%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SEV229^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n184.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 13:33:54 EDT 2014

% Result   : Timeout 300.10s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SEV229^5 : TPTP v6.1.0. Released v4.0.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n184.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 08:33:46 CDT 2014
% % CPUTime  : 300.10 
% 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 0x15a9d88>, <kernel.Type object at 0x15a9e18>) of role type named a_type
% Using role type
% Declaring a:Type
% FOF formula (<kernel.Constant object at 0x19e3248>, <kernel.DependentProduct object at 0x15a9440>) of role type named cE
% Using role type
% Declaring cE:(a->Prop)
% FOF formula (<kernel.Constant object at 0x15a95f0>, <kernel.DependentProduct object at 0x15a9ea8>) of role type named cD
% Using role type
% Declaring cD:(a->Prop)
% FOF formula (((eq ((a->Prop)->Prop)) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) of role conjecture named cX5209_pme
% Conjecture to prove = (((eq ((a->Prop)->Prop)) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))):Prop
% Parameter a_DUMMY:a.
% We need to prove ['(((eq ((a->Prop)->Prop)) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0))))))']
% Parameter a:Type.
% Parameter cE:(a->Prop).
% Parameter cD:(a->Prop).
% Trying to prove (((eq ((a->Prop)->Prop)) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0))))))
% Found eq_ref00:=(eq_ref0 b):(((eq ((a->Prop)->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq ((a->Prop)->Prop)) b) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0))))))
% Found ((eq_ref ((a->Prop)->Prop)) b) as proof of (((eq ((a->Prop)->Prop)) b) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0))))))
% Found ((eq_ref ((a->Prop)->Prop)) b) as proof of (((eq ((a->Prop)->Prop)) b) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0))))))
% Found ((eq_ref ((a->Prop)->Prop)) b) as proof of (((eq ((a->Prop)->Prop)) b) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0))))))
% Found eta_expansion000:=(eta_expansion00 (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))):(((eq ((a->Prop)->Prop)) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))) (fun (x:(a->Prop))=> (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))))
% Found (eta_expansion00 (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))) as proof of (((eq ((a->Prop)->Prop)) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))) b)
% Found ((eta_expansion0 Prop) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))) as proof of (((eq ((a->Prop)->Prop)) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))) b)
% Found (((eta_expansion (a->Prop)) Prop) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))) as proof of (((eq ((a->Prop)->Prop)) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))) b)
% Found (((eta_expansion (a->Prop)) Prop) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))) as proof of (((eq ((a->Prop)->Prop)) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))) b)
% Found (((eta_expansion (a->Prop)) Prop) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))) as proof of (((eq ((a->Prop)->Prop)) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))) b)
% Found x2:(P (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx))))))
% Found (fun (x2:(P (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))))=> x2) as proof of (P (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx))))))
% Found (fun (x2:(P (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))))=> x2) as proof of (P0 (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx))))))
% Found x2:(P (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx))))))
% Found (fun (x2:(P (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))))=> x2) as proof of (P (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx))))))
% Found (fun (x2:(P (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))))=> x2) as proof of (P0 (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx))))))
% Found x2:(P (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx))))))
% Found (fun (x2:(P (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))))=> x2) as proof of (P (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx))))))
% Found (fun (x2:(P (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))))=> x2) as proof of (P0 (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx))))))
% Found eq_ref00:=(eq_ref0 b):(((eq ((a->Prop)->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq ((a->Prop)->Prop)) b) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx))))))
% Found ((eq_ref ((a->Prop)->Prop)) b) as proof of (((eq ((a->Prop)->Prop)) b) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx))))))
% Found ((eq_ref ((a->Prop)->Prop)) b) as proof of (((eq ((a->Prop)->Prop)) b) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx))))))
% Found ((eq_ref ((a->Prop)->Prop)) b) as proof of (((eq ((a->Prop)->Prop)) b) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx))))))
% Found eta_expansion000:=(eta_expansion00 (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))):(((eq ((a->Prop)->Prop)) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) (fun (x:(a->Prop))=> ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))))
% Found (eta_expansion00 (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) as proof of (((eq ((a->Prop)->Prop)) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) b)
% Found ((eta_expansion0 Prop) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) as proof of (((eq ((a->Prop)->Prop)) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) b)
% Found (((eta_expansion (a->Prop)) Prop) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) as proof of (((eq ((a->Prop)->Prop)) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) b)
% Found (((eta_expansion (a->Prop)) Prop) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) as proof of (((eq ((a->Prop)->Prop)) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) b)
% Found (((eta_expansion (a->Prop)) Prop) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) as proof of (((eq ((a->Prop)->Prop)) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) b)
% Found eq_ref00:=(eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))):(((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found eq_ref00:=(eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))):(((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found x2:(P (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0))))))
% Found (fun (x2:(P (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))))=> x2) as proof of (P (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0))))))
% Found (fun (x2:(P (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))))=> x2) as proof of (P0 (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0))))))
% Found x2:(P (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0))))))
% Found (fun (x2:(P (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))))=> x2) as proof of (P (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0))))))
% Found (fun (x2:(P (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))))=> x2) as proof of (P0 (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0))))))
% Found x01:(P (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (fun (x01:(P (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))))=> x01) as proof of (P (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (fun (x01:(P (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))))=> x01) as proof of (P0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found x01:(P (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (fun (x01:(P (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))))=> x01) as proof of (P (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (fun (x01:(P (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))))=> x01) as proof of (P0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found eq_ref00:=(eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))):(((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found eq_ref00:=(eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))):(((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found eq_ref00:=(eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))):(((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found eq_ref00:=(eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))):(((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found x01:(P ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (fun (x01:(P ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))))=> x01) as proof of (P ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (fun (x01:(P ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))))=> x01) as proof of (P0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found x01:(P ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (fun (x01:(P ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))))=> x01) as proof of (P ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (fun (x01:(P ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))))=> x01) as proof of (P0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found x:(P (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx))))))
% Instantiate: b:=(fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx))))):((a->Prop)->Prop)
% Found x as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))):(((eq ((a->Prop)->Prop)) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0))))))
% Found (eq_ref0 (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) as proof of (((eq ((a->Prop)->Prop)) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) b)
% Found ((eq_ref ((a->Prop)->Prop)) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) as proof of (((eq ((a->Prop)->Prop)) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) b)
% Found ((eq_ref ((a->Prop)->Prop)) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) as proof of (((eq ((a->Prop)->Prop)) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) b)
% Found ((eq_ref ((a->Prop)->Prop)) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) as proof of (((eq ((a->Prop)->Prop)) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) b)
% Found x:(P (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx))))))
% Instantiate: f:=(fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx))))):((a->Prop)->Prop)
% Found x as proof of (P0 f)
% Found x:(P (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx))))))
% Instantiate: f:=(fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx))))):((a->Prop)->Prop)
% Found x as proof of (P0 f)
% Found eq_ref00:=(eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))):(((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found eq_ref00:=(eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))):(((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq ((a->Prop)->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq ((a->Prop)->Prop)) b) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0))))))
% Found ((eq_ref ((a->Prop)->Prop)) b) as proof of (((eq ((a->Prop)->Prop)) b) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0))))))
% Found ((eq_ref ((a->Prop)->Prop)) b) as proof of (((eq ((a->Prop)->Prop)) b) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0))))))
% Found ((eq_ref ((a->Prop)->Prop)) b) as proof of (((eq ((a->Prop)->Prop)) b) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0))))))
% Found eq_ref00:=(eq_ref0 (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))):(((eq ((a->Prop)->Prop)) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx))))))
% Found (eq_ref0 (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))) as proof of (((eq ((a->Prop)->Prop)) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))) b)
% Found ((eq_ref ((a->Prop)->Prop)) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))) as proof of (((eq ((a->Prop)->Prop)) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))) b)
% Found ((eq_ref ((a->Prop)->Prop)) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))) as proof of (((eq ((a->Prop)->Prop)) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))) b)
% Found ((eq_ref ((a->Prop)->Prop)) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))) as proof of (((eq ((a->Prop)->Prop)) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))) b)
% Found eq_ref00:=(eq_ref0 (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))):(((eq ((a->Prop)->Prop)) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0))))))
% Found (eq_ref0 (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) as proof of (((eq ((a->Prop)->Prop)) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) b)
% Found ((eq_ref ((a->Prop)->Prop)) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) as proof of (((eq ((a->Prop)->Prop)) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) b)
% Found ((eq_ref ((a->Prop)->Prop)) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) as proof of (((eq ((a->Prop)->Prop)) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) b)
% Found ((eq_ref ((a->Prop)->Prop)) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) as proof of (((eq ((a->Prop)->Prop)) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) b)
% Found x:(P0 b)
% Instantiate: b:=(fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx))))):((a->Prop)->Prop)
% Found (fun (x:(P0 b))=> x) as proof of (P0 (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx))))))
% Found (fun (P0:(((a->Prop)->Prop)->Prop)) (x:(P0 b))=> x) as proof of ((P0 b)->(P0 (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))))
% Found (fun (P0:(((a->Prop)->Prop)->Prop)) (x:(P0 b))=> x) as proof of (P b)
% Found x:(P (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0))))))
% Instantiate: b:=(fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0))))):((a->Prop)->Prop)
% Found x as proof of (P0 b)
% Found eta_expansion000:=(eta_expansion00 (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))):(((eq ((a->Prop)->Prop)) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))) (fun (x:(a->Prop))=> (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))))
% Found (eta_expansion00 (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))) as proof of (((eq ((a->Prop)->Prop)) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))) b)
% Found ((eta_expansion0 Prop) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))) as proof of (((eq ((a->Prop)->Prop)) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))) b)
% Found (((eta_expansion (a->Prop)) Prop) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))) as proof of (((eq ((a->Prop)->Prop)) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))) b)
% Found (((eta_expansion (a->Prop)) Prop) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))) as proof of (((eq ((a->Prop)->Prop)) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))) b)
% Found (((eta_expansion (a->Prop)) Prop) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))) as proof of (((eq ((a->Prop)->Prop)) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))) b)
% Found x3:(P (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx))))))
% Found (fun (x3:(P (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))))=> x3) as proof of (P (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx))))))
% Found (fun (x3:(P (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))))=> x3) as proof of (P0 (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx))))))
% Found eq_ref00:=(eq_ref0 b):(((eq ((a->Prop)->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq ((a->Prop)->Prop)) b) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0))))))
% Found ((eq_ref ((a->Prop)->Prop)) b) as proof of (((eq ((a->Prop)->Prop)) b) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0))))))
% Found ((eq_ref ((a->Prop)->Prop)) b) as proof of (((eq ((a->Prop)->Prop)) b) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0))))))
% Found ((eq_ref ((a->Prop)->Prop)) b) as proof of (((eq ((a->Prop)->Prop)) b) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0))))))
% Found eq_ref00:=(eq_ref0 (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))):(((eq ((a->Prop)->Prop)) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx))))))
% Found (eq_ref0 (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))) as proof of (((eq ((a->Prop)->Prop)) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))) b)
% Found ((eq_ref ((a->Prop)->Prop)) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))) as proof of (((eq ((a->Prop)->Prop)) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))) b)
% Found ((eq_ref ((a->Prop)->Prop)) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))) as proof of (((eq ((a->Prop)->Prop)) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))) b)
% Found ((eq_ref ((a->Prop)->Prop)) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))) as proof of (((eq ((a->Prop)->Prop)) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq ((a->Prop)->Prop)) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq ((a->Prop)->Prop)) b0) b)
% Found ((eq_ref ((a->Prop)->Prop)) b0) as proof of (((eq ((a->Prop)->Prop)) b0) b)
% Found ((eq_ref ((a->Prop)->Prop)) b0) as proof of (((eq ((a->Prop)->Prop)) b0) b)
% Found ((eq_ref ((a->Prop)->Prop)) b0) as proof of (((eq ((a->Prop)->Prop)) b0) b)
% Found eta_expansion000:=(eta_expansion00 (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))):(((eq ((a->Prop)->Prop)) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))) (fun (x:(a->Prop))=> (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))))
% Found (eta_expansion00 (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))) as proof of (((eq ((a->Prop)->Prop)) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))) b0)
% Found ((eta_expansion0 Prop) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))) as proof of (((eq ((a->Prop)->Prop)) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))) b0)
% Found (((eta_expansion (a->Prop)) Prop) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))) as proof of (((eq ((a->Prop)->Prop)) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))) b0)
% Found (((eta_expansion (a->Prop)) Prop) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))) as proof of (((eq ((a->Prop)->Prop)) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))) b0)
% Found (((eta_expansion (a->Prop)) Prop) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))) as proof of (((eq ((a->Prop)->Prop)) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))) b0)
% Found x:(P (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0))))))
% Instantiate: f:=(fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0))))):((a->Prop)->Prop)
% Found x as proof of (P0 f)
% Found x:(P (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0))))))
% Instantiate: f:=(fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0))))):((a->Prop)->Prop)
% Found x as proof of (P0 f)
% Found x0:(P (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Instantiate: b:=(forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))):Prop
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))):(((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found x0:(P (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Instantiate: b:=(forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))):Prop
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))):(((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq ((a->Prop)->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq ((a->Prop)->Prop)) b) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx))))))
% Found ((eq_ref ((a->Prop)->Prop)) b) as proof of (((eq ((a->Prop)->Prop)) b) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx))))))
% Found ((eq_ref ((a->Prop)->Prop)) b) as proof of (((eq ((a->Prop)->Prop)) b) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx))))))
% Found ((eq_ref ((a->Prop)->Prop)) b) as proof of (((eq ((a->Prop)->Prop)) b) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx))))))
% Found eta_expansion000:=(eta_expansion00 (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))):(((eq ((a->Prop)->Prop)) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) (fun (x:(a->Prop))=> ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))))
% Found (eta_expansion00 (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) as proof of (((eq ((a->Prop)->Prop)) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) b)
% Found ((eta_expansion0 Prop) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) as proof of (((eq ((a->Prop)->Prop)) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) b)
% Found (((eta_expansion (a->Prop)) Prop) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) as proof of (((eq ((a->Prop)->Prop)) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) b)
% Found (((eta_expansion (a->Prop)) Prop) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) as proof of (((eq ((a->Prop)->Prop)) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) b)
% Found (((eta_expansion (a->Prop)) Prop) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) as proof of (((eq ((a->Prop)->Prop)) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq ((a->Prop)->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq ((a->Prop)->Prop)) b) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx))))))
% Found ((eq_ref ((a->Prop)->Prop)) b) as proof of (((eq ((a->Prop)->Prop)) b) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx))))))
% Found ((eq_ref ((a->Prop)->Prop)) b) as proof of (((eq ((a->Prop)->Prop)) b) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx))))))
% Found ((eq_ref ((a->Prop)->Prop)) b) as proof of (((eq ((a->Prop)->Prop)) b) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx))))))
% Found eq_ref00:=(eq_ref0 (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))):(((eq ((a->Prop)->Prop)) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0))))))
% Found (eq_ref0 (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) as proof of (((eq ((a->Prop)->Prop)) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) b)
% Found ((eq_ref ((a->Prop)->Prop)) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) as proof of (((eq ((a->Prop)->Prop)) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) b)
% Found ((eq_ref ((a->Prop)->Prop)) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) as proof of (((eq ((a->Prop)->Prop)) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) b)
% Found ((eq_ref ((a->Prop)->Prop)) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) as proof of (((eq ((a->Prop)->Prop)) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq ((a->Prop)->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq ((a->Prop)->Prop)) b) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx))))))
% Found ((eq_ref ((a->Prop)->Prop)) b) as proof of (((eq ((a->Prop)->Prop)) b) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx))))))
% Found ((eq_ref ((a->Prop)->Prop)) b) as proof of (((eq ((a->Prop)->Prop)) b) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx))))))
% Found ((eq_ref ((a->Prop)->Prop)) b) as proof of (((eq ((a->Prop)->Prop)) b) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx))))))
% Found eq_ref00:=(eq_ref0 (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))):(((eq ((a->Prop)->Prop)) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0))))))
% Found (eq_ref0 (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) as proof of (((eq ((a->Prop)->Prop)) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) b)
% Found ((eq_ref ((a->Prop)->Prop)) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) as proof of (((eq ((a->Prop)->Prop)) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) b)
% Found ((eq_ref ((a->Prop)->Prop)) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) as proof of (((eq ((a->Prop)->Prop)) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) b)
% Found ((eq_ref ((a->Prop)->Prop)) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) as proof of (((eq ((a->Prop)->Prop)) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) b)
% Found x2:(P (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx))))))
% Found (fun (x2:(P (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))))=> x2) as proof of (P (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx))))))
% Found (fun (x2:(P (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))))=> x2) as proof of (P0 (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx))))))
% Found eq_ref00:=(eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))):(((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found eq_ref00:=(eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))):(((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found eq_ref00:=(eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))):(((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found eq_ref00:=(eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))):(((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found eq_ref00:=(eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))):(((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found eq_ref00:=(eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))):(((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found x2:(P (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx))))))
% Found (fun (x2:(P (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))))=> x2) as proof of (P (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx))))))
% Found (fun (x2:(P (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))))=> x2) as proof of (P0 (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx))))))
% Found x2:(P (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx))))))
% Found (fun (x2:(P (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))))=> x2) as proof of (P (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx))))))
% Found (fun (x2:(P (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))))=> x2) as proof of (P0 (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx))))))
% Found x2:(P1 (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0))))))
% Found (fun (x2:(P1 (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))))=> x2) as proof of (P1 (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0))))))
% Found (fun (x2:(P1 (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))))=> x2) as proof of (P2 (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0))))))
% Found x2:(P1 (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0))))))
% Found (fun (x2:(P1 (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))))=> x2) as proof of (P1 (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0))))))
% Found (fun (x2:(P1 (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))))=> x2) as proof of (P2 (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0))))))
% Found x2:(P1 (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0))))))
% Found (fun (x2:(P1 (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))))=> x2) as proof of (P1 (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0))))))
% Found (fun (x2:(P1 (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))))=> x2) as proof of (P2 (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0))))))
% Found x2:(P1 (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0))))))
% Found (fun (x2:(P1 (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))))=> x2) as proof of (P1 (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0))))))
% Found (fun (x2:(P1 (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))))=> x2) as proof of (P2 (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0))))))
% Found x01:(P1 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (fun (x01:(P1 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))))=> x01) as proof of (P1 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (fun (x01:(P1 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))))=> x01) as proof of (P2 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found x01:(P1 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (fun (x01:(P1 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))))=> x01) as proof of (P1 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (fun (x01:(P1 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))))=> x01) as proof of (P2 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found x01:(P1 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (fun (x01:(P1 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))))=> x01) as proof of (P1 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (fun (x01:(P1 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))))=> x01) as proof of (P2 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found x01:(P1 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (fun (x01:(P1 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))))=> x01) as proof of (P1 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (fun (x01:(P1 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))))=> x01) as proof of (P2 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found x3:(P (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0))))))
% Found (fun (x3:(P (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))))=> x3) as proof of (P (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0))))))
% Found (fun (x3:(P (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))))=> x3) as proof of (P0 (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0))))))
% Found eq_ref00:=(eq_ref0 b):(((eq ((a->Prop)->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq ((a->Prop)->Prop)) b) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx))))))
% Found ((eq_ref ((a->Prop)->Prop)) b) as proof of (((eq ((a->Prop)->Prop)) b) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx))))))
% Found ((eq_ref ((a->Prop)->Prop)) b) as proof of (((eq ((a->Prop)->Prop)) b) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx))))))
% Found ((eq_ref ((a->Prop)->Prop)) b) as proof of (((eq ((a->Prop)->Prop)) b) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx))))))
% Found eta_expansion000:=(eta_expansion00 (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))):(((eq ((a->Prop)->Prop)) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) (fun (x:(a->Prop))=> ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))))
% Found (eta_expansion00 (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) as proof of (((eq ((a->Prop)->Prop)) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) b)
% Found ((eta_expansion0 Prop) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) as proof of (((eq ((a->Prop)->Prop)) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) b)
% Found (((eta_expansion (a->Prop)) Prop) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) as proof of (((eq ((a->Prop)->Prop)) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) b)
% Found (((eta_expansion (a->Prop)) Prop) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) as proof of (((eq ((a->Prop)->Prop)) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) b)
% Found (((eta_expansion (a->Prop)) Prop) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) as proof of (((eq ((a->Prop)->Prop)) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq ((a->Prop)->Prop)) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq ((a->Prop)->Prop)) b0) b)
% Found ((eq_ref ((a->Prop)->Prop)) b0) as proof of (((eq ((a->Prop)->Prop)) b0) b)
% Found ((eq_ref ((a->Prop)->Prop)) b0) as proof of (((eq ((a->Prop)->Prop)) b0) b)
% Found ((eq_ref ((a->Prop)->Prop)) b0) as proof of (((eq ((a->Prop)->Prop)) b0) b)
% Found eta_expansion000:=(eta_expansion00 (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))):(((eq ((a->Prop)->Prop)) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) (fun (x:(a->Prop))=> ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))))
% Found (eta_expansion00 (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) as proof of (((eq ((a->Prop)->Prop)) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) b0)
% Found ((eta_expansion0 Prop) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) as proof of (((eq ((a->Prop)->Prop)) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) b0)
% Found (((eta_expansion (a->Prop)) Prop) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) as proof of (((eq ((a->Prop)->Prop)) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) b0)
% Found (((eta_expansion (a->Prop)) Prop) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) as proof of (((eq ((a->Prop)->Prop)) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) b0)
% Found (((eta_expansion (a->Prop)) Prop) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) as proof of (((eq ((a->Prop)->Prop)) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) b0)
% Found eq_ref00:=(eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))):(((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found x0:(P0 b)
% Instantiate: b:=(forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))):Prop
% Found (fun (x0:(P0 b))=> x0) as proof of (P0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (fun (P0:(Prop->Prop)) (x0:(P0 b))=> x0) as proof of ((P0 b)->(P0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))))
% Found (fun (P0:(Prop->Prop)) (x0:(P0 b))=> x0) as proof of (P b)
% Found eq_ref00:=(eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))):(((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found x0:(P0 b)
% Instantiate: b:=(forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))):Prop
% Found (fun (x0:(P0 b))=> x0) as proof of (P0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (fun (P0:(Prop->Prop)) (x0:(P0 b))=> x0) as proof of ((P0 b)->(P0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))))
% Found (fun (P0:(Prop->Prop)) (x0:(P0 b))=> x0) as proof of (P b)
% Found x02:(P (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (fun (x02:(P (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))))=> x02) as proof of (P (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (fun (x02:(P (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))))=> x02) as proof of (P0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found eq_ref00:=(eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))):(((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found x02:(P (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (fun (x02:(P (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))))=> x02) as proof of (P (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (fun (x02:(P (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))))=> x02) as proof of (P0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found eq_ref00:=(eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))):(((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found x0:(P ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Instantiate: b:=((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))):Prop
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))):(((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found x0:(P ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Instantiate: b:=((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))):Prop
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))):(((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq Prop) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq Prop) a0) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))
% Found eq_ref00:=(eq_ref0 a0):(((eq Prop) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq Prop) a0) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))
% Found eq_ref00:=(eq_ref0 a0):(((eq Prop) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq Prop) a0) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))
% Found eq_ref00:=(eq_ref0 a0):(((eq Prop) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq Prop) a0) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))
% Found eq_ref00:=(eq_ref0 a0):(((eq Prop) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq Prop) a0) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))
% Found eq_ref00:=(eq_ref0 a0):(((eq Prop) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq Prop) a0) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))
% Found eq_ref00:=(eq_ref0 b0):(((eq ((a->Prop)->Prop)) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq ((a->Prop)->Prop)) b0) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx))))))
% Found ((eq_ref ((a->Prop)->Prop)) b0) as proof of (((eq ((a->Prop)->Prop)) b0) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx))))))
% Found ((eq_ref ((a->Prop)->Prop)) b0) as proof of (((eq ((a->Prop)->Prop)) b0) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx))))))
% Found ((eq_ref ((a->Prop)->Prop)) b0) as proof of (((eq ((a->Prop)->Prop)) b0) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx))))))
% Found eta_expansion000:=(eta_expansion00 b):(((eq ((a->Prop)->Prop)) b) (fun (x:(a->Prop))=> (b x)))
% Found (eta_expansion00 b) as proof of (((eq ((a->Prop)->Prop)) b) b0)
% Found ((eta_expansion0 Prop) b) as proof of (((eq ((a->Prop)->Prop)) b) b0)
% Found (((eta_expansion (a->Prop)) Prop) b) as proof of (((eq ((a->Prop)->Prop)) b) b0)
% Found (((eta_expansion (a->Prop)) Prop) b) as proof of (((eq ((a->Prop)->Prop)) b) b0)
% Found (((eta_expansion (a->Prop)) Prop) b) as proof of (((eq ((a->Prop)->Prop)) b) b0)
% Found eq_ref00:=(eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))):(((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b0)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b0)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b0)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found eq_ref00:=(eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))):(((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b0)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b0)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b0)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found x0:(P ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Instantiate: b:=((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))):Prop
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))):(((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found x0:(P ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Instantiate: b:=((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))):Prop
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))):(((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found x2:(P (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0))))))
% Found (fun (x2:(P (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))))=> x2) as proof of (P (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0))))))
% Found (fun (x2:(P (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))))=> x2) as proof of (P0 (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0))))))
% Found eq_ref00:=(eq_ref0 b):(((eq ((a->Prop)->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq ((a->Prop)->Prop)) b) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0))))))
% Found ((eq_ref ((a->Prop)->Prop)) b) as proof of (((eq ((a->Prop)->Prop)) b) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0))))))
% Found ((eq_ref ((a->Prop)->Prop)) b) as proof of (((eq ((a->Prop)->Prop)) b) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0))))))
% Found ((eq_ref ((a->Prop)->Prop)) b) as proof of (((eq ((a->Prop)->Prop)) b) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0))))))
% Found eq_ref00:=(eq_ref0 (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))):(((eq ((a->Prop)->Prop)) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx))))))
% Found (eq_ref0 (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))) as proof of (((eq ((a->Prop)->Prop)) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))) b)
% Found ((eq_ref ((a->Prop)->Prop)) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))) as proof of (((eq ((a->Prop)->Prop)) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))) b)
% Found ((eq_ref ((a->Prop)->Prop)) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))) as proof of (((eq ((a->Prop)->Prop)) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))) b)
% Found ((eq_ref ((a->Prop)->Prop)) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))) as proof of (((eq ((a->Prop)->Prop)) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))) b)
% Found x2:(P (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx))))))
% Found (fun (x2:(P (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))))=> x2) as proof of (P (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx))))))
% Found (fun (x2:(P (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))))=> x2) as proof of (P0 (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx))))))
% Found eq_ref00:=(eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))):(((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b0)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b0)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b0)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x))
% Found eq_ref00:=(eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))):(((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b0)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b0)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b0)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x))
% Found x2:(P (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx))))))
% Found (fun (x2:(P (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))))=> x2) as proof of (P (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx))))))
% Found (fun (x2:(P (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))))=> x2) as proof of (P0 (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx))))))
% Found x2:(P (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx))))))
% Found (fun (x2:(P (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))))=> x2) as proof of (P (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx))))))
% Found (fun (x2:(P (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx)))))))=> x2) as proof of (P0 (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx))))))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found eq_ref00:=(eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))):(((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found eq_ref00:=(eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))):(((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found eq_ref00:=(eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))):(((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found eq_ref00:=(eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))):(((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found eq_ref00:=(eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))):(((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found eq_ref00:=(eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))):(((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found x2:(P (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0))))))
% Found (fun (x2:(P (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))))=> x2) as proof of (P (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0))))))
% Found (fun (x2:(P (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))))=> x2) as proof of (P0 (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0))))))
% Found x2:(P b)
% Found (fun (x2:(P b))=> x2) as proof of (P b)
% Found (fun (x2:(P b))=> x2) as proof of (P0 b)
% Found x2:(P b)
% Found (fun (x2:(P b))=> x2) as proof of (P b)
% Found (fun (x2:(P b))=> x2) as proof of (P0 b)
% Found x2:(P (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0))))))
% Found (fun (x2:(P (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))))=> x2) as proof of (P (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0))))))
% Found (fun (x2:(P (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))))=> x2) as proof of (P0 (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0))))))
% Found eq_ref00:=(eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))):(((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found eq_ref00:=(eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))):(((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found eq_ref00:=(eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))):(((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found eq_ref00:=(eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))):(((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found eq_ref00:=(eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))):(((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found eq_ref00:=(eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))):(((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found eq_ref00:=(eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))):(((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found eq_ref00:=(eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))):(((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found eq_ref00:=(eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))):(((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found eq_ref00:=(eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))):(((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found eq_ref00:=(eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))):(((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found eq_ref00:=(eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))):(((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found eq_ref00:=(eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))):(((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found eq_ref00:=(eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))):(((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found x01:(P b)
% Found (fun (x01:(P b))=> x01) as proof of (P b)
% Found (fun (x01:(P b))=> x01) as proof of (P0 b)
% Found x01:(P b)
% Found (fun (x01:(P b))=> x01) as proof of (P b)
% Found (fun (x01:(P b))=> x01) as proof of (P0 b)
% Found x01:(P (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (fun (x01:(P (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))))=> x01) as proof of (P (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (fun (x01:(P (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))))=> x01) as proof of (P0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found x01:(P (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (fun (x01:(P (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))))=> x01) as proof of (P (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (fun (x01:(P (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))))=> x01) as proof of (P0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found x01:(P1 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (fun (x01:(P1 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))))=> x01) as proof of (P1 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (fun (x01:(P1 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))))=> x01) as proof of (P2 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found x01:(P1 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (fun (x01:(P1 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))))=> x01) as proof of (P1 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (fun (x01:(P1 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))))=> x01) as proof of (P2 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found x01:(P1 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (fun (x01:(P1 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))))=> x01) as proof of (P1 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (fun (x01:(P1 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))))=> x01) as proof of (P2 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found x01:(P1 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (fun (x01:(P1 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))))=> x01) as proof of (P1 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (fun (x01:(P1 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))))=> x01) as proof of (P2 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found x01:(P1 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (fun (x01:(P1 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))))=> x01) as proof of (P1 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (fun (x01:(P1 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))))=> x01) as proof of (P2 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found x01:(P1 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (fun (x01:(P1 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))))=> x01) as proof of (P1 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (fun (x01:(P1 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))))=> x01) as proof of (P2 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found x01:(P1 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (fun (x01:(P1 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))))=> x01) as proof of (P1 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (fun (x01:(P1 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))))=> x01) as proof of (P2 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found x01:(P1 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (fun (x01:(P1 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))))=> x01) as proof of (P1 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (fun (x01:(P1 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))))=> x01) as proof of (P2 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found eq_ref00:=(eq_ref0 b0):(((eq ((a->Prop)->Prop)) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq ((a->Prop)->Prop)) b0) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0))))))
% Found ((eq_ref ((a->Prop)->Prop)) b0) as proof of (((eq ((a->Prop)->Prop)) b0) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0))))))
% Found ((eq_ref ((a->Prop)->Prop)) b0) as proof of (((eq ((a->Prop)->Prop)) b0) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0))))))
% Found ((eq_ref ((a->Prop)->Prop)) b0) as proof of (((eq ((a->Prop)->Prop)) b0) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0))))))
% Found eta_expansion000:=(eta_expansion00 b):(((eq ((a->Prop)->Prop)) b) (fun (x:(a->Prop))=> (b x)))
% Found (eta_expansion00 b) as proof of (((eq ((a->Prop)->Prop)) b) b0)
% Found ((eta_expansion0 Prop) b) as proof of (((eq ((a->Prop)->Prop)) b) b0)
% Found (((eta_expansion (a->Prop)) Prop) b) as proof of (((eq ((a->Prop)->Prop)) b) b0)
% Found (((eta_expansion (a->Prop)) Prop) b) as proof of (((eq ((a->Prop)->Prop)) b) b0)
% Found (((eta_expansion (a->Prop)) Prop) b) as proof of (((eq ((a->Prop)->Prop)) b) b0)
% Found x02:(P ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (fun (x02:(P ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))))=> x02) as proof of (P ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (fun (x02:(P ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))))=> x02) as proof of (P0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found eq_ref00:=(eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))):(((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found x02:(P ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (fun (x02:(P ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))))=> x02) as proof of (P ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (fun (x02:(P ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))))=> x02) as proof of (P0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found eq_ref00:=(eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))):(((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found x02:(P ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (fun (x02:(P ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))))=> x02) as proof of (P ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (fun (x02:(P ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))))=> x02) as proof of (P0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found eq_ref00:=(eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))):(((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found x02:(P ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (fun (x02:(P ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))))=> x02) as proof of (P ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (fun (x02:(P ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))))=> x02) as proof of (P0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found eq_ref00:=(eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))):(((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found eq_ref00:=(eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))):(((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found x0:(P0 b)
% Instantiate: b:=((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))):Prop
% Found (fun (x0:(P0 b))=> x0) as proof of (P0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (fun (P0:(Prop->Prop)) (x0:(P0 b))=> x0) as proof of ((P0 b)->(P0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))))
% Found (fun (P0:(Prop->Prop)) (x0:(P0 b))=> x0) as proof of (P b)
% Found eq_ref00:=(eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))):(((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found x0:(P0 b)
% Instantiate: b:=((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))):Prop
% Found (fun (x0:(P0 b))=> x0) as proof of (P0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (fun (P0:(Prop->Prop)) (x0:(P0 b))=> x0) as proof of ((P0 b)->(P0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))))
% Found (fun (P0:(Prop->Prop)) (x0:(P0 b))=> x0) as proof of (P b)
% Found eq_ref00:=(eq_ref0 b):(((eq ((a->Prop)->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq ((a->Prop)->Prop)) b) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx))))))
% Found ((eq_ref ((a->Prop)->Prop)) b) as proof of (((eq ((a->Prop)->Prop)) b) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx))))))
% Found ((eq_ref ((a->Prop)->Prop)) b) as proof of (((eq ((a->Prop)->Prop)) b) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx))))))
% Found ((eq_ref ((a->Prop)->Prop)) b) as proof of (((eq ((a->Prop)->Prop)) b) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx))))))
% Found eta_expansion000:=(eta_expansion00 (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))):(((eq ((a->Prop)->Prop)) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) (fun (x:(a->Prop))=> ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))))
% Found (eta_expansion00 (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) as proof of (((eq ((a->Prop)->Prop)) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) b)
% Found ((eta_expansion0 Prop) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) as proof of (((eq ((a->Prop)->Prop)) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) b)
% Found (((eta_expansion (a->Prop)) Prop) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) as proof of (((eq ((a->Prop)->Prop)) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) b)
% Found (((eta_expansion (a->Prop)) Prop) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) as proof of (((eq ((a->Prop)->Prop)) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) b)
% Found (((eta_expansion (a->Prop)) Prop) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) as proof of (((eq ((a->Prop)->Prop)) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq ((a->Prop)->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq ((a->Prop)->Prop)) b) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx))))))
% Found ((eq_ref ((a->Prop)->Prop)) b) as proof of (((eq ((a->Prop)->Prop)) b) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx))))))
% Found ((eq_ref ((a->Prop)->Prop)) b) as proof of (((eq ((a->Prop)->Prop)) b) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx))))))
% Found ((eq_ref ((a->Prop)->Prop)) b) as proof of (((eq ((a->Prop)->Prop)) b) (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx))))))
% Found eta_expansion000:=(eta_expansion00 (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))):(((eq ((a->Prop)->Prop)) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) (fun (x:(a->Prop))=> ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))))
% Found (eta_expansion00 (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) as proof of (((eq ((a->Prop)->Prop)) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) b)
% Found ((eta_expansion0 Prop) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) as proof of (((eq ((a->Prop)->Prop)) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) b)
% Found (((eta_expansion (a->Prop)) Prop) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) as proof of (((eq ((a->Prop)->Prop)) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) b)
% Found (((eta_expansion (a->Prop)) Prop) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) as proof of (((eq ((a->Prop)->Prop)) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) b)
% Found (((eta_expansion (a->Prop)) Prop) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) as proof of (((eq ((a->Prop)->Prop)) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) b)
% Found x0:(P (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Instantiate: b:=(forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))):Prop
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))):(((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found x0:(P (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Instantiate: b:=(forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))):Prop
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))):(((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found eq_ref00:=(eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))):(((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b0)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b0)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b0)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found eq_ref00:=(eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))):(((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b0)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b0)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b0)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b0)
% Found eq_ref00:=(eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))):(((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b0)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b0)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b0)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found eq_ref00:=(eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))):(((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b0)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b0)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b0)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found eq_ref00:=(eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))):(((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found eq_ref00:=(eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))):(((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found eq_ref00:=(eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))):(((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found eq_ref00:=(eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))):(((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found eq_ref00:=(eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))):(((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b0)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b0)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b0)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found eq_ref00:=(eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))):(((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b0)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b0)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b0)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found x2:(P (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0))))))
% Found (fun (x2:(P (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))))=> x2) as proof of (P (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0))))))
% Found (fun (x2:(P (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))))=> x2) as proof of (P0 (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0))))))
% Found x2:(P (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0))))))
% Found (fun (x2:(P (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))))=> x2) as proof of (P (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0))))))
% Found (fun (x2:(P (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))))=> x2) as proof of (P0 (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0))))))
% Found x2:(P (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0))))))
% Found (fun (x2:(P (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))))=> x2) as proof of (P (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0))))))
% Found (fun (x2:(P (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))))=> x2) as proof of (P0 (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0))))))
% Found x2:(P (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0))))))
% Found (fun (x2:(P (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))))=> x2) as proof of (P (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0))))))
% Found (fun (x2:(P (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))))=> x2) as proof of (P0 (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0))))))
% Found x01:(P (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (fun (x01:(P (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))))=> x01) as proof of (P (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (fun (x01:(P (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))))=> x01) as proof of (P0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found x01:(P (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (fun (x01:(P (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))))=> x01) as proof of (P (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (fun (x01:(P (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))))=> x01) as proof of (P0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found x01:(P (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (fun (x01:(P (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))))=> x01) as proof of (P (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (fun (x01:(P (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))))=> x01) as proof of (P0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found x01:(P (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (fun (x01:(P (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))))=> x01) as proof of (P (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (fun (x01:(P (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))))=> x01) as proof of (P0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found x2:(P b)
% Found (fun (x2:(P b))=> x2) as proof of (P b)
% Found (fun (x2:(P b))=> x2) as proof of (P0 b)
% Found x2:(P b)
% Found (fun (x2:(P b))=> x2) as proof of (P b)
% Found (fun (x2:(P b))=> x2) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found eq_ref00:=(eq_ref0 (b x)):(((eq Prop) (b x)) (b x))
% Found (eq_ref0 (b x)) as proof of (((eq Prop) (b x)) b0)
% Found ((eq_ref Prop) (b x)) as proof of (((eq Prop) (b x)) b0)
% Found ((eq_ref Prop) (b x)) as proof of (((eq Prop) (b x)) b0)
% Found ((eq_ref Prop) (b x)) as proof of (((eq Prop) (b x)) b0)
% Found eq_ref00:=(eq_ref0 (b x)):(((eq Prop) (b x)) (b x))
% Found (eq_ref0 (b x)) as proof of (((eq Prop) (b x)) b0)
% Found ((eq_ref Prop) (b x)) as proof of (((eq Prop) (b x)) b0)
% Found ((eq_ref Prop) (b x)) as proof of (((eq Prop) (b x)) b0)
% Found ((eq_ref Prop) (b x)) as proof of (((eq Prop) (b x)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found eq_ref00:=(eq_ref0 (b x)):(((eq Prop) (b x)) (b x))
% Found (eq_ref0 (b x)) as proof of (((eq Prop) (b x)) b0)
% Found ((eq_ref Prop) (b x)) as proof of (((eq Prop) (b x)) b0)
% Found ((eq_ref Prop) (b x)) as proof of (((eq Prop) (b x)) b0)
% Found ((eq_ref Prop) (b x)) as proof of (((eq Prop) (b x)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found eq_ref00:=(eq_ref0 (b x)):(((eq Prop) (b x)) (b x))
% Found (eq_ref0 (b x)) as proof of (((eq Prop) (b x)) b0)
% Found ((eq_ref Prop) (b x)) as proof of (((eq Prop) (b x)) b0)
% Found ((eq_ref Prop) (b x)) as proof of (((eq Prop) (b x)) b0)
% Found ((eq_ref Prop) (b x)) as proof of (((eq Prop) (b x)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found eq_ref00:=(eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))):(((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b0)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b0)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b0)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x))
% Found eq_ref00:=(eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))):(((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b0)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b0)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b0)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x))
% Found x01:(P b)
% Found (fun (x01:(P b))=> x01) as proof of (P b)
% Found (fun (x01:(P b))=> x01) as proof of (P0 b)
% Found x01:(P b)
% Found (fun (x01:(P b))=> x01) as proof of (P b)
% Found (fun (x01:(P b))=> x01) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found eq_ref00:=(eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))):(((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found eq_ref00:=(eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))):(((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found eq_ref00:=(eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))):(((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found eq_ref00:=(eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))):(((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found eq_ref00:=(eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))):(((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found eq_ref00:=(eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))):(((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found eq_ref00:=(eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))):(((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found eq_ref00:=(eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))):(((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found eq_ref00:=(eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))):(((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found eq_ref00:=(eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))):(((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found eq_ref00:=(eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))):(((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found eq_ref00:=(eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))):(((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found eq_ref00:=(eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))):(((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found eq_ref00:=(eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))):(((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found x01:(P b)
% Found (fun (x01:(P b))=> x01) as proof of (P b)
% Found (fun (x01:(P b))=> x01) as proof of (P0 b)
% Found x01:(P b)
% Found (fun (x01:(P b))=> x01) as proof of (P b)
% Found (fun (x01:(P b))=> x01) as proof of (P0 b)
% Found x01:(P (b x))
% Found (fun (x01:(P (b x)))=> x01) as proof of (P (b x))
% Found (fun (x01:(P (b x)))=> x01) as proof of (P0 (b x))
% Found x01:(P (b x))
% Found (fun (x01:(P (b x)))=> x01) as proof of (P (b x))
% Found (fun (x01:(P (b x)))=> x01) as proof of (P0 (b x))
% Found x01:(P ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (fun (x01:(P ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))))=> x01) as proof of (P ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (fun (x01:(P ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))))=> x01) as proof of (P0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found x01:(P ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (fun (x01:(P ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))))=> x01) as proof of (P ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (fun (x01:(P ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))))=> x01) as proof of (P0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found x02:(P (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (fun (x02:(P (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))))=> x02) as proof of (P (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (fun (x02:(P (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))))=> x02) as proof of (P0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found eq_ref00:=(eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))):(((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found x02:(P (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (fun (x02:(P (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))))=> x02) as proof of (P (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (fun (x02:(P (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))))=> x02) as proof of (P0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found eq_ref00:=(eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))):(((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found eq_ref00:=(eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))):(((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found eq_ref00:=(eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))):(((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found eq_ref00:=(eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))):(((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found eq_ref00:=(eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))):(((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found eq_ref00:=(eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))):(((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found eq_ref00:=(eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))):(((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found eq_ref00:=(eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))):(((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found eq_ref00:=(eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))):(((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found eq_ref00:=(eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))):(((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found eq_ref00:=(eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))):(((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found eq_ref00:=(eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))):(((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found eq_ref00:=(eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))):(((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (eq_ref0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found ((eq_ref Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) as proof of (((eq Prop) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found eq_ref00:=(eq_ref0 a0):(((eq Prop) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq Prop) a0) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))
% Found eq_ref00:=(eq_ref0 a0):(((eq Prop) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq Prop) a0) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))
% Found eq_ref00:=(eq_ref0 a0):(((eq Prop) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq Prop) a0) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))
% Found eq_ref00:=(eq_ref0 a0):(((eq Prop) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq Prop) a0) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))
% Found eq_ref00:=(eq_ref0 a0):(((eq Prop) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq Prop) a0) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))
% Found eq_ref00:=(eq_ref0 a0):(((eq Prop) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq Prop) a0) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))
% Found eq_ref00:=(eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))):(((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b0)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b0)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b0)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found eq_ref00:=(eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))):(((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b0)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b0)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b0)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b0)
% Found eq_ref00:=(eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))):(((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b0)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b0)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b0)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found eq_ref00:=(eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))):(((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b0)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b0)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b0)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found x01:(P ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (fun (x01:(P ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))))=> x01) as proof of (P ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (fun (x01:(P ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))))=> x01) as proof of (P0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found x01:(P ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (fun (x01:(P ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))))=> x01) as proof of (P ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (fun (x01:(P ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))))=> x01) as proof of (P0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found x01:(P ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (fun (x01:(P ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))))=> x01) as proof of (P ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (fun (x01:(P ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))))=> x01) as proof of (P0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found x01:(P ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (fun (x01:(P ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))))=> x01) as proof of (P ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (fun (x01:(P ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))))=> x01) as proof of (P0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found x01:(P ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (fun (x01:(P ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))))=> x01) as proof of (P ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (fun (x01:(P ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))))=> x01) as proof of (P0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found x01:(P ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (fun (x01:(P ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))))=> x01) as proof of (P ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found (fun (x01:(P ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0))))))=> x01) as proof of (P0 ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found eq_ref00:=(eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))):(((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b0)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b0)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b0)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found eq_ref00:=(eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))):(((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b0)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b0)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b0)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found eq_ref00:=(eq_ref0 (b x)):(((eq Prop) (b x)) (b x))
% Found (eq_ref0 (b x)) as proof of (((eq Prop) (b x)) b0)
% Found ((eq_ref Prop) (b x)) as proof of (((eq Prop) (b x)) b0)
% Found ((eq_ref Prop) (b x)) as proof of (((eq Prop) (b x)) b0)
% Found ((eq_ref Prop) (b x)) as proof of (((eq Prop) (b x)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found eq_ref00:=(eq_ref0 (b x)):(((eq Prop) (b x)) (b x))
% Found (eq_ref0 (b x)) as proof of (((eq Prop) (b x)) b0)
% Found ((eq_ref Prop) (b x)) as proof of (((eq Prop) (b x)) b0)
% Found ((eq_ref Prop) (b x)) as proof of (((eq Prop) (b x)) b0)
% Found ((eq_ref Prop) (b x)) as proof of (((eq Prop) (b x)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x))
% Found eq_ref00:=(eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))):(((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b0)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b0)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b0)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x))
% Found eq_ref00:=(eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))):(((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b0)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b0)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b0)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b0)
% Found eq_ref00:=(eq_ref0 (b x)):(((eq Prop) (b x)) (b x))
% Found (eq_ref0 (b x)) as proof of (((eq Prop) (b x)) b0)
% Found ((eq_ref Prop) (b x)) as proof of (((eq Prop) (b x)) b0)
% Found ((eq_ref Prop) (b x)) as proof of (((eq Prop) (b x)) b0)
% Found ((eq_ref Prop) (b x)) as proof of (((eq Prop) (b x)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found eq_ref00:=(eq_ref0 (b x)):(((eq Prop) (b x)) (b x))
% Found (eq_ref0 (b x)) as proof of (((eq Prop) (b x)) b0)
% Found ((eq_ref Prop) (b x)) as proof of (((eq Prop) (b x)) b0)
% Found ((eq_ref Prop) (b x)) as proof of (((eq Prop) (b x)) b0)
% Found ((eq_ref Prop) (b x)) as proof of (((eq Prop) (b x)) b0)
% Found x01:(P (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (fun (x01:(P (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))))=> x01) as proof of (P (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (fun (x01:(P (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))))=> x01) as proof of (P0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found x01:(P b)
% Found (fun (x01:(P b))=> x01) as proof of (P b)
% Found (fun (x01:(P b))=> x01) as proof of (P0 b)
% Found x01:(P (b x))
% Found (fun (x01:(P (b x)))=> x01) as proof of (P (b x))
% Found (fun (x01:(P (b x)))=> x01) as proof of (P0 (b x))
% Found x01:(P (b x))
% Found (fun (x01:(P (b x)))=> x01) as proof of (P (b x))
% Found (fun (x01:(P (b x)))=> x01) as proof of (P0 (b x))
% Found x:(P (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx))))))
% Instantiate: b:=(fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx))))):((a->Prop)->Prop)
% Found x as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))):(((eq ((a->Prop)->Prop)) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0))))))
% Found (eq_ref0 (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) as proof of (((eq ((a->Prop)->Prop)) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) b)
% Found ((eq_ref ((a->Prop)->Prop)) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) as proof of (((eq ((a->Prop)->Prop)) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) b)
% Found ((eq_ref ((a->Prop)->Prop)) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) as proof of (((eq ((a->Prop)->Prop)) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) b)
% Found ((eq_ref ((a->Prop)->Prop)) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) as proof of (((eq ((a->Prop)->Prop)) (fun (Xx:(a->Prop))=> ((and (forall (Xx0:a), ((Xx Xx0)->(cD Xx0)))) (forall (Xx0:a), ((Xx Xx0)->(cE Xx0)))))) b)
% Found x:(P (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx))))))
% Instantiate: f:=(fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx))))):((a->Prop)->Prop)
% Found x as proof of (P0 f)
% Found x:(P (fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx))))))
% Instantiate: f:=(fun (R:(a->Prop))=> (forall (Xx:a), ((R Xx)->((and (cD Xx)) (cE Xx))))):((a->Prop)->Prop)
% Found x as proof of (P0 f)
% Found eq_ref00:=(eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))):(((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found eq_ref00:=(eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))):(((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found eq_ref00:=(eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))):(((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found eq_ref00:=(eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))):(((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx)))))
% Found (eq_ref0 (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) as proof of (((eq Prop) (forall (Xx:a), ((x Xx)->((and (cD Xx)) (cE Xx))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (forall (Xx0:a), ((x Xx0)->(cD Xx0)))) (forall (Xx0:a), ((x Xx0)->(cE Xx0)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and
% EOF
%------------------------------------------------------------------------------