xx)->(cL Xx)))->P0)))=> (((((and_rect (forall (X:(fofType->Prop)) (Y:(fofType->Prop)), (((and (cL X)) (cL Y))->((or (forall (Xx:fofType), ((X Xx)->(Y Xx)))) (forall (Xx:fofType), ((Y Xx)->(X Xx))))))) (forall (Xx:(fofType->Prop)), ((cC Xx)->(cL Xx)))) P0) x3) x0)) (((eq Prop) (f x2)) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))))) (fun (x3:(forall (X:(fofType->Prop)) (Y:(fofType->Prop)), (((and (cL X)) (cL Y))->((or (forall (Xx:fofType), ((X Xx)->(Y Xx)))) (forall (Xx:fofType), ((Y Xx)->(X Xx))))))) (x4:(forall (Xx:(fofType->Prop)), ((cC Xx)->(cL Xx))))=> ((((((eq_trans Prop) (f x2)) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))) ((eq_ref Prop) (f x2))) ((eq_ref Prop) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))))))) as proof of (((eq Prop) (f x2)) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))))
% Found eq_ref00:=(eq_ref0 (f x2)):(((eq Prop) (f x2)) (f x2))
% Found (eq_ref0 (f x2)) as proof of (((eq Prop) (f x2)) b)
% Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) b)
% Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) b)
% Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) b)
% Found ((eq_trans0000 ((eq_ref Prop) (f x2))) ((eq_ref Prop) b)) as proof of (((eq Prop) (f x2)) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))))
% Found (((eq_trans000 ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))) ((eq_ref Prop) (f x2))) ((eq_ref Prop) b)) as proof of (((eq Prop) (f x2)) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))))
% Found ((((eq_trans00 ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))) ((eq_ref Prop) (f x2))) ((eq_ref Prop) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))))) as proof of (((eq Prop) (f x2)) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))))
% Found (((((eq_trans0 (f x2)) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))) ((eq_ref Prop) (f x2))) ((eq_ref Prop) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))))) as proof of (((eq Prop) (f x2)) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))))
% Found ((((((eq_trans Prop) (f x2)) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))) ((eq_ref Prop) (f x2))) ((eq_ref Prop) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))))) as proof of (((eq Prop) (f x2)) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))))
% Found (fun (x4:(forall (Xx:(fofType->Prop)), ((cC Xx)->(cL Xx))))=> ((((((eq_trans Prop) (f x2)) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))) ((eq_ref Prop) (f x2))) ((eq_ref Prop) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))))) as proof of (((eq Prop) (f x2)) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))))
% Found (fun (x3:(forall (X:(fofType->Prop)) (Y:(fofType->Prop)), (((and (cL X)) (cL Y))->((or (forall (Xx:fofType), ((X Xx)->(Y Xx)))) (forall (Xx:fofType), ((Y Xx)->(X Xx))))))) (x4:(forall (Xx:(fofType->Prop)), ((cC Xx)->(cL Xx))))=> ((((((eq_trans Prop) (f x2)) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))) ((eq_ref Prop) (f x2))) ((eq_ref Prop) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))))) as proof of ((forall (Xx:(fofType->Prop)), ((cC Xx)->(cL Xx)))->(((eq Prop) (f x2)) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))))
% Found (fun (x3:(forall (X:(fofType->Prop)) (Y:(fofType->Prop)), (((and (cL X)) (cL Y))->((or (forall (Xx:fofType), ((X Xx)->(Y Xx)))) (forall (Xx:fofType), ((Y Xx)->(X Xx))))))) (x4:(forall (Xx:(fofType->Prop)), ((cC Xx)->(cL Xx))))=> ((((((eq_trans Prop) (f x2)) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))) ((eq_ref Prop) (f x2))) ((eq_ref Prop) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))))) as proof of ((forall (X:(fofType->Prop)) (Y:(fofType->Prop)), (((and (cL X)) (cL Y))->((or (forall (Xx:fofType), ((X Xx)->(Y Xx)))) (forall (Xx:fofType), ((Y Xx)->(X Xx))))))->((forall (Xx:(fofType->Prop)), ((cC Xx)->(cL Xx)))->(((eq Prop) (f x2)) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))))))
% Found (and_rect10 (fun (x3:(forall (X:(fofType->Prop)) (Y:(fofType->Prop)), (((and (cL X)) (cL Y))->((or (forall (Xx:fofType), ((X Xx)->(Y Xx)))) (forall (Xx:fofType), ((Y Xx)->(X Xx))))))) (x4:(forall (Xx:(fofType->Prop)), ((cC Xx)->(cL Xx))))=> ((((((eq_trans Prop) (f x2)) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))) ((eq_ref Prop) (f x2))) ((eq_ref Prop) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))))))) as proof of (((eq Prop) (f x2)) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))))
% Found ((and_rect1 (((eq Prop) (f x2)) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))))) (fun (x3:(forall (X:(fofType->Prop)) (Y:(fofType->Prop)), (((and (cL X)) (cL Y))->((or (forall (Xx:fofType), ((X Xx)->(Y Xx)))) (forall (Xx:fofType), ((Y Xx)->(X Xx))))))) (x4:(forall (Xx:(fofType->Prop)), ((cC Xx)->(cL Xx))))=> ((((((eq_trans Prop) (f x2)) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))) ((eq_ref Prop) (f x2))) ((eq_ref Prop) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))))))) as proof of (((eq Prop) (f x2)) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))))
% Found (((fun (P0:Type) (x3:((forall (X:(fofType->Prop)) (Y:(fofType->Prop)), (((and (cL X)) (cL Y))->((or (forall (Xx:fofType), ((X Xx)->(Y Xx)))) (forall (Xx:fofType), ((Y Xx)->(X Xx))))))->((forall (Xx:(fofType->Prop)), ((cC Xx)->(cL Xx)))->P0)))=> (((((and_rect (forall (X:(fofType->Prop)) (Y:(fofType->Prop)), (((and (cL X)) (cL Y))->((or (forall (Xx:fofType), ((X Xx)->(Y Xx)))) (forall (Xx:fofType), ((Y Xx)->(X Xx))))))) (forall (Xx:(fofType->Prop)), ((cC Xx)->(cL Xx)))) P0) x3) x0)) (((eq Prop) (f x2)) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))))) (fun (x3:(forall (X:(fofType->Prop)) (Y:(fofType->Prop)), (((and (cL X)) (cL Y))->((or (forall (Xx:fofType), ((X Xx)->(Y Xx)))) (forall (Xx:fofType), ((Y Xx)->(X Xx))))))) (x4:(forall (Xx:(fofType->Prop)), ((cC Xx)->(cL Xx))))=> ((((((eq_trans Prop) (f x2)) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx))))))) ((eq_ref Prop) (f x2))) ((eq_ref Prop) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))))))) as proof of (((eq Prop) (f x2)) ((and (cC x2)) (forall (V:(fofType->Prop)), ((cC V)->(forall (Xx:fofType), ((x2 Xx)->(V Xx)))))))
% Found x01:(x2 Xx)
% Instantiate: x2:=V:(fofType->Prop)
% Found x01 as proof of (V Xx)
% Found (fun (x01:(x2 Xx))=> x01) as proof of (V Xx)
% Found (fun (Xx:fofType) (x01:(x2 Xx))=> x01) as proof of ((x2 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType) (x01:(x2 Xx))=> x01) as proof of (forall (Xx:fofType), ((x2 Xx)->(V Xx)))
% Found x000:(x0 Xx)
% Instantiate: x0:=V:(fofType->Prop)
% Found x000 as proof of (V Xx)
% Found (fun (x000:(x0 Xx))=> x000) as proof of (V Xx)
% Found (fun (Xx:fofType) (x000:(x0 Xx))=> x000) as proof of ((x0 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType) (x000:(x0 Xx))=> x000) as proof of (forall (Xx:fofType), ((x0 Xx)->(V Xx)))
% Found x000:(x0 Xx)
% Instantiate: x0:=V:(fofType->Prop)
% Found x000 as proof of (V Xx)
% Found (fun (x000:(x0 Xx))=> x000) as proof of (V Xx)
% Found (fun (Xx:fofType) (x000:(x0 Xx))=> x000) as proof of ((x0 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType) (x000:(x0 Xx))=> x000) as proof of (forall (Xx:fofType), ((x0 Xx)->(V Xx)))
% Found x000:(x0 Xx)
% Instantiate: x0:=V:(fofType->Prop)
% Found x000 as proof of (V Xx)
% Found (fun (x000:(x0 Xx))=> x000) as proof of (V Xx)
% Found (fun (Xx:fofType) (x000:(x0 Xx))=> x000) as proof of ((x0 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType) (x000:(x0 Xx))=> x000) as proof of (forall (Xx:fofType), ((x0 Xx)->(V Xx)))
% Found x01:(x2 Xx)
% Instantiate: x2:=V:(fofType->Prop)
% Found x01 as proof of (V Xx)
% Found (fun (x01:(x2 Xx))=> x01) as proof of (V Xx)
% Found (fun (Xx:fofType) (x01:(x2 Xx))=> x01) as proof of ((x2 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType) (x01:(x2 Xx))=> x01) as proof of (forall (Xx:fofType), ((x2 Xx)->(V Xx)))
% Found x01:(x2 Xx)
% Instantiate: x2:=V:(fofType->Prop)
% Found x01 as proof of (V Xx)
% Found (fun (x01:(x2 Xx))=> x01) as proof of (V Xx)
% Found (fun (Xx:fofType) (x01:(x2 Xx))=> x01) as proof of ((x2 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType) (x01:(x2 Xx))=> x01) as proof of (forall (Xx:fofType), ((x2 Xx)->(V Xx)))
% Found x0000000:=(x000000 x00):(V Xx)
% Found (x000000 x00) as proof of (V Xx)
% Found ((x00000 V) x00) as proof of (V Xx)
% Found (((fun (V0:(fofType->Prop)) (x001:(cC V0))=> (((x0000 V0) x001) x2)) V) x00) as proof of (V Xx)
% Found (((fun (V0:(fofType->Prop)) (x001:(cC V0))=> ((((fun (V0:(fofType->Prop)) (x001:(cC V0))=> (((x000 V0) x001) x1)) V0) x001) x2)) V) x00) as proof of (V Xx)
% Found (((fun (V0:(fofType->Prop)) (x001:(cC V0))=> ((((fun (V0:(fofType->Prop)) (x001:(cC V0))=> (((x000 V0) x001) x1)) V0) x001) x2)) V) x00) as proof of (V Xx)
% Found (fun (x000:(x0 Xx))=> (((fun (V0:(fofType->Prop)) (x001:(cC V0))=> ((((fun (V0:(fofType->Prop)) (x001:(cC V0))=> (((x000 V0) x001) x1)) V0) x001) x2)) V) x00)) as proof of (V Xx)
% Found (fun (Xx:fofType) (x000:(x0 Xx))=> (((fun (V0:(fofType->Prop)) (x001:(cC V0))=> ((((fun (V0:(fofType->Prop)) (x001:(cC V0))=> (((x000 V0) x001) x1)) V0) x001) x2)) V) x00)) as proof of ((x0 Xx)->(V Xx))
% Found (fun (x00:(cC V)) (Xx:fofType) (x000:(x0 Xx))=> (((fun (V0:(fofType->Prop)) (x001:(cC V0))=> ((((fun (V0:(fofType->Prop)) (x001:(cC V0))=> (((x000 V0) x001) x1)) V0) x001) x2)) V) x00)) as proof of (forall (Xx:fofType), ((x0 Xx)->(V Xx)))
% Found (fun (V:(fofType->Prop)) (x00:(cC V)) (Xx:fofType) (x000:(x0 Xx))=> (((fun (V0:(fofType->Prop)) (x001:(cC V0))=> ((((fun (V0:(fofType->Prop)) (x001:(cC V0))=> (((x000 V0) x001) x1)) V0) x001) x2)) V) x00)) as proof of ((cC V)->(forall (Xx:fofType), ((x0 Xx)->(V Xx))))
% Found (fun (V:(fofType->Prop)) (x00:(cC V)) (Xx:fofType) (x000:(x0 Xx))=> (((fun (V0:(fofType->Prop)) (x001:(cC V0))=> ((((fun (V0:(fofType->Prop)) (x001:(cC V0))=> (((x000 V0) x001) x1)) V0) x001) x2)) V) x00)) as proof of b
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x0) Xx)):((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x0) Xx)):((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x0) Xx)):((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of b
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x2) Xx)):((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x2) Xx)) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx)) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of b
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x0) Xx)):((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Instantiate: b:=(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C)))):Prop
% Found iff_trans as proof of b
% Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Instantiate: b:=(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C)))):Prop
% Found iff_trans as proof of b
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) b) Xx)):((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Instantiate: b:=(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C)))):Prop
% Found iff_trans as proof of b
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x2) Xx)):((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x2) Xx)) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx)) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) b) Xx)):((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) b) Xx)):((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) f) Xx)):((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) f) Xx)):((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) f) Xx)):((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) f) Xx)):((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) b) Xx)):((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x0) Xx)):((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of b
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x2) Xx)):((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x2) Xx)) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx)) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of b
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) b) Xx)):((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) b) Xx)):((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) b) Xx)):((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) f) Xx)):((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) b) Xx)):((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) f) Xx)):((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) b) Xx)):((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) f) Xx)):((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) f) Xx)):((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) f) Xx)):((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) f) Xx)):((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x0) Xx)):((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of b
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x0) Xx)):((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of b
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x2) Xx)):((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x2) Xx)) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx)) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of b
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) b) Xx)):((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x0) Xx)):((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) b) Xx)):((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) b) Xx)):((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x2) Xx)):((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x2) Xx)) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx)) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) b) Xx)):((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) b) Xx)):((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) b) Xx)):((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x0) Xx)):((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) f) Xx)):((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) f) Xx)):((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) f) Xx)):((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) f) Xx)):((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) f) Xx)):((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) f) Xx)):((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x0) Xx)):((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) f) Xx)):((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) f) Xx)):((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x2) Xx)):((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x2) Xx)) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx)) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x0) Xx)):((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of b
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x0) Xx)):((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of b
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x0) Xx)):((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x2) Xx)):((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x2) Xx)) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx)) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of b
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x0) Xx)):((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of b
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x0) Xx)):((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of b
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x2) Xx)):((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x2) Xx)) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx)) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of b
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) b) Xx)):((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) b) Xx)):((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) b) Xx)):((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) f) Xx)):((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) f) Xx)):((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) f) Xx)):((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) f) Xx)):((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) f) Xx)):((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) f) Xx)):((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x0) Xx)):((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) f) Xx)):((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) f) Xx)):((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) f) Xx)):((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x2) Xx)):((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x2) Xx)) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx)) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) f) Xx)):((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x0) Xx)):((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x0) Xx)):((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of b
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x0) Xx)):((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of b
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x2) Xx)):((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x2) Xx)) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx)) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of b
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x0) Xx)):((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x0) Xx)):((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) f) Xx)):((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x2) Xx)):((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x2) Xx)) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx)) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) f) Xx)):((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) f) Xx)):((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) f) Xx)):((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) f) Xx)):((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) f) Xx)):((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) f) Xx)):((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) f) Xx)):((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x0) Xx)):((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) f) Xx)):((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) f) Xx)):((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) f) Xx)):((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) f) Xx)):((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) b) Xx)):((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) b) Xx)):((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) b) Xx)):((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) b) Xx)):((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx)) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr b)) (((eq (fofType->Prop)) b) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr b)->((or (Xr b)) (((eq (fofType->Prop)) b) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x0) Xx)):((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x2) Xx)):((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x2) Xx)) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx)) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x0) Xx)):((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x0) Xx)):((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x0) Xx)):((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x0) Xx)):((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x2) Xx)):((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x2) Xx)) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx)) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x2)) (((eq (fofType->Prop)) x2) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x2)->((or (Xr x2)) (((eq (fofType->Prop)) x2) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) f) Xx)):((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) f) Xx)):((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found iff_sym:=(fun (A:Prop) (B:Prop) (H:((iff A) B))=> ((((conj (B->A)) (A->B)) (((proj2 (A->B)) (B->A)) H)) (((proj1 (A->B)) (B->A)) H))):(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% Instantiate: b:=(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A))):Prop
% Found iff_sym as proof of b
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) f) Xx)):((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) f) Xx)):((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) f) Xx)):((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) f) Xx)):((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx)) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr f)) (((eq (fofType->Prop)) f) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr f)->((or (Xr f)) (((eq (fofType->Prop)) f) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x0) Xx)):((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found or_introl00:=(or_introl0 (((eq (fofType->Prop)) x0) Xx)):((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (or_introl0 (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx)) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx)))
% Found (fun (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop))=> ((or_introl (Xr x0)) (((eq (fofType->Prop)) x0) Xx))) as proof of (forall (Xx:(fofType->Prop)), ((Xr x0)->((or (Xr x0)) (((eq (fofType->Prop)) x0) Xx))))
% Found (fun (Xr:((fofType->Prop)->Pro
% EOF
%------------------------------------------------------------------------------