TSTP Solution File: SEV385^5 by cocATP---0.2.0

%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SEV385^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n106.star.cs.uiowa.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory   : 32286.75MB
% OS       : Linux 2.6.32-431.20.3.el6.x86_64
% CPULimit : 300s
% DateTime : Thu Jul 17 13:34:07 EDT 2014

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

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SEV385^5 : TPTP v6.1.0. Released v4.0.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n106.star.cs.uiowa.edu
% % Model    : x86_64 x86_64
% % CPU      : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% % Memory   : 32286.75MB
% % OS       : Linux 2.6.32-431.20.3.el6.x86_64
% % CPULimit : 300
% % DateTime : Thu Jul 17 09:02:51 CDT 2014
% % CPUTime  : 300.11 
% Python 2.7.5
% Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% FOF formula (<kernel.Constant object at 0xe688c0>, <kernel.Type object at 0xe68518>) of role type named b_type
% Using role type
% Declaring b:Type
% FOF formula (<kernel.Constant object at 0xe680e0>, <kernel.Type object at 0xb6d5f0>) of role type named a_type
% Using role type
% Declaring a:Type
% FOF formula (<kernel.Constant object at 0x10de6c8>, <kernel.Constant object at 0xe688c0>) of role type named x
% Using role type
% Declaring x:b
% FOF formula (<kernel.Constant object at 0xe685f0>, <kernel.Constant object at 0xe688c0>) of role type named y
% Using role type
% Declaring y:a
% FOF formula ((ex (b->a)) (fun (Xs:(b->a))=> ((and (forall (Xx_6:b), ((((eq b) x) Xx_6)->(((eq a) y) (Xs Xx_6))))) (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (Xs Xx_7))))) ((fun (Xx:b) (Xy:b)=> (((eq b) Xx) Xy)) Xy0))))))))) of role conjecture named cX6004_pme
% Conjecture to prove = ((ex (b->a)) (fun (Xs:(b->a))=> ((and (forall (Xx_6:b), ((((eq b) x) Xx_6)->(((eq a) y) (Xs Xx_6))))) (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (Xs Xx_7))))) ((fun (Xx:b) (Xy:b)=> (((eq b) Xx) Xy)) Xy0))))))))):Prop
% We need to prove ['((ex (b->a)) (fun (Xs:(b->a))=> ((and (forall (Xx_6:b), ((((eq b) x) Xx_6)->(((eq a) y) (Xs Xx_6))))) (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (Xs Xx_7))))) ((fun (Xx:b) (Xy:b)=> (((eq b) Xx) Xy)) Xy0)))))))))']
% Parameter b:Type.
% Parameter a:Type.
% Parameter x:b.
% Parameter y:a.
% Trying to prove ((ex (b->a)) (fun (Xs:(b->a))=> ((and (forall (Xx_6:b), ((((eq b) x) Xx_6)->(((eq a) y) (Xs Xx_6))))) (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (Xs Xx_7))))) ((fun (Xx:b) (Xy:b)=> (((eq b) Xx) Xy)) Xy0)))))))))
% Found eq_ref00:=(eq_ref0 (x0 Xx_6)):(((eq a) (x0 Xx_6)) (x0 Xx_6))
% Found (eq_ref0 (x0 Xx_6)) as proof of (((eq a) (x0 Xx_6)) y)
% Found ((eq_ref a) (x0 Xx_6)) as proof of (((eq a) (x0 Xx_6)) y)
% Found ((eq_ref a) (x0 Xx_6)) as proof of (((eq a) (x0 Xx_6)) y)
% Found ((eq_ref a) (x0 Xx_6)) as proof of (((eq a) (x0 Xx_6)) y)
% Found (eq_sym000 ((eq_ref a) (x0 Xx_6))) as proof of (((eq a) y) (x0 Xx_6))
% Found ((eq_sym00 y) ((eq_ref a) (x0 Xx_6))) as proof of (((eq a) y) (x0 Xx_6))
% Found (((eq_sym0 (x0 Xx_6)) y) ((eq_ref a) (x0 Xx_6))) as proof of (((eq a) y) (x0 Xx_6))
% Found ((((eq_sym a) (x0 Xx_6)) y) ((eq_ref a) (x0 Xx_6))) as proof of (((eq a) y) (x0 Xx_6))
% Found (fun (x1:(((eq b) x) Xx_6))=> ((((eq_sym a) (x0 Xx_6)) y) ((eq_ref a) (x0 Xx_6)))) as proof of (((eq a) y) (x0 Xx_6))
% Found (fun (Xx_6:b) (x1:(((eq b) x) Xx_6))=> ((((eq_sym a) (x0 Xx_6)) y) ((eq_ref a) (x0 Xx_6)))) as proof of ((((eq b) x) Xx_6)->(((eq a) y) (x0 Xx_6)))
% Found (fun (Xx_6:b) (x1:(((eq b) x) Xx_6))=> ((((eq_sym a) (x0 Xx_6)) y) ((eq_ref a) (x0 Xx_6)))) as proof of (forall (Xx_6:b), ((((eq b) x) Xx_6)->(((eq a) y) (x0 Xx_6))))
% Found eq_ref00:=(eq_ref0 (x0 Xx_6)):(((eq a) (x0 Xx_6)) (x0 Xx_6))
% Found (eq_ref0 (x0 Xx_6)) as proof of (((eq a) (x0 Xx_6)) y)
% Found ((eq_ref a) (x0 Xx_6)) as proof of (((eq a) (x0 Xx_6)) y)
% Found ((eq_ref a) (x0 Xx_6)) as proof of (((eq a) (x0 Xx_6)) y)
% Found ((eq_ref a) (x0 Xx_6)) as proof of (((eq a) (x0 Xx_6)) y)
% Found (eq_sym000 ((eq_ref a) (x0 Xx_6))) as proof of (((eq a) y) (x0 Xx_6))
% Found ((eq_sym00 y) ((eq_ref a) (x0 Xx_6))) as proof of (((eq a) y) (x0 Xx_6))
% Found (((eq_sym0 (x0 Xx_6)) y) ((eq_ref a) (x0 Xx_6))) as proof of (((eq a) y) (x0 Xx_6))
% Found ((((eq_sym a) (x0 Xx_6)) y) ((eq_ref a) (x0 Xx_6))) as proof of (((eq a) y) (x0 Xx_6))
% Found (fun (x00:(((eq b) x) Xx_6))=> ((((eq_sym a) (x0 Xx_6)) y) ((eq_ref a) (x0 Xx_6)))) as proof of (((eq a) y) (x0 Xx_6))
% Found (fun (Xx_6:b) (x00:(((eq b) x) Xx_6))=> ((((eq_sym a) (x0 Xx_6)) y) ((eq_ref a) (x0 Xx_6)))) as proof of ((((eq b) x) Xx_6)->(((eq a) y) (x0 Xx_6)))
% Found (fun (Xx_6:b) (x00:(((eq b) x) Xx_6))=> ((((eq_sym a) (x0 Xx_6)) y) ((eq_ref a) (x0 Xx_6)))) as proof of (forall (Xx_6:b), ((((eq b) x) Xx_6)->(((eq a) y) (x0 Xx_6))))
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xs:(b->a))=> ((and (forall (Xx_6:b), ((((eq b) x) Xx_6)->(((eq a) y) (Xs Xx_6))))) (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (Xs Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy)))))))))):(((eq ((b->a)->Prop)) (fun (Xs:(b->a))=> ((and (forall (Xx_6:b), ((((eq b) x) Xx_6)->(((eq a) y) (Xs Xx_6))))) (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (Xs Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy)))))))))) (fun (x0:(b->a))=> ((and (forall (Xx_6:b), ((((eq b) x) Xx_6)->(((eq a) y) (x0 Xx_6))))) (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy))))))))))
% Found (eta_expansion_dep00 (fun (Xs:(b->a))=> ((and (forall (Xx_6:b), ((((eq b) x) Xx_6)->(((eq a) y) (Xs Xx_6))))) (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (Xs Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy)))))))))) as proof of (((eq ((b->a)->Prop)) (fun (Xs:(b->a))=> ((and (forall (Xx_6:b), ((((eq b) x) Xx_6)->(((eq a) y) (Xs Xx_6))))) (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (Xs Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy)))))))))) b0)
% Found ((eta_expansion_dep0 (fun (x1:(b->a))=> Prop)) (fun (Xs:(b->a))=> ((and (forall (Xx_6:b), ((((eq b) x) Xx_6)->(((eq a) y) (Xs Xx_6))))) (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (Xs Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy)))))))))) as proof of (((eq ((b->a)->Prop)) (fun (Xs:(b->a))=> ((and (forall (Xx_6:b), ((((eq b) x) Xx_6)->(((eq a) y) (Xs Xx_6))))) (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (Xs Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy)))))))))) b0)
% Found (((eta_expansion_dep (b->a)) (fun (x1:(b->a))=> Prop)) (fun (Xs:(b->a))=> ((and (forall (Xx_6:b), ((((eq b) x) Xx_6)->(((eq a) y) (Xs Xx_6))))) (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (Xs Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy)))))))))) as proof of (((eq ((b->a)->Prop)) (fun (Xs:(b->a))=> ((and (forall (Xx_6:b), ((((eq b) x) Xx_6)->(((eq a) y) (Xs Xx_6))))) (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (Xs Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy)))))))))) b0)
% Found (((eta_expansion_dep (b->a)) (fun (x1:(b->a))=> Prop)) (fun (Xs:(b->a))=> ((and (forall (Xx_6:b), ((((eq b) x) Xx_6)->(((eq a) y) (Xs Xx_6))))) (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (Xs Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy)))))))))) as proof of (((eq ((b->a)->Prop)) (fun (Xs:(b->a))=> ((and (forall (Xx_6:b), ((((eq b) x) Xx_6)->(((eq a) y) (Xs Xx_6))))) (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (Xs Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy)))))))))) b0)
% Found (((eta_expansion_dep (b->a)) (fun (x1:(b->a))=> Prop)) (fun (Xs:(b->a))=> ((and (forall (Xx_6:b), ((((eq b) x) Xx_6)->(((eq a) y) (Xs Xx_6))))) (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (Xs Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy)))))))))) as proof of (((eq ((b->a)->Prop)) (fun (Xs:(b->a))=> ((and (forall (Xx_6:b), ((((eq b) x) Xx_6)->(((eq a) y) (Xs Xx_6))))) (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (Xs Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy)))))))))) b0)
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xs:(b->a))=> ((and (forall (Xx_6:b), ((((eq b) x) Xx_6)->(((eq a) y) (Xs Xx_6))))) (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (Xs Xx_7))))) ((eq b) Xy0))))))))):(((eq ((b->a)->Prop)) (fun (Xs:(b->a))=> ((and (forall (Xx_6:b), ((((eq b) x) Xx_6)->(((eq a) y) (Xs Xx_6))))) (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (Xs Xx_7))))) ((eq b) Xy0))))))))) (fun (x0:(b->a))=> ((and (forall (Xx_6:b), ((((eq b) x) Xx_6)->(((eq a) y) (x0 Xx_6))))) (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) ((eq b) Xy0)))))))))
% Found (eta_expansion_dep00 (fun (Xs:(b->a))=> ((and (forall (Xx_6:b), ((((eq b) x) Xx_6)->(((eq a) y) (Xs Xx_6))))) (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (Xs Xx_7))))) ((eq b) Xy0))))))))) as proof of (((eq ((b->a)->Prop)) (fun (Xs:(b->a))=> ((and (forall (Xx_6:b), ((((eq b) x) Xx_6)->(((eq a) y) (Xs Xx_6))))) (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (Xs Xx_7))))) ((eq b) Xy0))))))))) b0)
% Found ((eta_expansion_dep0 (fun (x1:(b->a))=> Prop)) (fun (Xs:(b->a))=> ((and (forall (Xx_6:b), ((((eq b) x) Xx_6)->(((eq a) y) (Xs Xx_6))))) (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (Xs Xx_7))))) ((eq b) Xy0))))))))) as proof of (((eq ((b->a)->Prop)) (fun (Xs:(b->a))=> ((and (forall (Xx_6:b), ((((eq b) x) Xx_6)->(((eq a) y) (Xs Xx_6))))) (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (Xs Xx_7))))) ((eq b) Xy0))))))))) b0)
% Found (((eta_expansion_dep (b->a)) (fun (x1:(b->a))=> Prop)) (fun (Xs:(b->a))=> ((and (forall (Xx_6:b), ((((eq b) x) Xx_6)->(((eq a) y) (Xs Xx_6))))) (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (Xs Xx_7))))) ((eq b) Xy0))))))))) as proof of (((eq ((b->a)->Prop)) (fun (Xs:(b->a))=> ((and (forall (Xx_6:b), ((((eq b) x) Xx_6)->(((eq a) y) (Xs Xx_6))))) (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (Xs Xx_7))))) ((eq b) Xy0))))))))) b0)
% Found (((eta_expansion_dep (b->a)) (fun (x1:(b->a))=> Prop)) (fun (Xs:(b->a))=> ((and (forall (Xx_6:b), ((((eq b) x) Xx_6)->(((eq a) y) (Xs Xx_6))))) (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (Xs Xx_7))))) ((eq b) Xy0))))))))) as proof of (((eq ((b->a)->Prop)) (fun (Xs:(b->a))=> ((and (forall (Xx_6:b), ((((eq b) x) Xx_6)->(((eq a) y) (Xs Xx_6))))) (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (Xs Xx_7))))) ((eq b) Xy0))))))))) b0)
% Found (((eta_expansion_dep (b->a)) (fun (x1:(b->a))=> Prop)) (fun (Xs:(b->a))=> ((and (forall (Xx_6:b), ((((eq b) x) Xx_6)->(((eq a) y) (Xs Xx_6))))) (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (Xs Xx_7))))) ((eq b) Xy0))))))))) as proof of (((eq ((b->a)->Prop)) (fun (Xs:(b->a))=> ((and (forall (Xx_6:b), ((((eq b) x) Xx_6)->(((eq a) y) (Xs Xx_6))))) (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (Xs Xx_7))))) ((eq b) Xy0))))))))) b0)
% Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) ((and (forall (Xx_6:b), ((((eq b) x) Xx_6)->(((eq a) y) (x0 Xx_6))))) (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy)))))))))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) ((and (forall (Xx_6:b), ((((eq b) x) Xx_6)->(((eq a) y) (x0 Xx_6))))) (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy)))))))))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) ((and (forall (Xx_6:b), ((((eq b) x) Xx_6)->(((eq a) y) (x0 Xx_6))))) (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy)))))))))
% Found (fun (x0:(b->a))=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) ((and (forall (Xx_6:b), ((((eq b) x) Xx_6)->(((eq a) y) (x0 Xx_6))))) (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy)))))))))
% Found (fun (x0:(b->a))=> ((eq_ref Prop) (f x0))) as proof of (forall (x0:(b->a)), (((eq Prop) (f x0)) ((and (forall (Xx_6:b), ((((eq b) x) Xx_6)->(((eq a) y) (x0 Xx_6))))) (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy))))))))))
% Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) ((and (forall (Xx_6:b), ((((eq b) x) Xx_6)->(((eq a) y) (x0 Xx_6))))) (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy)))))))))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) ((and (forall (Xx_6:b), ((((eq b) x) Xx_6)->(((eq a) y) (x0 Xx_6))))) (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy)))))))))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) ((and (forall (Xx_6:b), ((((eq b) x) Xx_6)->(((eq a) y) (x0 Xx_6))))) (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy)))))))))
% Found (fun (x0:(b->a))=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) ((and (forall (Xx_6:b), ((((eq b) x) Xx_6)->(((eq a) y) (x0 Xx_6))))) (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy)))))))))
% Found (fun (x0:(b->a))=> ((eq_ref Prop) (f x0))) as proof of (forall (x0:(b->a)), (((eq Prop) (f x0)) ((and (forall (Xx_6:b), ((((eq b) x) Xx_6)->(((eq a) y) (x0 Xx_6))))) (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy))))))))))
% Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) ((and (forall (Xx_6:b), ((((eq b) x) Xx_6)->(((eq a) y) (x0 Xx_6))))) (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) ((eq b) Xy0))))))))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) ((and (forall (Xx_6:b), ((((eq b) x) Xx_6)->(((eq a) y) (x0 Xx_6))))) (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) ((eq b) Xy0))))))))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) ((and (forall (Xx_6:b), ((((eq b) x) Xx_6)->(((eq a) y) (x0 Xx_6))))) (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) ((eq b) Xy0))))))))
% Found (fun (x0:(b->a))=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) ((and (forall (Xx_6:b), ((((eq b) x) Xx_6)->(((eq a) y) (x0 Xx_6))))) (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) ((eq b) Xy0))))))))
% Found (fun (x0:(b->a))=> ((eq_ref Prop) (f x0))) as proof of (forall (x0:(b->a)), (((eq Prop) (f x0)) ((and (forall (Xx_6:b), ((((eq b) x) Xx_6)->(((eq a) y) (x0 Xx_6))))) (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) ((eq b) Xy0)))))))))
% Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) ((and (forall (Xx_6:b), ((((eq b) x) Xx_6)->(((eq a) y) (x0 Xx_6))))) (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) ((eq b) Xy0))))))))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) ((and (forall (Xx_6:b), ((((eq b) x) Xx_6)->(((eq a) y) (x0 Xx_6))))) (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) ((eq b) Xy0))))))))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) ((and (forall (Xx_6:b), ((((eq b) x) Xx_6)->(((eq a) y) (x0 Xx_6))))) (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) ((eq b) Xy0))))))))
% Found (fun (x0:(b->a))=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) ((and (forall (Xx_6:b), ((((eq b) x) Xx_6)->(((eq a) y) (x0 Xx_6))))) (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) ((eq b) Xy0))))))))
% Found (fun (x0:(b->a))=> ((eq_ref Prop) (f x0))) as proof of (forall (x0:(b->a)), (((eq Prop) (f x0)) ((and (forall (Xx_6:b), ((((eq b) x) Xx_6)->(((eq a) y) (x0 Xx_6))))) (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) ((eq b) Xy0)))))))))
% Found eta_expansion_dep000:=(eta_expansion_dep00 a0):(((eq ((b->a)->Prop)) a0) (fun (x:(b->a))=> (a0 x)))
% Found (eta_expansion_dep00 a0) as proof of (((eq ((b->a)->Prop)) a0) b0)
% Found ((eta_expansion_dep0 (fun (x1:(b->a))=> Prop)) a0) as proof of (((eq ((b->a)->Prop)) a0) b0)
% Found (((eta_expansion_dep (b->a)) (fun (x1:(b->a))=> Prop)) a0) as proof of (((eq ((b->a)->Prop)) a0) b0)
% Found (((eta_expansion_dep (b->a)) (fun (x1:(b->a))=> Prop)) a0) as proof of (((eq ((b->a)->Prop)) a0) b0)
% Found (((eta_expansion_dep (b->a)) (fun (x1:(b->a))=> Prop)) a0) as proof of (((eq ((b->a)->Prop)) a0) b0)
% Found eta_expansion000:=(eta_expansion00 b0):(((eq ((b->a)->Prop)) b0) (fun (x:(b->a))=> (b0 x)))
% Found (eta_expansion00 b0) as proof of (((eq ((b->a)->Prop)) b0) (fun (Xs:(b->a))=> ((and (forall (Xx_6:b), ((((eq b) x) Xx_6)->(((eq a) y) (Xs Xx_6))))) (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (Xs Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy))))))))))
% Found ((eta_expansion0 Prop) b0) as proof of (((eq ((b->a)->Prop)) b0) (fun (Xs:(b->a))=> ((and (forall (Xx_6:b), ((((eq b) x) Xx_6)->(((eq a) y) (Xs Xx_6))))) (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (Xs Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy))))))))))
% Found (((eta_expansion (b->a)) Prop) b0) as proof of (((eq ((b->a)->Prop)) b0) (fun (Xs:(b->a))=> ((and (forall (Xx_6:b), ((((eq b) x) Xx_6)->(((eq a) y) (Xs Xx_6))))) (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (Xs Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy))))))))))
% Found (((eta_expansion (b->a)) Prop) b0) as proof of (((eq ((b->a)->Prop)) b0) (fun (Xs:(b->a))=> ((and (forall (Xx_6:b), ((((eq b) x) Xx_6)->(((eq a) y) (Xs Xx_6))))) (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (Xs Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy))))))))))
% Found (((eta_expansion (b->a)) Prop) b0) as proof of (((eq ((b->a)->Prop)) b0) (fun (Xs:(b->a))=> ((and (forall (Xx_6:b), ((((eq b) x) Xx_6)->(((eq a) y) (Xs Xx_6))))) (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (Xs Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy))))))))))
% Found eq_ref00:=(eq_ref0 b0):(((eq ((b->a)->Prop)) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq ((b->a)->Prop)) b0) (fun (Xs:(b->a))=> ((and (forall (Xx_6:b), ((((eq b) x) Xx_6)->(((eq a) y) (Xs Xx_6))))) (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (Xs Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy))))))))))
% Found ((eq_ref ((b->a)->Prop)) b0) as proof of (((eq ((b->a)->Prop)) b0) (fun (Xs:(b->a))=> ((and (forall (Xx_6:b), ((((eq b) x) Xx_6)->(((eq a) y) (Xs Xx_6))))) (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (Xs Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy))))))))))
% Found ((eq_ref ((b->a)->Prop)) b0) as proof of (((eq ((b->a)->Prop)) b0) (fun (Xs:(b->a))=> ((and (forall (Xx_6:b), ((((eq b) x) Xx_6)->(((eq a) y) (Xs Xx_6))))) (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (Xs Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy))))))))))
% Found ((eq_ref ((b->a)->Prop)) b0) as proof of (((eq ((b->a)->Prop)) b0) (fun (Xs:(b->a))=> ((and (forall (Xx_6:b), ((((eq b) x) Xx_6)->(((eq a) y) (Xs Xx_6))))) (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (Xs Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy))))))))))
% Found eq_ref00:=(eq_ref0 (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy)))))))):(((eq Prop) (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy)))))))) (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy))))))))
% Found (eq_ref0 (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy)))))))) as proof of (((eq Prop) (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy)))))))) b0)
% Found ((eq_ref Prop) (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy)))))))) as proof of (((eq Prop) (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy)))))))) b0)
% Found ((eq_ref Prop) (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy)))))))) as proof of (((eq Prop) (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy)))))))) b0)
% Found ((eq_ref Prop) (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy)))))))) as proof of (((eq Prop) (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy)))))))) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq ((b->a)->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq ((b->a)->Prop)) a0) b0)
% Found ((eq_ref ((b->a)->Prop)) a0) as proof of (((eq ((b->a)->Prop)) a0) b0)
% Found ((eq_ref ((b->a)->Prop)) a0) as proof of (((eq ((b->a)->Prop)) a0) b0)
% Found ((eq_ref ((b->a)->Prop)) a0) as proof of (((eq ((b->a)->Prop)) a0) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq ((b->a)->Prop)) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq ((b->a)->Prop)) b0) (fun (Xs:(b->a))=> ((and (forall (Xx_6:b), ((((eq b) x) Xx_6)->(((eq a) y) (Xs Xx_6))))) (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (Xs Xx_7))))) ((eq b) Xy0)))))))))
% Found ((eq_ref ((b->a)->Prop)) b0) as proof of (((eq ((b->a)->Prop)) b0) (fun (Xs:(b->a))=> ((and (forall (Xx_6:b), ((((eq b) x) Xx_6)->(((eq a) y) (Xs Xx_6))))) (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (Xs Xx_7))))) ((eq b) Xy0)))))))))
% Found ((eq_ref ((b->a)->Prop)) b0) as proof of (((eq ((b->a)->Prop)) b0) (fun (Xs:(b->a))=> ((and (forall (Xx_6:b), ((((eq b) x) Xx_6)->(((eq a) y) (Xs Xx_6))))) (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (Xs Xx_7))))) ((eq b) Xy0)))))))))
% Found ((eq_ref ((b->a)->Prop)) b0) as proof of (((eq ((b->a)->Prop)) b0) (fun (Xs:(b->a))=> ((and (forall (Xx_6:b), ((((eq b) x) Xx_6)->(((eq a) y) (Xs Xx_6))))) (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (Xs Xx_7))))) ((eq b) Xy0)))))))))
% Found eq_ref00:=(eq_ref0 (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) ((eq b) Xy0))))))):(((eq Prop) (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) ((eq b) Xy0))))))) (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) ((eq b) Xy0)))))))
% Found (eq_ref0 (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) ((eq b) Xy0))))))) as proof of (((eq Prop) (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) ((eq b) Xy0))))))) b0)
% Found ((eq_ref Prop) (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) ((eq b) Xy0))))))) as proof of (((eq Prop) (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) ((eq b) Xy0))))))) b0)
% Found ((eq_ref Prop) (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) ((eq b) Xy0))))))) as proof of (((eq Prop) (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) ((eq b) Xy0))))))) b0)
% Found ((eq_ref Prop) (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) ((eq b) Xy0))))))) as proof of (((eq Prop) (forall (Xy_56:a), ((((eq a) y) Xy_56)->((ex b) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) ((eq b) Xy0))))))) b0)
% Found eta_expansion000:=(eta_expansion00 (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy))))):(((eq (b->Prop)) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy))))) (fun (x1:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) x1) Xy)))))
% Found (eta_expansion00 (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy))))) as proof of (((eq (b->Prop)) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy))))) b0)
% Found ((eta_expansion0 Prop) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy))))) as proof of (((eq (b->Prop)) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy))))) b0)
% Found (((eta_expansion b) Prop) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy))))) as proof of (((eq (b->Prop)) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy))))) b0)
% Found (((eta_expansion b) Prop) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy))))) as proof of (((eq (b->Prop)) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy))))) b0)
% Found (((eta_expansion b) Prop) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy))))) as proof of (((eq (b->Prop)) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy))))) b0)
% Found eq_ref00:=(eq_ref0 (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy))))):(((eq (b->Prop)) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy))))) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy)))))
% Found (eq_ref0 (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy))))) as proof of (((eq (b->Prop)) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy))))) b0)
% Found ((eq_ref (b->Prop)) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy))))) as proof of (((eq (b->Prop)) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy))))) b0)
% Found ((eq_ref (b->Prop)) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy))))) as proof of (((eq (b->Prop)) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy))))) b0)
% Found ((eq_ref (b->Prop)) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy))))) as proof of (((eq (b->Prop)) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy))))) b0)
% Found eta_expansion000:=(eta_expansion00 (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) ((eq b) Xy0)))):(((eq (b->Prop)) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) ((eq b) Xy0)))) (fun (x1:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) ((eq b) x1))))
% Found (eta_expansion00 (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) ((eq b) Xy0)))) as proof of (((eq (b->Prop)) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) ((eq b) Xy0)))) b0)
% Found ((eta_expansion0 Prop) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) ((eq b) Xy0)))) as proof of (((eq (b->Prop)) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) ((eq b) Xy0)))) b0)
% Found (((eta_expansion b) Prop) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) ((eq b) Xy0)))) as proof of (((eq (b->Prop)) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) ((eq b) Xy0)))) b0)
% Found (((eta_expansion b) Prop) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) ((eq b) Xy0)))) as proof of (((eq (b->Prop)) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) ((eq b) Xy0)))) b0)
% Found (((eta_expansion b) Prop) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) ((eq b) Xy0)))) as proof of (((eq (b->Prop)) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) ((eq b) Xy0)))) b0)
% Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) x1) Xy))))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) x1) Xy))))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) x1) Xy))))
% Found (fun (x1:b)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) x1) Xy))))
% Found (fun (x1:b)=> ((eq_ref Prop) (f x1))) as proof of (forall (x1:b), (((eq Prop) (f x1)) (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) x1) Xy)))))
% Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) x1) Xy))))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) x1) Xy))))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) x1) Xy))))
% Found (fun (x1:b)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) x1) Xy))))
% Found (fun (x1:b)=> ((eq_ref Prop) (f x1))) as proof of (forall (x1:b), (((eq Prop) (f x1)) (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) x1) Xy)))))
% Found eq_ref00:=(eq_ref0 (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy))))):(((eq (b->Prop)) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy))))) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy)))))
% Found (eq_ref0 (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy))))) as proof of (((eq (b->Prop)) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy))))) b0)
% Found ((eq_ref (b->Prop)) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy))))) as proof of (((eq (b->Prop)) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy))))) b0)
% Found ((eq_ref (b->Prop)) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy))))) as proof of (((eq (b->Prop)) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy))))) b0)
% Found ((eq_ref (b->Prop)) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy))))) as proof of (((eq (b->Prop)) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy))))) b0)
% Found eq_ref00:=(eq_ref0 (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) ((eq b) Xy0)))):(((eq (b->Prop)) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) ((eq b) Xy0)))) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) ((eq b) Xy0))))
% Found (eq_ref0 (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) ((eq b) Xy0)))) as proof of (((eq (b->Prop)) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) ((eq b) Xy0)))) b0)
% Found ((eq_ref (b->Prop)) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) ((eq b) Xy0)))) as proof of (((eq (b->Prop)) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) ((eq b) Xy0)))) b0)
% Found ((eq_ref (b->Prop)) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) ((eq b) Xy0)))) as proof of (((eq (b->Prop)) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) ((eq b) Xy0)))) b0)
% Found ((eq_ref (b->Prop)) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) ((eq b) Xy0)))) as proof of (((eq (b->Prop)) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) ((eq b) Xy0)))) b0)
% Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) x1) Xy))))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) x1) Xy))))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) x1) Xy))))
% Found (fun (x1:b)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) x1) Xy))))
% Found (fun (x1:b)=> ((eq_ref Prop) (f x1))) as proof of (forall (x1:b), (((eq Prop) (f x1)) (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) x1) Xy)))))
% Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) x1) Xy))))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) x1) Xy))))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) x1) Xy))))
% Found (fun (x1:b)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) x1) Xy))))
% Found (fun (x1:b)=> ((eq_ref Prop) (f x1))) as proof of (forall (x1:b), (((eq Prop) (f x1)) (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) x1) Xy)))))
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy))))):(((eq (b->Prop)) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy))))) (fun (x1:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) x1) Xy)))))
% Found (eta_expansion_dep00 (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy))))) as proof of (((eq (b->Prop)) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy))))) b0)
% Found ((eta_expansion_dep0 (fun (x2:b)=> Prop)) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy))))) as proof of (((eq (b->Prop)) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy))))) b0)
% Found (((eta_expansion_dep b) (fun (x2:b)=> Prop)) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy))))) as proof of (((eq (b->Prop)) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy))))) b0)
% Found (((eta_expansion_dep b) (fun (x2:b)=> Prop)) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy))))) as proof of (((eq (b->Prop)) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy))))) b0)
% Found (((eta_expansion_dep b) (fun (x2:b)=> Prop)) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy))))) as proof of (((eq (b->Prop)) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) Xy0) Xy))))) b0)
% Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) ((eq b) x1)))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) ((eq b) x1)))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) ((eq b) x1)))
% Found (fun (x1:b)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) ((eq b) x1)))
% Found (fun (x1:b)=> ((eq_ref Prop) (f x1))) as proof of (forall (x1:b), (((eq Prop) (f x1)) (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) ((eq b) x1))))
% Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) ((eq b) x1)))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) ((eq b) x1)))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) ((eq b) x1)))
% Found (fun (x1:b)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) ((eq b) x1)))
% Found (fun (x1:b)=> ((eq_ref Prop) (f x1))) as proof of (forall (x1:b), (((eq Prop) (f x1)) (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) ((eq b) x1))))
% Found eta_expansion000:=(eta_expansion00 (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) ((eq b) Xy0)))):(((eq (b->Prop)) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) ((eq b) Xy0)))) (fun (x1:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) ((eq b) x1))))
% Found (eta_expansion00 (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) ((eq b) Xy0)))) as proof of (((eq (b->Prop)) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) ((eq b) Xy0)))) b0)
% Found ((eta_expansion0 Prop) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) ((eq b) Xy0)))) as proof of (((eq (b->Prop)) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) ((eq b) Xy0)))) b0)
% Found (((eta_expansion b) Prop) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) ((eq b) Xy0)))) as proof of (((eq (b->Prop)) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) ((eq b) Xy0)))) b0)
% Found (((eta_expansion b) Prop) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) ((eq b) Xy0)))) as proof of (((eq (b->Prop)) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) ((eq b) Xy0)))) b0)
% Found (((eta_expansion b) Prop) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) ((eq b) Xy0)))) as proof of (((eq (b->Prop)) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) ((eq b) Xy0)))) b0)
% Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) ((eq b) x1)))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) ((eq b) x1)))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) ((eq b) x1)))
% Found (fun (x1:b)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) ((eq b) x1)))
% Found (fun (x1:b)=> ((eq_ref Prop) (f x1))) as proof of (forall (x1:b), (((eq Prop) (f x1)) (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) ((eq b) x1))))
% Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) ((eq b) x1)))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) ((eq b) x1)))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) ((eq b) x1)))
% Found (fun (x1:b)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) ((eq b) x1)))
% Found (fun (x1:b)=> ((eq_ref Prop) (f x1))) as proof of (forall (x1:b), (((eq Prop) (f x1)) (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) ((eq b) x1))))
% Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) x1) Xy))))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) x1) Xy))))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) x1) Xy))))
% Found (fun (x1:b)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) x1) Xy))))
% Found (fun (x1:b)=> ((eq_ref Prop) (f x1))) as proof of (forall (x1:b), (((eq Prop) (f x1)) (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) x1) Xy)))))
% Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) x1) Xy))))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) x1) Xy))))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) x1) Xy))))
% Found (fun (x1:b)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) x1) Xy))))
% Found (fun (x1:b)=> ((eq_ref Prop) (f x1))) as proof of (forall (x1:b), (((eq Prop) (f x1)) (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) x1) Xy)))))
% Found eta_expansion000:=(eta_expansion00 (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) ((eq b) Xy0)))):(((eq (b->Prop)) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) ((eq b) Xy0)))) (fun (x1:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) ((eq b) x1))))
% Found (eta_expansion00 (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) ((eq b) Xy0)))) as proof of (((eq (b->Prop)) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) ((eq b) Xy0)))) b0)
% Found ((eta_expansion0 Prop) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) ((eq b) Xy0)))) as proof of (((eq (b->Prop)) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) ((eq b) Xy0)))) b0)
% Found (((eta_expansion b) Prop) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) ((eq b) Xy0)))) as proof of (((eq (b->Prop)) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) ((eq b) Xy0)))) b0)
% Found (((eta_expansion b) Prop) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) ((eq b) Xy0)))) as proof of (((eq (b->Prop)) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) ((eq b) Xy0)))) b0)
% Found (((eta_expansion b) Prop) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) ((eq b) Xy0)))) as proof of (((eq (b->Prop)) (fun (Xy0:b)=> (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) ((eq b) Xy0)))) b0)
% Found x000:=(x00 (fun (x2:a)=> (P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))))):((P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7)))))->(P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))))
% Found (x00 (fun (x2:a)=> (P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))))) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7)))))
% Found (x00 (fun (x2:a)=> (P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))))) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7)))))
% Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) x1) Xy))))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) x1) Xy))))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) x1) Xy))))
% Found (fun (x1:b)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) x1) Xy))))
% Found (fun (x1:b)=> ((eq_ref Prop) (f x1))) as proof of (forall (x1:b), (((eq Prop) (f x1)) (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) x1) Xy)))))
% Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) x1) Xy))))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) x1) Xy))))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) x1) Xy))))
% Found (fun (x1:b)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) x1) Xy))))
% Found (fun (x1:b)=> ((eq_ref Prop) (f x1))) as proof of (forall (x1:b), (((eq Prop) (f x1)) (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) (fun (Xy:b)=> (((eq b) x1) Xy)))))
% Found eq_ref00:=(eq_ref0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))):(((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7)))))
% Found (eq_ref0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) as proof of (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) b0)
% Found ((eq_ref (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) as proof of (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) b0)
% Found ((eq_ref (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) as proof of (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) b0)
% Found ((eq_ref (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) as proof of (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) (fun (Xy:b)=> (((eq b) x1) Xy)))
% Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) (fun (Xy:b)=> (((eq b) x1) Xy)))
% Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) (fun (Xy:b)=> (((eq b) x1) Xy)))
% Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) (fun (Xy:b)=> (((eq b) x1) Xy)))
% Found x000:=(x00 (fun (x2:a)=> (P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))))):((P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7)))))->(P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))))
% Found (x00 (fun (x2:a)=> (P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))))) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7)))))
% Found (x00 (fun (x2:a)=> (P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))))) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7)))))
% Found eta_expansion000:=(eta_expansion00 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))):(((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) (fun (x1:b)=> ((and (((eq b) x) x1)) (((eq a) Xy_56) (x0 x1)))))
% Found (eta_expansion00 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) as proof of (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) b0)
% Found ((eta_expansion0 Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) as proof of (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) b0)
% Found (((eta_expansion b) Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) as proof of (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) b0)
% Found (((eta_expansion b) Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) as proof of (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) b0)
% Found (((eta_expansion b) Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) as proof of (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) (fun (Xy:b)=> (((eq b) x1) Xy)))
% Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) (fun (Xy:b)=> (((eq b) x1) Xy)))
% Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) (fun (Xy:b)=> (((eq b) x1) Xy)))
% Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) (fun (Xy:b)=> (((eq b) x1) Xy)))
% Found x000:=(x00 (fun (x2:a)=> (P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))))):((P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7)))))->(P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))))
% Found (x00 (fun (x2:a)=> (P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))))) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7)))))
% Found (x00 (fun (x2:a)=> (P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))))) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7)))))
% Found x000:=(x00 (fun (x2:a)=> (P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))))):((P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7)))))->(P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))))
% Found (x00 (fun (x2:a)=> (P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))))) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7)))))
% Found (x00 (fun (x2:a)=> (P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))))) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7)))))
% Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) ((eq b) x1)))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) ((eq b) x1)))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) ((eq b) x1)))
% Found (fun (x1:b)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) ((eq b) x1)))
% Found (fun (x1:b)=> ((eq_ref Prop) (f x1))) as proof of (forall (x1:b), (((eq Prop) (f x1)) (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) ((eq b) x1))))
% Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) ((eq b) x1)))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) ((eq b) x1)))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) ((eq b) x1)))
% Found (fun (x1:b)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) ((eq b) x1)))
% Found (fun (x1:b)=> ((eq_ref Prop) (f x1))) as proof of (forall (x1:b), (((eq Prop) (f x1)) (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) ((eq b) x1))))
% Found x000:=(x00 (fun (x2:a)=> (P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))))):((P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7)))))->(P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))))
% Found (x00 (fun (x2:a)=> (P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))))) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7)))))
% Found (x00 (fun (x2:a)=> (P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))))) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7)))))
% Found x000:=(x00 (fun (x2:a)=> (P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))))):((P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7)))))->(P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))))
% Found (x00 (fun (x2:a)=> (P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))))) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7)))))
% Found (x00 (fun (x2:a)=> (P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))))) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7)))))
% Found x000:=(x00 (fun (x2:a)=> (P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))))):((P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7)))))->(P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))))
% Found (x00 (fun (x2:a)=> (P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))))) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7)))))
% Found (x00 (fun (x2:a)=> (P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))))) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7)))))
% Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) ((eq b) x1)))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) ((eq b) x1)))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) ((eq b) x1)))
% Found (fun (x1:b)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) ((eq b) x1)))
% Found (fun (x1:b)=> ((eq_ref Prop) (f x1))) as proof of (forall (x1:b), (((eq Prop) (f x1)) (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) ((eq b) x1))))
% Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) ((eq b) x1)))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) ((eq b) x1)))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) ((eq b) x1)))
% Found (fun (x1:b)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) ((eq b) x1)))
% Found (fun (x1:b)=> ((eq_ref Prop) (f x1))) as proof of (forall (x1:b), (((eq Prop) (f x1)) (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) ((eq b) x1))))
% Found eq_ref00:=(eq_ref0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))):(((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7)))))
% Found (eq_ref0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) as proof of (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) b0)
% Found ((eq_ref (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) as proof of (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) b0)
% Found ((eq_ref (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) as proof of (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) b0)
% Found ((eq_ref (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) as proof of (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) ((eq b) x1))
% Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) ((eq b) x1))
% Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) ((eq b) x1))
% Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) ((eq b) x1))
% Found x000:=(x00 (fun (x2:a)=> (P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))))):((P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7)))))->(P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))))
% Found (x00 (fun (x2:a)=> (P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))))) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7)))))
% Found (x00 (fun (x2:a)=> (P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))))) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7)))))
% Found eta_expansion0000:=(eta_expansion000 P):((P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))->(P (fun (x1:b)=> ((and (((eq b) x) x1)) (((eq a) y) (x0 x1))))))
% Found (eta_expansion000 P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found ((eta_expansion00 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found (((eta_expansion0 Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found ((((eta_expansion b) Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found ((((eta_expansion b) Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found eta_expansion000:=(eta_expansion00 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))):(((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) (fun (x1:b)=> ((and (((eq b) x) x1)) (((eq a) Xy_56) (x0 x1)))))
% Found (eta_expansion00 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) as proof of (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) b0)
% Found ((eta_expansion0 Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) as proof of (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) b0)
% Found (((eta_expansion b) Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) as proof of (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) b0)
% Found (((eta_expansion b) Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) as proof of (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) b0)
% Found (((eta_expansion b) Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) as proof of (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) ((eq b) x1))
% Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) ((eq b) x1))
% Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) ((eq b) x1))
% Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) ((eq b) x1))
% Found eta_expansion0000:=(eta_expansion000 P):((P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))->(P (fun (x1:b)=> ((and (((eq b) x) x1)) (((eq a) y) (x0 x1))))))
% Found (eta_expansion000 P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found ((eta_expansion00 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found (((eta_expansion0 Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found ((((eta_expansion b) Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found ((((eta_expansion b) Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))):(((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) (fun (x1:b)=> ((and (((eq b) x) x1)) (((eq a) y) (x0 x1)))))
% Found (eta_expansion_dep00 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) as proof of (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) b0)
% Found ((eta_expansion_dep0 (fun (x3:b)=> Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) as proof of (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) b0)
% Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) as proof of (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) b0)
% Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) as proof of (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) b0)
% Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) as proof of (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) b0)
% Found eta_expansion_dep000:=(eta_expansion_dep00 b0):(((eq (b->Prop)) b0) (fun (x:b)=> (b0 x)))
% Found (eta_expansion_dep00 b0) as proof of (((eq (b->Prop)) b0) (fun (Xy:b)=> (((eq b) x1) Xy)))
% Found ((eta_expansion_dep0 (fun (x3:b)=> Prop)) b0) as proof of (((eq (b->Prop)) b0) (fun (Xy:b)=> (((eq b) x1) Xy)))
% Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) b0) as proof of (((eq (b->Prop)) b0) (fun (Xy:b)=> (((eq b) x1) Xy)))
% Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) b0) as proof of (((eq (b->Prop)) b0) (fun (Xy:b)=> (((eq b) x1) Xy)))
% Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) b0) as proof of (((eq (b->Prop)) b0) (fun (Xy:b)=> (((eq b) x1) Xy)))
% Found x000:=(x00 (fun (x2:a)=> (P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))))):((P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7)))))->(P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))))
% Found (x00 (fun (x2:a)=> (P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))))) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7)))))
% Found (x00 (fun (x2:a)=> (P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))))) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7)))))
% Found x000:=(x00 (fun (x2:a)=> (P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))))):((P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7)))))->(P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))))
% Found (x00 (fun (x2:a)=> (P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))))) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7)))))
% Found (x00 (fun (x2:a)=> (P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))))) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7)))))
% Found eq_ref00:=(eq_ref0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))):(((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found (eq_ref0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) as proof of (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) b0)
% Found ((eq_ref (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) as proof of (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) b0)
% Found ((eq_ref (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) as proof of (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) b0)
% Found ((eq_ref (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) as proof of (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) b0)
% Found eta_expansion_dep000:=(eta_expansion_dep00 b0):(((eq (b->Prop)) b0) (fun (x:b)=> (b0 x)))
% Found (eta_expansion_dep00 b0) as proof of (((eq (b->Prop)) b0) (fun (Xy:b)=> (((eq b) x1) Xy)))
% Found ((eta_expansion_dep0 (fun (x3:b)=> Prop)) b0) as proof of (((eq (b->Prop)) b0) (fun (Xy:b)=> (((eq b) x1) Xy)))
% Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) b0) as proof of (((eq (b->Prop)) b0) (fun (Xy:b)=> (((eq b) x1) Xy)))
% Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) b0) as proof of (((eq (b->Prop)) b0) (fun (Xy:b)=> (((eq b) x1) Xy)))
% Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) b0) as proof of (((eq (b->Prop)) b0) (fun (Xy:b)=> (((eq b) x1) Xy)))
% Found eta_expansion0000:=(eta_expansion000 P):((P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))->(P (fun (x1:b)=> ((and (((eq b) x) x1)) (((eq a) y) (x0 x1))))))
% Found (eta_expansion000 P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found ((eta_expansion00 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found (((eta_expansion0 Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found ((((eta_expansion b) Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found ((((eta_expansion b) Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found eta_expansion0000:=(eta_expansion000 P):((P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))->(P (fun (x1:b)=> ((and (((eq b) x) x1)) (((eq a) y) (x0 x1))))))
% Found (eta_expansion000 P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found ((eta_expansion00 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found (((eta_expansion0 Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found ((((eta_expansion b) Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found ((((eta_expansion b) Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))):(((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) (fun (x1:b)=> ((and (((eq b) x) x1)) (((eq a) y) (x0 x1)))))
% Found (eta_expansion_dep00 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) as proof of (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) b0)
% Found ((eta_expansion_dep0 (fun (x3:b)=> Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) as proof of (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) b0)
% Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) as proof of (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) b0)
% Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) as proof of (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) b0)
% Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) as proof of (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) b0)
% Found eta_expansion_dep000:=(eta_expansion_dep00 b0):(((eq (b->Prop)) b0) (fun (x:b)=> (b0 x)))
% Found (eta_expansion_dep00 b0) as proof of (((eq (b->Prop)) b0) (fun (Xy:b)=> (((eq b) x1) Xy)))
% Found ((eta_expansion_dep0 (fun (x3:b)=> Prop)) b0) as proof of (((eq (b->Prop)) b0) (fun (Xy:b)=> (((eq b) x1) Xy)))
% Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) b0) as proof of (((eq (b->Prop)) b0) (fun (Xy:b)=> (((eq b) x1) Xy)))
% Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) b0) as proof of (((eq (b->Prop)) b0) (fun (Xy:b)=> (((eq b) x1) Xy)))
% Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) b0) as proof of (((eq (b->Prop)) b0) (fun (Xy:b)=> (((eq b) x1) Xy)))
% Found x000:=(x00 (fun (x2:a)=> (P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))))):((P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7)))))->(P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))))
% Found (x00 (fun (x2:a)=> (P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))))) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7)))))
% Found (x00 (fun (x2:a)=> (P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))))) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7)))))
% Found x000:=(x00 (fun (x2:a)=> (P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))))):((P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7)))))->(P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))))
% Found (x00 (fun (x2:a)=> (P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))))) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7)))))
% Found (x00 (fun (x2:a)=> (P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7))))))) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7)))))
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))):(((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) (fun (x1:b)=> ((and (((eq b) x) x1)) (((eq a) y) (x0 x1)))))
% Found (eta_expansion_dep00 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) as proof of (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) b0)
% Found ((eta_expansion_dep0 (fun (x3:b)=> Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) as proof of (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) b0)
% Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) as proof of (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) b0)
% Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) as proof of (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) b0)
% Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) as proof of (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) b0)
% Found eta_expansion_dep000:=(eta_expansion_dep00 b0):(((eq (b->Prop)) b0) (fun (x:b)=> (b0 x)))
% Found (eta_expansion_dep00 b0) as proof of (((eq (b->Prop)) b0) (fun (Xy:b)=> (((eq b) x1) Xy)))
% Found ((eta_expansion_dep0 (fun (x3:b)=> Prop)) b0) as proof of (((eq (b->Prop)) b0) (fun (Xy:b)=> (((eq b) x1) Xy)))
% Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) b0) as proof of (((eq (b->Prop)) b0) (fun (Xy:b)=> (((eq b) x1) Xy)))
% Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) b0) as proof of (((eq (b->Prop)) b0) (fun (Xy:b)=> (((eq b) x1) Xy)))
% Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) b0) as proof of (((eq (b->Prop)) b0) (fun (Xy:b)=> (((eq b) x1) Xy)))
% Found eta_expansion0000:=(eta_expansion000 P):((P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))->(P (fun (x1:b)=> ((and (((eq b) x) x1)) (((eq a) y) (x0 x1))))))
% Found (eta_expansion000 P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found ((eta_expansion00 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found (((eta_expansion0 Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found ((((eta_expansion b) Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found ((((eta_expansion b) Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found eta_expansion0000:=(eta_expansion000 P):((P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))->(P (fun (x1:b)=> ((and (((eq b) x) x1)) (((eq a) y) (x0 x1))))))
% Found (eta_expansion000 P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found ((eta_expansion00 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found (((eta_expansion0 Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found ((((eta_expansion b) Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found ((((eta_expansion b) Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found eta_expansion0000:=(eta_expansion000 P):((P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))->(P (fun (x1:b)=> ((and (((eq b) x) x1)) (((eq a) y) (x0 x1))))))
% Found (eta_expansion000 P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found ((eta_expansion00 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found (((eta_expansion0 Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found ((((eta_expansion b) Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found ((((eta_expansion b) Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found eta_expansion0000:=(eta_expansion000 P):((P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))->(P (fun (x1:b)=> ((and (((eq b) x) x1)) (((eq a) y) (x0 x1))))))
% Found (eta_expansion000 P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found ((eta_expansion00 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found (((eta_expansion0 Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found ((((eta_expansion b) Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found ((((eta_expansion b) Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found eta_expansion0000:=(eta_expansion000 P):((P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))->(P (fun (x1:b)=> ((and (((eq b) x) x1)) (((eq a) y) (x0 x1))))))
% Found (eta_expansion000 P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found ((eta_expansion00 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found (((eta_expansion0 Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found ((((eta_expansion b) Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found ((((eta_expansion b) Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found eta_expansion0000:=(eta_expansion000 P):((P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))->(P (fun (x1:b)=> ((and (((eq b) x) x1)) (((eq a) y) (x0 x1))))))
% Found (eta_expansion000 P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found ((eta_expansion00 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found (((eta_expansion0 Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found ((((eta_expansion b) Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found ((((eta_expansion b) Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found eta_expansion0000:=(eta_expansion000 P):((P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))->(P (fun (x1:b)=> ((and (((eq b) x) x1)) (((eq a) y) (x0 x1))))))
% Found (eta_expansion000 P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found ((eta_expansion00 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found (((eta_expansion0 Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found ((((eta_expansion b) Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found ((((eta_expansion b) Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found eta_expansion0000:=(eta_expansion000 P):((P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))->(P (fun (x1:b)=> ((and (((eq b) x) x1)) (((eq a) y) (x0 x1))))))
% Found (eta_expansion000 P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found ((eta_expansion00 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found (((eta_expansion0 Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found ((((eta_expansion b) Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found ((((eta_expansion b) Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found eta_expansion0000:=(eta_expansion000 P):((P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))->(P (fun (x1:b)=> ((and (((eq b) x) x1)) (((eq a) y) (x0 x1))))))
% Found (eta_expansion000 P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found ((eta_expansion00 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found (((eta_expansion0 Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found ((((eta_expansion b) Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found ((((eta_expansion b) Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found eta_expansion0000:=(eta_expansion000 P):((P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))->(P (fun (x1:b)=> ((and (((eq b) x) x1)) (((eq a) y) (x0 x1))))))
% Found (eta_expansion000 P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found ((eta_expansion00 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found (((eta_expansion0 Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found ((((eta_expansion b) Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found ((((eta_expansion b) Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found eq_ref00:=(eq_ref0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))):(((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found (eq_ref0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) as proof of (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) b0)
% Found ((eq_ref (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) as proof of (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) b0)
% Found ((eq_ref (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) as proof of (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) b0)
% Found ((eq_ref (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) as proof of (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) b0)
% Found eta_expansion_dep000:=(eta_expansion_dep00 b0):(((eq (b->Prop)) b0) (fun (x:b)=> (b0 x)))
% Found (eta_expansion_dep00 b0) as proof of (((eq (b->Prop)) b0) ((eq b) x1))
% Found ((eta_expansion_dep0 (fun (x3:b)=> Prop)) b0) as proof of (((eq (b->Prop)) b0) ((eq b) x1))
% Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) b0) as proof of (((eq (b->Prop)) b0) ((eq b) x1))
% Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) b0) as proof of (((eq (b->Prop)) b0) ((eq b) x1))
% Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) b0) as proof of (((eq (b->Prop)) b0) ((eq b) x1))
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))):(((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) (fun (x1:b)=> ((and (((eq b) x) x1)) (((eq a) y) (x0 x1)))))
% Found (eta_expansion_dep00 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) as proof of (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) b0)
% Found ((eta_expansion_dep0 (fun (x3:b)=> Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) as proof of (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) b0)
% Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) as proof of (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) b0)
% Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) as proof of (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) b0)
% Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) as proof of (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) b0)
% Found eta_expansion_dep000:=(eta_expansion_dep00 b0):(((eq (b->Prop)) b0) (fun (x:b)=> (b0 x)))
% Found (eta_expansion_dep00 b0) as proof of (((eq (b->Prop)) b0) ((eq b) x1))
% Found ((eta_expansion_dep0 (fun (x3:b)=> Prop)) b0) as proof of (((eq (b->Prop)) b0) ((eq b) x1))
% Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) b0) as proof of (((eq (b->Prop)) b0) ((eq b) x1))
% Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) b0) as proof of (((eq (b->Prop)) b0) ((eq b) x1))
% Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) b0) as proof of (((eq (b->Prop)) b0) ((eq b) x1))
% Found eta_expansion0000:=(eta_expansion000 P):((P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))->(P (fun (x1:b)=> ((and (((eq b) x) x1)) (((eq a) y) (x0 x1))))))
% Found (eta_expansion000 P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found ((eta_expansion00 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found (((eta_expansion0 Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found ((((eta_expansion b) Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found ((((eta_expansion b) Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found eta_expansion0000:=(eta_expansion000 P):((P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))->(P (fun (x1:b)=> ((and (((eq b) x) x1)) (((eq a) y) (x0 x1))))))
% Found (eta_expansion000 P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found ((eta_expansion00 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found (((eta_expansion0 Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found ((((eta_expansion b) Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found ((((eta_expansion b) Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found eq_ref00:=(eq_ref0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))):(((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found (eq_ref0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) as proof of (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) b0)
% Found ((eq_ref (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) as proof of (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) b0)
% Found ((eq_ref (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) as proof of (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) b0)
% Found ((eq_ref (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) as proof of (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) b0)
% Found eta_expansion_dep000:=(eta_expansion_dep00 b0):(((eq (b->Prop)) b0) (fun (x:b)=> (b0 x)))
% Found (eta_expansion_dep00 b0) as proof of (((eq (b->Prop)) b0) ((eq b) x1))
% Found ((eta_expansion_dep0 (fun (x3:b)=> Prop)) b0) as proof of (((eq (b->Prop)) b0) ((eq b) x1))
% Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) b0) as proof of (((eq (b->Prop)) b0) ((eq b) x1))
% Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) b0) as proof of (((eq (b->Prop)) b0) ((eq b) x1))
% Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) b0) as proof of (((eq (b->Prop)) b0) ((eq b) x1))
% Found eta_expansion000:=(eta_expansion00 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))):(((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) (fun (x1:b)=> ((and (((eq b) x) x1)) (((eq a) y) (x0 x1)))))
% Found (eta_expansion00 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) as proof of (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) b0)
% Found ((eta_expansion0 Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) as proof of (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) b0)
% Found (((eta_expansion b) Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) as proof of (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) b0)
% Found (((eta_expansion b) Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) as proof of (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) b0)
% Found (((eta_expansion b) Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) as proof of (((eq (b->Prop)) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) b0)
% Found eta_expansion_dep000:=(eta_expansion_dep00 b0):(((eq (b->Prop)) b0) (fun (x:b)=> (b0 x)))
% Found (eta_expansion_dep00 b0) as proof of (((eq (b->Prop)) b0) ((eq b) x1))
% Found ((eta_expansion_dep0 (fun (x3:b)=> Prop)) b0) as proof of (((eq (b->Prop)) b0) ((eq b) x1))
% Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) b0) as proof of (((eq (b->Prop)) b0) ((eq b) x1))
% Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) b0) as proof of (((eq (b->Prop)) b0) ((eq b) x1))
% Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) b0) as proof of (((eq (b->Prop)) b0) ((eq b) x1))
% Found eta_expansion0000:=(eta_expansion000 P):((P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))->(P (fun (x1:b)=> ((and (((eq b) x) x1)) (((eq a) y) (x0 x1))))))
% Found (eta_expansion000 P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found ((eta_expansion00 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found (((eta_expansion0 Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found ((((eta_expansion b) Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found ((((eta_expansion b) Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found eta_expansion0000:=(eta_expansion000 P):((P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))->(P (fun (x1:b)=> ((and (((eq b) x) x1)) (((eq a) y) (x0 x1))))))
% Found (eta_expansion000 P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found ((eta_expansion00 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found (((eta_expansion0 Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found ((((eta_expansion b) Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found ((((eta_expansion b) Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found eta_expansion0000:=(eta_expansion000 P):((P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))->(P (fun (x1:b)=> ((and (((eq b) x) x1)) (((eq a) y) (x0 x1))))))
% Found (eta_expansion000 P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found ((eta_expansion00 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found (((eta_expansion0 Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found ((((eta_expansion b) Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found ((((eta_expansion b) Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found eta_expansion0000:=(eta_expansion000 P):((P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))->(P (fun (x1:b)=> ((and (((eq b) x) x1)) (((eq a) y) (x0 x1))))))
% Found (eta_expansion000 P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found ((eta_expansion00 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found (((eta_expansion0 Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found ((((eta_expansion b) Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found ((((eta_expansion b) Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found eta_expansion0000:=(eta_expansion000 P):((P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))->(P (fun (x1:b)=> ((and (((eq b) x) x1)) (((eq a) y) (x0 x1))))))
% Found (eta_expansion000 P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found ((eta_expansion00 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found (((eta_expansion0 Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found ((((eta_expansion b) Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found ((((eta_expansion b) Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found eta_expansion0000:=(eta_expansion000 P):((P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))->(P (fun (x1:b)=> ((and (((eq b) x) x1)) (((eq a) y) (x0 x1))))))
% Found (eta_expansion000 P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found ((eta_expansion00 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found (((eta_expansion0 Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found ((((eta_expansion b) Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found ((((eta_expansion b) Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found eta_expansion0000:=(eta_expansion000 P):((P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))->(P (fun (x1:b)=> ((and (((eq b) x) x1)) (((eq a) y) (x0 x1))))))
% Found (eta_expansion000 P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found ((eta_expansion00 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found (((eta_expansion0 Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found ((((eta_expansion b) Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found ((((eta_expansion b) Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found eta_expansion0000:=(eta_expansion000 P):((P (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))->(P (fun (x1:b)=> ((and (((eq b) x) x1)) (((eq a) y) (x0 x1))))))
% Found (eta_expansion000 P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found ((eta_expansion00 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found (((eta_expansion0 Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found ((((eta_expansion b) Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found ((((eta_expansion b) Prop) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7))))) P) as proof of (P0 (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) y) (x0 Xx_7)))))
% Found eta_expansion_dep000:=(eta_expansion_dep00 b0):(((eq (b->Prop)) b0) (fun (x:b)=> (b0 x)))
% Found (eta_expansion_dep00 b0) as proof of (((eq (b->Prop)) b0) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7)))))
% Found ((eta_expansion_dep0 (fun (x3:b)=> Prop)) b0) as proof of (((eq (b->Prop)) b0) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7)))))
% Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) b0) as proof of (((eq (b->Prop)) b0) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7)))))
% Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) b0) as proof of (((eq (b->Prop)) b0) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7)))))
% Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) b0) as proof of (((eq (b->Prop)) b0) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7)))))
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xy:b)=> (((eq b) x1) Xy))):(((eq (b->Prop)) (fun (Xy:b)=> (((eq b) x1) Xy))) (fun (x:b)=> (((eq b) x1) x)))
% Found (eta_expansion_dep00 (fun (Xy:b)=> (((eq b) x1) Xy))) as proof of (((eq (b->Prop)) (fun (Xy:b)=> (((eq b) x1) Xy))) b0)
% Found ((eta_expansion_dep0 (fun (x3:b)=> Prop)) (fun (Xy:b)=> (((eq b) x1) Xy))) as proof of (((eq (b->Prop)) (fun (Xy:b)=> (((eq b) x1) Xy))) b0)
% Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) (fun (Xy:b)=> (((eq b) x1) Xy))) as proof of (((eq (b->Prop)) (fun (Xy:b)=> (((eq b) x1) Xy))) b0)
% Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) (fun (Xy:b)=> (((eq b) x1) Xy))) as proof of (((eq (b->Prop)) (fun (Xy:b)=> (((eq b) x1) Xy))) b0)
% Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) (fun (Xy:b)=> (((eq b) x1) Xy))) as proof of (((eq (b->Prop)) (fun (Xy:b)=> (((eq b) x1) Xy))) b0)
% Found eta_expansion_dep000:=(eta_expansion_dep00 b0):(((eq (b->Prop)) b0) (fun (x:b)=> (b0 x)))
% Found (eta_expansion_dep00 b0) as proof of (((eq (b->Prop)) b0) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7)))))
% Found ((eta_expansion_dep0 (fun (x3:b)=> Prop)) b0) as proof of (((eq (b->Prop)) b0) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7)))))
% Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) b0) as proof of (((eq (b->Prop)) b0) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7)))))
% Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) b0) as proof of (((eq (b->Prop)) b0) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7)))))
% Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) b0) as proof of (((eq (b->Prop)) b0) (fun (Xx_7:b)=> ((and (((eq b) x) Xx_7)) (((eq a) Xy_56) (x0 Xx_7)))))
% Found eta_expansion000:=(eta_expansion00 (fun (Xy:b)=> (((eq b) x1) Xy))):(((eq (b->Prop)) (fun (Xy:b)=> (((eq b) x1) Xy))) (fun (x:b)=> (((eq b) x1) x)))
% Found (eta_expansion00 (fun (Xy:b)=> (((eq b) x1) Xy))) as proof of (((eq (b->Prop)) (fun (Xy:b)=> (((eq b) x1) Xy))) b0)
% Found ((eta_expansion0 Prop) (fun (Xy:b)=> (((eq b) x1) Xy))) as proof of (((eq (b->Prop)) (fun (Xy:b)=> (((eq b) x1) Xy))) b0)
% Found (((eta_expansion b) Prop) (fun (Xy:b)=> (((eq b) x1) Xy))) as proof of (((eq (b->Prop)) (fun (Xy:b)=> (((eq b) x1) Xy))) b0)
% Found (((eta_expansion b) Prop) (fun (Xy:b)=> (((eq b) x1) Xy))) as proof of (((eq (b->Prop)) (fun (Xy:b)=> (((eq b) x1) Xy))) b0)
% Found (((eta_expansion b) Prop) (fun (Xy:b)=> (((eq b) x1) Xy))) as proof of (((eq (b->Prop)) (fun (Xy:b)=> (((eq b) x1) Xy))) b0)
% Found x000:=(x00 (fun (x2:a)=> (P (fun (Xy:b)=> (((eq b) x1) Xy))))):((P (fun (Xy:b)=> (((eq b) x1) Xy)))->(P (fun (Xy:b)=> (((eq b) x1) Xy))))
% Found (x00 (fun (x2:a)=> (P (fun (Xy:b)=> (((eq b) x1) Xy))))) as proof of (P0 (fun (Xy:b)=> (((eq b) x1) Xy)))
% Found (x00 (fun (x2:a)=> (P (fun (Xy:b)=> (((eq b) x1) Xy))))) as proof of (P0 (fun (Xy:b)=> (((eq b) x1) Xy)))
% Found x000:=(x00 (fun (x2:a)=> (P (fun (Xy:b)=> (((eq b) x1) Xy))))):((P (fun (Xy:b)=> (((eq b) x1) Xy)))->(P (fun (Xy:b)=> (((eq b) x1) Xy))))
% Found (x00 (fun (x2:a)=> (P (fun (Xy:b)=> (((eq b) x1) Xy))))) as proof of (P0 (fun (Xy:b)=> (((eq b) x1) Xy)))
% Found (x00 (fun (x2:a)=> (P (fun (Xy:b)=> (((eq b) x1) Xy))))) as proof of (P0 (fun (Xy:b)=> (((eq b) x1) Xy)))
% Found x000:=(x00 (fun (x2:a)=> (P (fun (Xy:b)=> (((eq b) x1) Xy))))):((P (fun (Xy:b)=> (((eq b) x1) Xy)))->(P (fun (Xy:b)=> (((eq b) x1) Xy))))
% Found (x00 (fun (x2:a)=> (P (fun (Xy:b)=> (((eq b) x1) Xy))))) as proof of (P0 (fun (Xy:b)=> (((eq b) x1) Xy)))
% Found (x00 (fun (x2:a)=> (P (fun (Xy:b)=> (((eq b) x1) Xy))))) as proof of (P0 (fun (Xy:b)=> (((eq b) x1) Xy)))
% Found x000:=(x00 (fun (x2:a)=> (P (fun (Xy:b)=> (((eq b) x1) Xy))))):((P (fun (Xy:b)=> (((eq b) x1) Xy)))->(P (fun (Xy:b)=> (((eq b) x1) Xy))))
% Found (x00 (fun (x2:a)=> (P (fun (Xy:b)=> (((eq b) x1) Xy))))) as proof of (P0 (fun (Xy:b)=> (((eq b) x1) Xy)))
% Found (x00 (fun (x2:a)=> (P (fun (Xy:b)=> (((eq b) x1) Xy))))) as proof of (P0 (fun (Xy:b)=> (((eq b) x1) Xy)))
% Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (Xy:b)=> (((eq b) x1) Xy)))->(P (fun (x:b)=> (((eq b) x1) x))))
% Found (eta_expansion_dep000 P) as proof of (P0 (fun (Xy:b)=> (((eq b) x1) Xy)))
% Found ((eta_expansion_dep00 (fun (Xy:b)=> (((eq b) x1) Xy))) P) as proof of (P0 (fun (Xy:b)=> (((eq b) x1) Xy)))
% Found (((eta_expansion_dep0 (fun (x3:b)=> Prop)) (fun (Xy:b)=> (((eq b) x1) Xy))) P) as proof of (P0 (fun (Xy:b)=> (((eq b) x1) Xy)))
% Found ((((eta_expansion_dep b) (fun (x3:b)=> Prop)) (fun (Xy:b)=> (((eq b) x1) Xy))) P) as proof of (P0 (fun (Xy:b)=> (((eq b) x1) Xy)))
% Found ((((eta_expansion_dep b) (fun (x3:b)=> Prop)) (fun (Xy:b)=> (((eq b) x1) Xy))) P) as proof of (P0 (fun (Xy:b)=> (((eq b) x1) Xy)))
% Found x000:=(x00 (fun (x2:a)=> (P ((and (((eq b) x) x10)) (((eq a) Xy_56) (x0 x10)))))):((P ((and (((eq b) x) x10)) (((eq a) Xy_56) (x0 x10))))->(P ((and (((eq b) x) x10)) (((eq a) Xy_56) (x0 x10)))))
% Found (x00 (fun (x2:a)=> (P ((and (((eq b) x) x10)) (((eq a) Xy_56) (x0 x10)))))) as proof of (P0 ((and (((eq b) x) x10)) (((eq a) Xy_56) (x0 x10))))
% Found (x00 (fun (x2:a)=> (P ((and (((eq b) x) x10)) (((eq a) Xy_56) (x0 x10)))))) as proof of (P0 ((and (((eq b) x) x10)) (((eq a) Xy_56) (x0 x10))))
% Found x000:=(x00 (fun (x2:a)=> (P ((and
% EOF
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