TSTP Solution File: SYO265^5 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SYO265^5 : TPTP v7.5.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Tue Mar 29 00:51:02 EDT 2022
% Result : Timeout 289.63s 289.97s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SYO265^5 : TPTP v7.5.0. Released v4.0.0.
% 0.03/0.11 % Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.32 % Computer : n007.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPUModel : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % RAMPerCPU : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % DateTime : Fri Mar 11 23:00:15 EST 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.12/0.33 Python 2.7.5
% 3.32/3.52 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox2/benchmark/', '/export/starexec/sandbox2/benchmark/']
% 3.32/3.52 FOF formula (<kernel.Constant object at 0x145b6c8>, <kernel.Type object at 0x145b7a0>) of role type named a_type
% 3.32/3.52 Using role type
% 3.32/3.52 Declaring a:Type
% 3.32/3.52 FOF formula (<kernel.Constant object at 0x145f098>, <kernel.Constant object at 0x145b6c8>) of role type named x
% 3.32/3.52 Using role type
% 3.32/3.52 Declaring x:a
% 3.32/3.52 FOF formula (((eq (a->Prop)) ((fun (Xx:a) (Xy:a)=> (((eq a) Xx) Xy)) x)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) of role conjecture named cX5210
% 3.32/3.52 Conjecture to prove = (((eq (a->Prop)) ((fun (Xx:a) (Xy:a)=> (((eq a) Xx) Xy)) x)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))):Prop
% 3.32/3.52 We need to prove ['(((eq (a->Prop)) ((fun (Xx:a) (Xy:a)=> (((eq a) Xx) Xy)) x)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))']
% 3.32/3.52 Parameter a:Type.
% 3.32/3.52 Parameter x:a.
% 3.32/3.52 Trying to prove (((eq (a->Prop)) ((fun (Xx:a) (Xy:a)=> (((eq a) Xx) Xy)) x)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 3.32/3.52 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (Xy:a)=> (((eq a) x) Xy)))->(P (fun (x0:a)=> (((eq a) x) x0))))
% 3.32/3.52 Found (eta_expansion_dep000 P) as proof of (P0 (fun (Xy:a)=> (((eq a) x) Xy)))
% 3.32/3.52 Found ((eta_expansion_dep00 (fun (Xy:a)=> (((eq a) x) Xy))) P) as proof of (P0 (fun (Xy:a)=> (((eq a) x) Xy)))
% 3.32/3.52 Found (((eta_expansion_dep0 (fun (x1:a)=> Prop)) (fun (Xy:a)=> (((eq a) x) Xy))) P) as proof of (P0 (fun (Xy:a)=> (((eq a) x) Xy)))
% 3.32/3.52 Found ((((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xy:a)=> (((eq a) x) Xy))) P) as proof of (P0 (fun (Xy:a)=> (((eq a) x) Xy)))
% 3.32/3.52 Found ((((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xy:a)=> (((eq a) x) Xy))) P) as proof of (P0 (fun (Xy:a)=> (((eq a) x) Xy)))
% 3.32/3.52 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (Xy:a)=> (((eq a) x) Xy)))->(P (fun (x0:a)=> (((eq a) x) x0))))
% 3.32/3.52 Found (eta_expansion_dep000 P) as proof of (P0 (fun (Xy:a)=> (((eq a) x) Xy)))
% 3.32/3.52 Found ((eta_expansion_dep00 (fun (Xy:a)=> (((eq a) x) Xy))) P) as proof of (P0 (fun (Xy:a)=> (((eq a) x) Xy)))
% 3.32/3.52 Found (((eta_expansion_dep0 (fun (x1:a)=> Prop)) (fun (Xy:a)=> (((eq a) x) Xy))) P) as proof of (P0 (fun (Xy:a)=> (((eq a) x) Xy)))
% 3.32/3.52 Found ((((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xy:a)=> (((eq a) x) Xy))) P) as proof of (P0 (fun (Xy:a)=> (((eq a) x) Xy)))
% 3.32/3.52 Found ((((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xy:a)=> (((eq a) x) Xy))) P) as proof of (P0 (fun (Xy:a)=> (((eq a) x) Xy)))
% 3.32/3.52 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (Xy:a)=> (((eq a) x) Xy)))->(P (fun (x0:a)=> (((eq a) x) x0))))
% 3.32/3.52 Found (eta_expansion_dep000 P) as proof of (P0 (fun (Xy:a)=> (((eq a) x) Xy)))
% 3.32/3.52 Found ((eta_expansion_dep00 (fun (Xy:a)=> (((eq a) x) Xy))) P) as proof of (P0 (fun (Xy:a)=> (((eq a) x) Xy)))
% 3.32/3.52 Found (((eta_expansion_dep0 (fun (x1:a)=> Prop)) (fun (Xy:a)=> (((eq a) x) Xy))) P) as proof of (P0 (fun (Xy:a)=> (((eq a) x) Xy)))
% 3.32/3.52 Found ((((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xy:a)=> (((eq a) x) Xy))) P) as proof of (P0 (fun (Xy:a)=> (((eq a) x) Xy)))
% 3.32/3.52 Found ((((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xy:a)=> (((eq a) x) Xy))) P) as proof of (P0 (fun (Xy:a)=> (((eq a) x) Xy)))
% 3.32/3.52 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xy:a)=> (((eq a) x) Xy))):(((eq (a->Prop)) (fun (Xy:a)=> (((eq a) x) Xy))) (fun (x0:a)=> (((eq a) x) x0)))
% 3.32/3.52 Found (eta_expansion_dep00 (fun (Xy:a)=> (((eq a) x) Xy))) as proof of (((eq (a->Prop)) (fun (Xy:a)=> (((eq a) x) Xy))) b)
% 3.32/3.52 Found ((eta_expansion_dep0 (fun (x1:a)=> Prop)) (fun (Xy:a)=> (((eq a) x) Xy))) as proof of (((eq (a->Prop)) (fun (Xy:a)=> (((eq a) x) Xy))) b)
% 3.32/3.52 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xy:a)=> (((eq a) x) Xy))) as proof of (((eq (a->Prop)) (fun (Xy:a)=> (((eq a) x) Xy))) b)
% 3.32/3.52 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xy:a)=> (((eq a) x) Xy))) as proof of (((eq (a->Prop)) (fun (Xy:a)=> (((eq a) x) Xy))) b)
% 3.32/3.52 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xy:a)=> (((eq a) x) Xy))) as proof of (((eq (a->Prop)) (fun (Xy:a)=> (((eq a) x) Xy))) b)
% 9.29/9.49 Found eta_expansion000:=(eta_expansion00 b):(((eq (a->Prop)) b) (fun (x:a)=> (b x)))
% 9.29/9.49 Found (eta_expansion00 b) as proof of (((eq (a->Prop)) b) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 9.29/9.49 Found ((eta_expansion0 Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 9.29/9.49 Found (((eta_expansion a) Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 9.29/9.49 Found (((eta_expansion a) Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 9.29/9.49 Found (((eta_expansion a) Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 9.29/9.49 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P ((eq a) x))->(P (fun (x0:a)=> (((eq a) x) x0))))
% 9.29/9.49 Found (eta_expansion_dep000 P) as proof of (P0 ((eq a) x))
% 9.29/9.49 Found ((eta_expansion_dep00 ((eq a) x)) P) as proof of (P0 ((eq a) x))
% 9.29/9.49 Found (((eta_expansion_dep0 (fun (x1:a)=> Prop)) ((eq a) x)) P) as proof of (P0 ((eq a) x))
% 9.29/9.49 Found ((((eta_expansion_dep a) (fun (x1:a)=> Prop)) ((eq a) x)) P) as proof of (P0 ((eq a) x))
% 9.29/9.49 Found ((((eta_expansion_dep a) (fun (x1:a)=> Prop)) ((eq a) x)) P) as proof of (P0 ((eq a) x))
% 9.29/9.49 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P ((eq a) x))->(P (fun (x0:a)=> (((eq a) x) x0))))
% 9.29/9.49 Found (eta_expansion_dep000 P) as proof of (P0 ((eq a) x))
% 9.29/9.49 Found ((eta_expansion_dep00 ((eq a) x)) P) as proof of (P0 ((eq a) x))
% 9.29/9.49 Found (((eta_expansion_dep0 (fun (x1:a)=> Prop)) ((eq a) x)) P) as proof of (P0 ((eq a) x))
% 9.29/9.49 Found ((((eta_expansion_dep a) (fun (x1:a)=> Prop)) ((eq a) x)) P) as proof of (P0 ((eq a) x))
% 9.29/9.49 Found ((((eta_expansion_dep a) (fun (x1:a)=> Prop)) ((eq a) x)) P) as proof of (P0 ((eq a) x))
% 9.29/9.49 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P ((eq a) x))->(P (fun (x0:a)=> (((eq a) x) x0))))
% 9.29/9.49 Found (eta_expansion_dep000 P) as proof of (P0 ((eq a) x))
% 9.29/9.49 Found ((eta_expansion_dep00 ((eq a) x)) P) as proof of (P0 ((eq a) x))
% 9.29/9.49 Found (((eta_expansion_dep0 (fun (x1:a)=> Prop)) ((eq a) x)) P) as proof of (P0 ((eq a) x))
% 9.29/9.49 Found ((((eta_expansion_dep a) (fun (x1:a)=> Prop)) ((eq a) x)) P) as proof of (P0 ((eq a) x))
% 9.29/9.49 Found ((((eta_expansion_dep a) (fun (x1:a)=> Prop)) ((eq a) x)) P) as proof of (P0 ((eq a) x))
% 9.29/9.49 Found eta_expansion000:=(eta_expansion00 ((eq a) x)):(((eq (a->Prop)) ((eq a) x)) (fun (x0:a)=> (((eq a) x) x0)))
% 9.29/9.49 Found (eta_expansion00 ((eq a) x)) as proof of (((eq (a->Prop)) ((eq a) x)) b)
% 9.29/9.49 Found ((eta_expansion0 Prop) ((eq a) x)) as proof of (((eq (a->Prop)) ((eq a) x)) b)
% 9.29/9.49 Found (((eta_expansion a) Prop) ((eq a) x)) as proof of (((eq (a->Prop)) ((eq a) x)) b)
% 9.29/9.49 Found (((eta_expansion a) Prop) ((eq a) x)) as proof of (((eq (a->Prop)) ((eq a) x)) b)
% 9.29/9.49 Found (((eta_expansion a) Prop) ((eq a) x)) as proof of (((eq (a->Prop)) ((eq a) x)) b)
% 9.29/9.49 Found eta_expansion000:=(eta_expansion00 b):(((eq (a->Prop)) b) (fun (x:a)=> (b x)))
% 9.29/9.49 Found (eta_expansion00 b) as proof of (((eq (a->Prop)) b) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 9.29/9.49 Found ((eta_expansion0 Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 9.29/9.49 Found (((eta_expansion a) Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 9.29/9.49 Found (((eta_expansion a) Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 9.29/9.49 Found (((eta_expansion a) Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 9.29/9.49 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))):(((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) (fun (x0:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))))
% 9.29/9.49 Found (eta_expansion_dep00 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 10.09/10.29 Found ((eta_expansion_dep0 (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 10.09/10.29 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 10.09/10.29 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 10.09/10.29 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 10.09/10.29 Found eq_ref00:=(eq_ref0 b):(((eq (a->Prop)) b) b)
% 10.09/10.29 Found (eq_ref0 b) as proof of (((eq (a->Prop)) b) (fun (Xy:a)=> (((eq a) x) Xy)))
% 10.09/10.29 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xy:a)=> (((eq a) x) Xy)))
% 10.09/10.29 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xy:a)=> (((eq a) x) Xy)))
% 10.09/10.29 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xy:a)=> (((eq a) x) Xy)))
% 10.09/10.29 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))->(P (fun (x0:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))))
% 10.09/10.29 Found (eta_expansion_dep000 P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 10.09/10.29 Found ((eta_expansion_dep00 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 10.09/10.29 Found (((eta_expansion_dep0 (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 10.09/10.29 Found ((((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 10.09/10.29 Found ((((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 10.09/10.29 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))->(P (fun (x0:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))))
% 10.09/10.29 Found (eta_expansion_dep000 P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 10.09/10.29 Found ((eta_expansion_dep00 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 10.09/10.29 Found (((eta_expansion_dep0 (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 10.09/10.29 Found ((((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 10.09/10.29 Found ((((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 13.35/13.51 Found eq_ref000:=(eq_ref00 P):((P (((eq a) x) x0))->(P (((eq a) x) x0)))
% 13.35/13.51 Found (eq_ref00 P) as proof of (P0 (((eq a) x) x0))
% 13.35/13.51 Found ((eq_ref0 (((eq a) x) x0)) P) as proof of (P0 (((eq a) x) x0))
% 13.35/13.51 Found (((eq_ref Prop) (((eq a) x) x0)) P) as proof of (P0 (((eq a) x) x0))
% 13.35/13.51 Found (((eq_ref Prop) (((eq a) x) x0)) P) as proof of (P0 (((eq a) x) x0))
% 13.35/13.51 Found eq_ref000:=(eq_ref00 P):((P (((eq a) x) x0))->(P (((eq a) x) x0)))
% 13.35/13.51 Found (eq_ref00 P) as proof of (P0 (((eq a) x) x0))
% 13.35/13.51 Found ((eq_ref0 (((eq a) x) x0)) P) as proof of (P0 (((eq a) x) x0))
% 13.35/13.51 Found (((eq_ref Prop) (((eq a) x) x0)) P) as proof of (P0 (((eq a) x) x0))
% 13.35/13.51 Found (((eq_ref Prop) (((eq a) x) x0)) P) as proof of (P0 (((eq a) x) x0))
% 13.35/13.51 Found eq_ref00:=(eq_ref0 (((eq a) x) x0)):(((eq Prop) (((eq a) x) x0)) (((eq a) x) x0))
% 13.35/13.51 Found (eq_ref0 (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 13.35/13.51 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 13.35/13.51 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 13.35/13.51 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 13.35/13.51 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 13.35/13.51 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 13.35/13.51 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 13.35/13.51 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 13.35/13.51 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 13.35/13.51 Found eq_ref00:=(eq_ref0 (((eq a) x) x0)):(((eq Prop) (((eq a) x) x0)) (((eq a) x) x0))
% 13.35/13.51 Found (eq_ref0 (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 13.35/13.51 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 13.35/13.51 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 13.35/13.51 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 13.35/13.51 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 13.35/13.51 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 13.35/13.51 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 13.35/13.51 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 13.35/13.51 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 13.35/13.51 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))):(((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) (fun (x0:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))))
% 13.35/13.51 Found (eta_expansion_dep00 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 13.35/13.51 Found ((eta_expansion_dep0 (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 13.35/13.51 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 13.35/13.51 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 13.35/13.51 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 13.35/13.51 Found eq_ref00:=(eq_ref0 b):(((eq (a->Prop)) b) b)
% 15.39/15.59 Found (eq_ref0 b) as proof of (((eq (a->Prop)) b) ((eq a) x))
% 15.39/15.59 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) ((eq a) x))
% 15.39/15.59 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) ((eq a) x))
% 15.39/15.59 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) ((eq a) x))
% 15.39/15.59 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))->(P (fun (x0:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))))
% 15.39/15.59 Found (eta_expansion_dep000 P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 15.39/15.59 Found ((eta_expansion_dep00 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 15.39/15.59 Found (((eta_expansion_dep0 (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 15.39/15.59 Found ((((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 15.39/15.59 Found ((((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 15.39/15.59 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))->(P (fun (x0:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))))
% 15.39/15.59 Found (eta_expansion_dep000 P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 15.39/15.59 Found ((eta_expansion_dep00 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 15.39/15.59 Found (((eta_expansion_dep0 (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 15.39/15.59 Found ((((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 15.39/15.59 Found ((((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 15.39/15.59 Found eq_ref000:=(eq_ref00 P):((P (((eq a) x) x0))->(P (((eq a) x) x0)))
% 15.39/15.59 Found (eq_ref00 P) as proof of (P0 (((eq a) x) x0))
% 15.39/15.59 Found ((eq_ref0 (((eq a) x) x0)) P) as proof of (P0 (((eq a) x) x0))
% 15.39/15.59 Found (((eq_ref Prop) (((eq a) x) x0)) P) as proof of (P0 (((eq a) x) x0))
% 15.39/15.59 Found (((eq_ref Prop) (((eq a) x) x0)) P) as proof of (P0 (((eq a) x) x0))
% 15.39/15.59 Found eq_ref000:=(eq_ref00 P):((P (((eq a) x) x0))->(P (((eq a) x) x0)))
% 15.39/15.59 Found (eq_ref00 P) as proof of (P0 (((eq a) x) x0))
% 15.39/15.59 Found ((eq_ref0 (((eq a) x) x0)) P) as proof of (P0 (((eq a) x) x0))
% 15.39/15.59 Found (((eq_ref Prop) (((eq a) x) x0)) P) as proof of (P0 (((eq a) x) x0))
% 15.39/15.59 Found (((eq_ref Prop) (((eq a) x) x0)) P) as proof of (P0 (((eq a) x) x0))
% 15.39/15.59 Found eq_ref00:=(eq_ref0 (((eq a) x) x0)):(((eq Prop) (((eq a) x) x0)) (((eq a) x) x0))
% 15.39/15.59 Found (eq_ref0 (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 15.39/15.59 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 15.39/15.59 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 15.39/15.59 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 15.39/15.59 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 15.39/15.59 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 15.39/15.59 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 24.08/24.29 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 24.08/24.29 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 24.08/24.29 Found eq_ref00:=(eq_ref0 (((eq a) x) x0)):(((eq Prop) (((eq a) x) x0)) (((eq a) x) x0))
% 24.08/24.29 Found (eq_ref0 (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 24.08/24.29 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 24.08/24.29 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 24.08/24.29 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 24.08/24.29 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 24.08/24.29 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 24.08/24.29 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 24.08/24.29 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 24.08/24.29 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 24.08/24.29 Found eq_ref000:=(eq_ref00 P):((P ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))->(P ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))))
% 24.08/24.29 Found (eq_ref00 P) as proof of (P0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 24.08/24.29 Found ((eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P) as proof of (P0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 24.08/24.29 Found (((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P) as proof of (P0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 24.08/24.29 Found (((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P) as proof of (P0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 24.08/24.29 Found eq_ref000:=(eq_ref00 P):((P ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))->(P ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))))
% 24.08/24.29 Found (eq_ref00 P) as proof of (P0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 24.08/24.29 Found ((eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P) as proof of (P0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 24.08/24.29 Found (((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P) as proof of (P0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 24.08/24.29 Found (((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P) as proof of (P0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 24.08/24.29 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 24.08/24.29 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 24.08/24.29 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 24.08/24.29 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 24.08/24.29 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 24.08/24.29 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 24.08/24.29 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 24.08/24.29 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 24.08/24.29 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 24.08/24.29 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 24.08/24.29 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 27.28/27.48 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 27.28/27.48 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 27.28/27.48 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 27.28/27.48 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 27.28/27.48 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 27.28/27.48 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 27.28/27.48 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 27.28/27.48 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 27.31/27.48 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 27.31/27.48 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 27.31/27.48 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 27.31/27.48 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 27.31/27.48 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 27.31/27.48 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 27.31/27.48 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 27.31/27.48 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 27.31/27.48 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 27.31/27.48 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 27.31/27.48 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 27.31/27.48 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 27.31/27.48 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 27.31/27.48 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 27.31/27.48 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 27.31/27.48 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 27.31/27.48 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 27.31/27.48 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 27.31/27.48 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 27.31/27.48 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 27.31/27.48 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 27.31/27.48 Found eq_ref000:=(eq_ref00 P):((P ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))->(P ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))))
% 27.31/27.48 Found (eq_ref00 P) as proof of (P0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 27.31/27.48 Found ((eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P) as proof of (P0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 28.74/28.97 Found (((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P) as proof of (P0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 28.74/28.97 Found (((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P) as proof of (P0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 28.74/28.97 Found eq_ref000:=(eq_ref00 P):((P ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))->(P ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))))
% 28.74/28.97 Found (eq_ref00 P) as proof of (P0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 28.74/28.97 Found ((eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P) as proof of (P0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 28.74/28.97 Found (((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P) as proof of (P0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 28.74/28.97 Found (((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P) as proof of (P0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 28.74/28.97 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 28.74/28.97 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 28.74/28.97 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 28.74/28.97 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 28.74/28.97 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 28.74/28.97 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 28.74/28.97 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 28.74/28.97 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 28.74/28.97 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 28.74/28.97 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 28.74/28.97 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 28.74/28.97 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 28.74/28.97 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 28.74/28.97 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 28.74/28.97 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 28.74/28.97 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 28.74/28.97 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 28.74/28.97 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 28.74/28.97 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 28.74/28.97 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 28.74/28.97 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 28.74/28.97 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 33.92/34.14 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 33.92/34.14 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 33.92/34.14 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 33.92/34.14 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 33.92/34.14 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 33.92/34.14 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 33.92/34.14 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 33.92/34.14 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 33.92/34.14 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 33.92/34.14 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 33.92/34.14 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 33.92/34.14 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 33.92/34.14 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 33.92/34.14 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 33.92/34.14 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 33.92/34.14 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 33.92/34.14 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 33.92/34.14 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 33.92/34.14 Found x0:(P ((fun (Xx:a) (Xy:a)=> (((eq a) Xx) Xy)) x))
% 33.92/34.14 Instantiate: b:=((fun (Xx:a) (Xy:a)=> (((eq a) Xx) Xy)) x):(a->Prop)
% 33.92/34.14 Found x0 as proof of (P0 b)
% 33.92/34.14 Found eta_expansion000:=(eta_expansion00 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))):(((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) (fun (x0:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))))
% 33.92/34.14 Found (eta_expansion00 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 33.92/34.14 Found ((eta_expansion0 Prop) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 33.92/34.14 Found (((eta_expansion a) Prop) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 33.92/34.14 Found (((eta_expansion a) Prop) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 33.92/34.14 Found (((eta_expansion a) Prop) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 33.92/34.14 Found x0:(P ((fun (Xx:a) (Xy:a)=> (((eq a) Xx) Xy)) x))
% 33.92/34.14 Instantiate: f:=((fun (Xx:a) (Xy:a)=> (((eq a) Xx) Xy)) x):(a->Prop)
% 33.92/34.14 Found x0 as proof of (P0 f)
% 33.92/34.14 Found eq_ref00:=(eq_ref0 (f x00)):(((eq Prop) (f x00)) (f x00))
% 33.92/34.14 Found (eq_ref0 (f x00)) as proof of (((eq Prop) (f x00)) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x00) Xy)))))
% 33.92/34.14 Found ((eq_ref Prop) (f x00)) as proof of (((eq Prop) (f x00)) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x00) Xy)))))
% 35.90/36.14 Found ((eq_ref Prop) (f x00)) as proof of (((eq Prop) (f x00)) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x00) Xy)))))
% 35.90/36.14 Found (fun (x00:a)=> ((eq_ref Prop) (f x00))) as proof of (((eq Prop) (f x00)) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x00) Xy)))))
% 35.90/36.14 Found (fun (x00:a)=> ((eq_ref Prop) (f x00))) as proof of (forall (x0:a), (((eq Prop) (f x0)) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))))
% 35.90/36.14 Found x0:(P ((fun (Xx:a) (Xy:a)=> (((eq a) Xx) Xy)) x))
% 35.90/36.14 Instantiate: f:=((fun (Xx:a) (Xy:a)=> (((eq a) Xx) Xy)) x):(a->Prop)
% 35.90/36.14 Found x0 as proof of (P0 f)
% 35.90/36.14 Found eq_ref00:=(eq_ref0 (f x00)):(((eq Prop) (f x00)) (f x00))
% 35.90/36.14 Found (eq_ref0 (f x00)) as proof of (((eq Prop) (f x00)) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x00) Xy)))))
% 35.90/36.14 Found ((eq_ref Prop) (f x00)) as proof of (((eq Prop) (f x00)) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x00) Xy)))))
% 35.90/36.14 Found ((eq_ref Prop) (f x00)) as proof of (((eq Prop) (f x00)) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x00) Xy)))))
% 35.90/36.14 Found (fun (x00:a)=> ((eq_ref Prop) (f x00))) as proof of (((eq Prop) (f x00)) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x00) Xy)))))
% 35.90/36.14 Found (fun (x00:a)=> ((eq_ref Prop) (f x00))) as proof of (forall (x0:a), (((eq Prop) (f x0)) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))))
% 35.90/36.14 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 35.90/36.14 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 35.90/36.14 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 35.90/36.14 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 35.90/36.14 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 35.90/36.14 Found eq_ref00:=(eq_ref0 (((eq a) x) x0)):(((eq Prop) (((eq a) x) x0)) (((eq a) x) x0))
% 35.90/36.14 Found (eq_ref0 (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 35.90/36.14 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 35.90/36.14 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 35.90/36.14 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 35.90/36.14 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 35.90/36.14 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 35.90/36.14 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 35.90/36.14 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 35.90/36.14 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 35.90/36.14 Found eq_ref00:=(eq_ref0 (((eq a) x) x0)):(((eq Prop) (((eq a) x) x0)) (((eq a) x) x0))
% 35.90/36.14 Found (eq_ref0 (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 35.90/36.14 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 35.90/36.14 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 35.90/36.14 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 35.90/36.14 Found x0:(P ((eq a) x))
% 35.90/36.14 Instantiate: b:=((eq a) x):(a->Prop)
% 35.90/36.14 Found x0 as proof of (P0 b)
% 35.90/36.14 Found eta_expansion000:=(eta_expansion00 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))):(((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) (fun (x0:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))))
% 35.90/36.14 Found (eta_expansion00 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 35.90/36.14 Found ((eta_expansion0 Prop) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 37.07/37.27 Found (((eta_expansion a) Prop) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 37.07/37.27 Found (((eta_expansion a) Prop) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 37.07/37.27 Found (((eta_expansion a) Prop) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 37.07/37.27 Found eta_expansion000:=(eta_expansion00 (fun (Xy:a)=> (((eq a) x) Xy))):(((eq (a->Prop)) (fun (Xy:a)=> (((eq a) x) Xy))) (fun (x0:a)=> (((eq a) x) x0)))
% 37.07/37.27 Found (eta_expansion00 (fun (Xy:a)=> (((eq a) x) Xy))) as proof of (((eq (a->Prop)) (fun (Xy:a)=> (((eq a) x) Xy))) b)
% 37.07/37.27 Found ((eta_expansion0 Prop) (fun (Xy:a)=> (((eq a) x) Xy))) as proof of (((eq (a->Prop)) (fun (Xy:a)=> (((eq a) x) Xy))) b)
% 37.07/37.27 Found (((eta_expansion a) Prop) (fun (Xy:a)=> (((eq a) x) Xy))) as proof of (((eq (a->Prop)) (fun (Xy:a)=> (((eq a) x) Xy))) b)
% 37.07/37.27 Found (((eta_expansion a) Prop) (fun (Xy:a)=> (((eq a) x) Xy))) as proof of (((eq (a->Prop)) (fun (Xy:a)=> (((eq a) x) Xy))) b)
% 37.07/37.27 Found (((eta_expansion a) Prop) (fun (Xy:a)=> (((eq a) x) Xy))) as proof of (((eq (a->Prop)) (fun (Xy:a)=> (((eq a) x) Xy))) b)
% 37.07/37.27 Found eta_expansion000:=(eta_expansion00 b):(((eq (a->Prop)) b) (fun (x:a)=> (b x)))
% 37.07/37.27 Found (eta_expansion00 b) as proof of (((eq (a->Prop)) b) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 37.07/37.27 Found ((eta_expansion0 Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 37.07/37.27 Found (((eta_expansion a) Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 37.07/37.27 Found (((eta_expansion a) Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 37.07/37.27 Found (((eta_expansion a) Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 37.07/37.27 Found eq_ref000:=(eq_ref00 P):((P (fun (Xy:a)=> (((eq a) x) Xy)))->(P (fun (Xy:a)=> (((eq a) x) Xy))))
% 37.07/37.27 Found (eq_ref00 P) as proof of (P0 (fun (Xy:a)=> (((eq a) x) Xy)))
% 37.07/37.27 Found ((eq_ref0 (fun (Xy:a)=> (((eq a) x) Xy))) P) as proof of (P0 (fun (Xy:a)=> (((eq a) x) Xy)))
% 37.07/37.27 Found (((eq_ref (a->Prop)) (fun (Xy:a)=> (((eq a) x) Xy))) P) as proof of (P0 (fun (Xy:a)=> (((eq a) x) Xy)))
% 37.07/37.27 Found (((eq_ref (a->Prop)) (fun (Xy:a)=> (((eq a) x) Xy))) P) as proof of (P0 (fun (Xy:a)=> (((eq a) x) Xy)))
% 37.07/37.27 Found eta_expansion000:=(eta_expansion00 (fun (Xy:a)=> (((eq a) x) Xy))):(((eq (a->Prop)) (fun (Xy:a)=> (((eq a) x) Xy))) (fun (x0:a)=> (((eq a) x) x0)))
% 37.07/37.27 Found (eta_expansion00 (fun (Xy:a)=> (((eq a) x) Xy))) as proof of (((eq (a->Prop)) (fun (Xy:a)=> (((eq a) x) Xy))) b)
% 37.07/37.27 Found ((eta_expansion0 Prop) (fun (Xy:a)=> (((eq a) x) Xy))) as proof of (((eq (a->Prop)) (fun (Xy:a)=> (((eq a) x) Xy))) b)
% 37.07/37.27 Found (((eta_expansion a) Prop) (fun (Xy:a)=> (((eq a) x) Xy))) as proof of (((eq (a->Prop)) (fun (Xy:a)=> (((eq a) x) Xy))) b)
% 37.07/37.27 Found (((eta_expansion a) Prop) (fun (Xy:a)=> (((eq a) x) Xy))) as proof of (((eq (a->Prop)) (fun (Xy:a)=> (((eq a) x) Xy))) b)
% 37.07/37.27 Found (((eta_expansion a) Prop) (fun (Xy:a)=> (((eq a) x) Xy))) as proof of (((eq (a->Prop)) (fun (Xy:a)=> (((eq a) x) Xy))) b)
% 37.07/37.27 Found eta_expansion000:=(eta_expansion00 b):(((eq (a->Prop)) b) (fun (x:a)=> (b x)))
% 37.07/37.27 Found (eta_expansion00 b) as proof of (((eq (a->Prop)) b) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 37.07/37.27 Found ((eta_expansion0 Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 37.07/37.27 Found (((eta_expansion a) Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 39.62/39.83 Found (((eta_expansion a) Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 39.62/39.83 Found (((eta_expansion a) Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 39.62/39.83 Found x0:(P ((eq a) x))
% 39.62/39.83 Instantiate: f:=((eq a) x):(a->Prop)
% 39.62/39.83 Found x0 as proof of (P0 f)
% 39.62/39.83 Found eq_ref00:=(eq_ref0 (f x00)):(((eq Prop) (f x00)) (f x00))
% 39.62/39.83 Found (eq_ref0 (f x00)) as proof of (((eq Prop) (f x00)) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x00) Xy)))))
% 39.62/39.83 Found ((eq_ref Prop) (f x00)) as proof of (((eq Prop) (f x00)) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x00) Xy)))))
% 39.62/39.83 Found ((eq_ref Prop) (f x00)) as proof of (((eq Prop) (f x00)) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x00) Xy)))))
% 39.62/39.83 Found (fun (x00:a)=> ((eq_ref Prop) (f x00))) as proof of (((eq Prop) (f x00)) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x00) Xy)))))
% 39.62/39.83 Found (fun (x00:a)=> ((eq_ref Prop) (f x00))) as proof of (forall (x0:a), (((eq Prop) (f x0)) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))))
% 39.62/39.83 Found x0:(P ((eq a) x))
% 39.62/39.83 Instantiate: f:=((eq a) x):(a->Prop)
% 39.62/39.83 Found x0 as proof of (P0 f)
% 39.62/39.83 Found eq_ref00:=(eq_ref0 (f x00)):(((eq Prop) (f x00)) (f x00))
% 39.62/39.83 Found (eq_ref0 (f x00)) as proof of (((eq Prop) (f x00)) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x00) Xy)))))
% 39.62/39.83 Found ((eq_ref Prop) (f x00)) as proof of (((eq Prop) (f x00)) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x00) Xy)))))
% 39.62/39.83 Found ((eq_ref Prop) (f x00)) as proof of (((eq Prop) (f x00)) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x00) Xy)))))
% 39.62/39.83 Found (fun (x00:a)=> ((eq_ref Prop) (f x00))) as proof of (((eq Prop) (f x00)) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x00) Xy)))))
% 39.62/39.83 Found (fun (x00:a)=> ((eq_ref Prop) (f x00))) as proof of (forall (x0:a), (((eq Prop) (f x0)) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))))
% 39.62/39.83 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 39.62/39.83 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 39.62/39.83 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 39.62/39.83 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 39.62/39.83 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 39.62/39.83 Found eq_ref00:=(eq_ref0 (((eq a) x) x0)):(((eq Prop) (((eq a) x) x0)) (((eq a) x) x0))
% 39.62/39.83 Found (eq_ref0 (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 39.62/39.83 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 39.62/39.83 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 39.62/39.83 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 39.62/39.83 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 39.62/39.83 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 39.62/39.83 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 39.62/39.83 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 39.62/39.83 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 39.62/39.83 Found eq_ref00:=(eq_ref0 (((eq a) x) x0)):(((eq Prop) (((eq a) x) x0)) (((eq a) x) x0))
% 39.62/39.83 Found (eq_ref0 (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 39.62/39.83 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 39.62/39.83 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 39.62/39.83 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 39.62/39.83 Found eta_expansion_dep000:=(eta_expansion_dep00 ((eq a) x)):(((eq (a->Prop)) ((eq a) x)) (fun (x0:a)=> (((eq a) x) x0)))
% 39.62/39.83 Found (eta_expansion_dep00 ((eq a) x)) as proof of (((eq (a->Prop)) ((eq a) x)) b)
% 39.62/39.83 Found ((eta_expansion_dep0 (fun (x1:a)=> Prop)) ((eq a) x)) as proof of (((eq (a->Prop)) ((eq a) x)) b)
% 41.32/41.55 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) ((eq a) x)) as proof of (((eq (a->Prop)) ((eq a) x)) b)
% 41.32/41.55 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) ((eq a) x)) as proof of (((eq (a->Prop)) ((eq a) x)) b)
% 41.32/41.55 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) ((eq a) x)) as proof of (((eq (a->Prop)) ((eq a) x)) b)
% 41.32/41.55 Found eta_expansion000:=(eta_expansion00 b):(((eq (a->Prop)) b) (fun (x:a)=> (b x)))
% 41.32/41.55 Found (eta_expansion00 b) as proof of (((eq (a->Prop)) b) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 41.32/41.55 Found ((eta_expansion0 Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 41.32/41.55 Found (((eta_expansion a) Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 41.32/41.55 Found (((eta_expansion a) Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 41.32/41.55 Found (((eta_expansion a) Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 41.32/41.55 Found eq_ref000:=(eq_ref00 P):((P ((eq a) x))->(P ((eq a) x)))
% 41.32/41.55 Found (eq_ref00 P) as proof of (P0 ((eq a) x))
% 41.32/41.55 Found ((eq_ref0 ((eq a) x)) P) as proof of (P0 ((eq a) x))
% 41.32/41.55 Found (((eq_ref (a->Prop)) ((eq a) x)) P) as proof of (P0 ((eq a) x))
% 41.32/41.55 Found (((eq_ref (a->Prop)) ((eq a) x)) P) as proof of (P0 ((eq a) x))
% 41.32/41.55 Found eta_expansion000:=(eta_expansion00 ((eq a) x)):(((eq (a->Prop)) ((eq a) x)) (fun (x0:a)=> (((eq a) x) x0)))
% 41.32/41.55 Found (eta_expansion00 ((eq a) x)) as proof of (((eq (a->Prop)) ((eq a) x)) b)
% 41.32/41.55 Found ((eta_expansion0 Prop) ((eq a) x)) as proof of (((eq (a->Prop)) ((eq a) x)) b)
% 41.32/41.55 Found (((eta_expansion a) Prop) ((eq a) x)) as proof of (((eq (a->Prop)) ((eq a) x)) b)
% 41.32/41.55 Found (((eta_expansion a) Prop) ((eq a) x)) as proof of (((eq (a->Prop)) ((eq a) x)) b)
% 41.32/41.55 Found (((eta_expansion a) Prop) ((eq a) x)) as proof of (((eq (a->Prop)) ((eq a) x)) b)
% 41.32/41.55 Found eta_expansion000:=(eta_expansion00 b):(((eq (a->Prop)) b) (fun (x:a)=> (b x)))
% 41.32/41.55 Found (eta_expansion00 b) as proof of (((eq (a->Prop)) b) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 41.32/41.55 Found ((eta_expansion0 Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 41.32/41.55 Found (((eta_expansion a) Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 41.32/41.55 Found (((eta_expansion a) Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 41.32/41.55 Found (((eta_expansion a) Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 41.32/41.55 Found eq_ref00:=(eq_ref0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))):(((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 41.32/41.55 Found (eq_ref0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 41.32/41.55 Found ((eq_ref (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 41.32/41.55 Found ((eq_ref (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 41.32/41.55 Found ((eq_ref (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 41.32/41.55 Found x0:(P0 b)
% 41.32/41.55 Instantiate: b:=(fun (Xy:a)=> (forall (P:(a->Prop)), ((P x)->(P Xy)))):(a->Prop)
% 41.32/41.55 Found (fun (x0:(P0 b))=> x0) as proof of (P0 (fun (Xy:a)=> (((eq a) x) Xy)))
% 46.34/46.56 Found (fun (P0:((a->Prop)->Prop)) (x0:(P0 b))=> x0) as proof of ((P0 b)->(P0 (fun (Xy:a)=> (((eq a) x) Xy))))
% 46.34/46.56 Found (fun (P0:((a->Prop)->Prop)) (x0:(P0 b))=> x0) as proof of (P b)
% 46.34/46.56 Found x0:(P (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 46.34/46.56 Instantiate: b:=(fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))):(a->Prop)
% 46.34/46.56 Found x0 as proof of (P0 b)
% 46.34/46.56 Found eq_ref00:=(eq_ref0 (fun (Xy:a)=> (((eq a) x) Xy))):(((eq (a->Prop)) (fun (Xy:a)=> (((eq a) x) Xy))) (fun (Xy:a)=> (((eq a) x) Xy)))
% 46.34/46.56 Found (eq_ref0 (fun (Xy:a)=> (((eq a) x) Xy))) as proof of (((eq (a->Prop)) (fun (Xy:a)=> (((eq a) x) Xy))) b)
% 46.34/46.56 Found ((eq_ref (a->Prop)) (fun (Xy:a)=> (((eq a) x) Xy))) as proof of (((eq (a->Prop)) (fun (Xy:a)=> (((eq a) x) Xy))) b)
% 46.34/46.56 Found ((eq_ref (a->Prop)) (fun (Xy:a)=> (((eq a) x) Xy))) as proof of (((eq (a->Prop)) (fun (Xy:a)=> (((eq a) x) Xy))) b)
% 46.34/46.56 Found ((eq_ref (a->Prop)) (fun (Xy:a)=> (((eq a) x) Xy))) as proof of (((eq (a->Prop)) (fun (Xy:a)=> (((eq a) x) Xy))) b)
% 46.34/46.56 Found eta_expansion000:=(eta_expansion00 (fun (Xy:a)=> (((eq a) x) Xy))):(((eq (a->Prop)) (fun (Xy:a)=> (((eq a) x) Xy))) (fun (x0:a)=> (((eq a) x) x0)))
% 46.34/46.56 Found (eta_expansion00 (fun (Xy:a)=> (((eq a) x) Xy))) as proof of (((eq (a->Prop)) (fun (Xy:a)=> (((eq a) x) Xy))) b0)
% 46.34/46.56 Found ((eta_expansion0 Prop) (fun (Xy:a)=> (((eq a) x) Xy))) as proof of (((eq (a->Prop)) (fun (Xy:a)=> (((eq a) x) Xy))) b0)
% 46.34/46.56 Found (((eta_expansion a) Prop) (fun (Xy:a)=> (((eq a) x) Xy))) as proof of (((eq (a->Prop)) (fun (Xy:a)=> (((eq a) x) Xy))) b0)
% 46.34/46.56 Found (((eta_expansion a) Prop) (fun (Xy:a)=> (((eq a) x) Xy))) as proof of (((eq (a->Prop)) (fun (Xy:a)=> (((eq a) x) Xy))) b0)
% 46.34/46.56 Found (((eta_expansion a) Prop) (fun (Xy:a)=> (((eq a) x) Xy))) as proof of (((eq (a->Prop)) (fun (Xy:a)=> (((eq a) x) Xy))) b0)
% 46.34/46.56 Found eq_ref00:=(eq_ref0 b0):(((eq (a->Prop)) b0) b0)
% 46.34/46.56 Found (eq_ref0 b0) as proof of (((eq (a->Prop)) b0) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 46.34/46.56 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 46.34/46.56 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 46.34/46.56 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 46.34/46.56 Found x0:(P (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 46.34/46.56 Instantiate: f:=(fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))):(a->Prop)
% 46.34/46.56 Found x0 as proof of (P0 f)
% 46.34/46.56 Found eq_ref00:=(eq_ref0 (f x00)):(((eq Prop) (f x00)) (f x00))
% 46.34/46.56 Found (eq_ref0 (f x00)) as proof of (((eq Prop) (f x00)) (((eq a) x) x00))
% 46.34/46.56 Found ((eq_ref Prop) (f x00)) as proof of (((eq Prop) (f x00)) (((eq a) x) x00))
% 46.34/46.56 Found ((eq_ref Prop) (f x00)) as proof of (((eq Prop) (f x00)) (((eq a) x) x00))
% 46.34/46.56 Found (fun (x00:a)=> ((eq_ref Prop) (f x00))) as proof of (((eq Prop) (f x00)) (((eq a) x) x00))
% 46.34/46.56 Found (fun (x00:a)=> ((eq_ref Prop) (f x00))) as proof of (forall (x0:a), (((eq Prop) (f x0)) (((eq a) x) x0)))
% 46.34/46.56 Found x0:(P (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 46.34/46.56 Instantiate: f:=(fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))):(a->Prop)
% 46.34/46.56 Found x0 as proof of (P0 f)
% 46.34/46.56 Found eq_ref00:=(eq_ref0 (f x00)):(((eq Prop) (f x00)) (f x00))
% 46.34/46.56 Found (eq_ref0 (f x00)) as proof of (((eq Prop) (f x00)) (((eq a) x) x00))
% 46.34/46.56 Found ((eq_ref Prop) (f x00)) as proof of (((eq Prop) (f x00)) (((eq a) x) x00))
% 46.34/46.56 Found ((eq_ref Prop) (f x00)) as proof of (((eq Prop) (f x00)) (((eq a) x) x00))
% 46.34/46.56 Found (fun (x00:a)=> ((eq_ref Prop) (f x00))) as proof of (((eq Prop) (f x00)) (((eq a) x) x00))
% 46.34/46.56 Found (fun (x00:a)=> ((eq_ref Prop) (f x00))) as proof of (forall (x0:a), (((eq Prop) (f x0)) (((eq a) x) x0)))
% 46.34/46.56 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))):(((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) (fun (x0:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))))
% 47.87/48.13 Found (eta_expansion_dep00 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 47.87/48.13 Found ((eta_expansion_dep0 (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 47.87/48.13 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 47.87/48.13 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 47.87/48.13 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 47.87/48.13 Found x0:(P0 b)
% 47.87/48.13 Instantiate: b:=(fun (b0:a)=> (forall (P:(a->Prop)), ((P x)->(P b0)))):(a->Prop)
% 47.87/48.13 Found (fun (x0:(P0 b))=> x0) as proof of (P0 ((eq a) x))
% 47.87/48.13 Found (fun (P0:((a->Prop)->Prop)) (x0:(P0 b))=> x0) as proof of ((P0 b)->(P0 ((eq a) x)))
% 47.87/48.13 Found (fun (P0:((a->Prop)->Prop)) (x0:(P0 b))=> x0) as proof of (P b)
% 47.87/48.13 Found x0:(P (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 47.87/48.13 Instantiate: b:=(fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))):(a->Prop)
% 47.87/48.13 Found x0 as proof of (P0 b)
% 47.87/48.13 Found eq_ref00:=(eq_ref0 ((eq a) x)):(((eq (a->Prop)) ((eq a) x)) ((eq a) x))
% 47.87/48.13 Found (eq_ref0 ((eq a) x)) as proof of (((eq (a->Prop)) ((eq a) x)) b)
% 47.87/48.13 Found ((eq_ref (a->Prop)) ((eq a) x)) as proof of (((eq (a->Prop)) ((eq a) x)) b)
% 47.87/48.13 Found ((eq_ref (a->Prop)) ((eq a) x)) as proof of (((eq (a->Prop)) ((eq a) x)) b)
% 47.87/48.13 Found ((eq_ref (a->Prop)) ((eq a) x)) as proof of (((eq (a->Prop)) ((eq a) x)) b)
% 47.87/48.13 Found x1:(P (((eq a) x) x0))
% 47.87/48.13 Instantiate: b:=(((eq a) x) x0):Prop
% 47.87/48.13 Found x1 as proof of (P0 b)
% 47.87/48.13 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 47.87/48.13 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 47.87/48.13 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 47.87/48.13 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 47.87/48.13 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 47.87/48.13 Found x1:(P (((eq a) x) x0))
% 47.87/48.13 Instantiate: b:=(((eq a) x) x0):Prop
% 47.87/48.13 Found x1 as proof of (P0 b)
% 47.87/48.13 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 47.87/48.13 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 47.87/48.13 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 47.87/48.13 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 51.97/52.20 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 51.97/52.20 Found eta_expansion_dep000:=(eta_expansion_dep00 ((eq a) x)):(((eq (a->Prop)) ((eq a) x)) (fun (x0:a)=> (((eq a) x) x0)))
% 51.97/52.20 Found (eta_expansion_dep00 ((eq a) x)) as proof of (((eq (a->Prop)) ((eq a) x)) b0)
% 51.97/52.20 Found ((eta_expansion_dep0 (fun (x1:a)=> Prop)) ((eq a) x)) as proof of (((eq (a->Prop)) ((eq a) x)) b0)
% 51.97/52.20 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) ((eq a) x)) as proof of (((eq (a->Prop)) ((eq a) x)) b0)
% 51.97/52.20 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) ((eq a) x)) as proof of (((eq (a->Prop)) ((eq a) x)) b0)
% 51.97/52.20 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) ((eq a) x)) as proof of (((eq (a->Prop)) ((eq a) x)) b0)
% 51.97/52.20 Found eta_expansion000:=(eta_expansion00 b0):(((eq (a->Prop)) b0) (fun (x:a)=> (b0 x)))
% 51.97/52.20 Found (eta_expansion00 b0) as proof of (((eq (a->Prop)) b0) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 51.97/52.20 Found ((eta_expansion0 Prop) b0) as proof of (((eq (a->Prop)) b0) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 51.97/52.20 Found (((eta_expansion a) Prop) b0) as proof of (((eq (a->Prop)) b0) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 51.97/52.20 Found (((eta_expansion a) Prop) b0) as proof of (((eq (a->Prop)) b0) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 51.97/52.20 Found (((eta_expansion a) Prop) b0) as proof of (((eq (a->Prop)) b0) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 51.97/52.20 Found eta_expansion000:=(eta_expansion00 b):(((eq (a->Prop)) b) (fun (x:a)=> (b x)))
% 51.97/52.20 Found (eta_expansion00 b) as proof of (((eq (a->Prop)) b) (fun (Xy:a)=> (((eq a) x) Xy)))
% 51.97/52.20 Found ((eta_expansion0 Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xy:a)=> (((eq a) x) Xy)))
% 51.97/52.20 Found (((eta_expansion a) Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xy:a)=> (((eq a) x) Xy)))
% 51.97/52.20 Found (((eta_expansion a) Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xy:a)=> (((eq a) x) Xy)))
% 51.97/52.20 Found (((eta_expansion a) Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xy:a)=> (((eq a) x) Xy)))
% 51.97/52.20 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))):(((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) (fun (x0:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))))
% 51.97/52.20 Found (eta_expansion_dep00 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 51.97/52.20 Found ((eta_expansion_dep0 (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 51.97/52.20 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 51.97/52.20 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 51.97/52.20 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 51.97/52.20 Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq (a->Prop)) b) (fun (x:a)=> (b x)))
% 51.97/52.20 Found (eta_expansion_dep00 b) as proof of (((eq (a->Prop)) b) (fun (Xy:a)=> (((eq a) x) Xy)))
% 51.97/52.20 Found ((eta_expansion_dep0 (fun (x1:a)=> Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xy:a)=> (((eq a) x) Xy)))
% 52.95/53.18 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xy:a)=> (((eq a) x) Xy)))
% 52.95/53.18 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xy:a)=> (((eq a) x) Xy)))
% 52.95/53.18 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xy:a)=> (((eq a) x) Xy)))
% 52.95/53.18 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))):(((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) (fun (x0:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))))
% 52.95/53.18 Found (eta_expansion_dep00 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 52.95/53.18 Found ((eta_expansion_dep0 (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 52.95/53.18 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 52.95/53.18 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 52.95/53.18 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 52.95/53.18 Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq (a->Prop)) b) (fun (x:a)=> (b x)))
% 52.95/53.18 Found (eta_expansion_dep00 b) as proof of (((eq (a->Prop)) b) (fun (Xy:a)=> (((eq a) x) Xy)))
% 52.95/53.18 Found ((eta_expansion_dep0 (fun (x1:a)=> Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xy:a)=> (((eq a) x) Xy)))
% 52.95/53.18 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xy:a)=> (((eq a) x) Xy)))
% 52.95/53.18 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xy:a)=> (((eq a) x) Xy)))
% 52.95/53.18 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xy:a)=> (((eq a) x) Xy)))
% 52.95/53.18 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))):(((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) (fun (x0:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))))
% 52.95/53.18 Found (eta_expansion_dep00 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 52.95/53.18 Found ((eta_expansion_dep0 (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 52.95/53.18 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 52.95/53.18 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 52.95/53.18 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 52.95/53.18 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))->(P (fun (x0:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))))
% 54.35/54.61 Found (eta_expansion_dep000 P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 54.35/54.61 Found ((eta_expansion_dep00 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 54.35/54.61 Found (((eta_expansion_dep0 (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 54.35/54.61 Found ((((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 54.35/54.61 Found ((((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 54.35/54.61 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))):(((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) (fun (x0:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))))
% 54.35/54.61 Found (eta_expansion_dep00 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 54.35/54.61 Found ((eta_expansion_dep0 (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 54.35/54.61 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 54.35/54.61 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 54.35/54.61 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 54.35/54.61 Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq (a->Prop)) b) (fun (x:a)=> (b x)))
% 54.35/54.61 Found (eta_expansion_dep00 b) as proof of (((eq (a->Prop)) b) (fun (Xy:a)=> (((eq a) x) Xy)))
% 54.35/54.61 Found ((eta_expansion_dep0 (fun (x1:a)=> Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xy:a)=> (((eq a) x) Xy)))
% 54.35/54.61 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xy:a)=> (((eq a) x) Xy)))
% 54.35/54.61 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xy:a)=> (((eq a) x) Xy)))
% 54.35/54.61 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xy:a)=> (((eq a) x) Xy)))
% 54.35/54.61 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))->(P1 (fun (x0:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))))
% 54.35/54.61 Found (eta_expansion_dep000 P1) as proof of (P2 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 54.35/54.61 Found ((eta_expansion_dep00 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P1) as proof of (P2 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 54.35/54.61 Found (((eta_expansion_dep0 (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P1) as proof of (P2 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 55.09/55.30 Found ((((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P1) as proof of (P2 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 55.09/55.30 Found ((((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P1) as proof of (P2 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 55.09/55.30 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))->(P1 (fun (x0:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))))
% 55.09/55.30 Found (eta_expansion_dep000 P1) as proof of (P2 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 55.09/55.30 Found ((eta_expansion_dep00 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P1) as proof of (P2 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 55.09/55.30 Found (((eta_expansion_dep0 (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P1) as proof of (P2 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 55.09/55.30 Found ((((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P1) as proof of (P2 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 55.09/55.30 Found ((((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P1) as proof of (P2 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 55.09/55.30 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))->(P1 (fun (x0:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))))
% 55.09/55.30 Found (eta_expansion_dep000 P1) as proof of (P2 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 55.09/55.30 Found ((eta_expansion_dep00 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P1) as proof of (P2 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 55.09/55.30 Found (((eta_expansion_dep0 (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P1) as proof of (P2 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 55.09/55.30 Found ((((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P1) as proof of (P2 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 55.09/55.30 Found ((((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P1) as proof of (P2 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 55.09/55.30 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))->(P1 (fun (x0:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))))
% 55.09/55.30 Found (eta_expansion_dep000 P1) as proof of (P2 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 55.09/55.30 Found ((eta_expansion_dep00 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P1) as proof of (P2 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 55.09/55.30 Found (((eta_expansion_dep0 (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P1) as proof of (P2 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 55.09/55.30 Found ((((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P1) as proof of (P2 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 59.64/59.86 Found ((((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P1) as proof of (P2 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 59.64/59.86 Found x01:(P b)
% 59.64/59.86 Found (fun (x01:(P b))=> x01) as proof of (P b)
% 59.64/59.86 Found (fun (x01:(P b))=> x01) as proof of (P0 b)
% 59.64/59.86 Found x0:(P (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 59.64/59.86 Instantiate: f:=(fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))):(a->Prop)
% 59.64/59.86 Found x0 as proof of (P0 f)
% 59.64/59.86 Found eq_ref00:=(eq_ref0 (f x00)):(((eq Prop) (f x00)) (f x00))
% 59.64/59.86 Found (eq_ref0 (f x00)) as proof of (((eq Prop) (f x00)) (((eq a) x) x00))
% 59.64/59.86 Found ((eq_ref Prop) (f x00)) as proof of (((eq Prop) (f x00)) (((eq a) x) x00))
% 59.64/59.86 Found ((eq_ref Prop) (f x00)) as proof of (((eq Prop) (f x00)) (((eq a) x) x00))
% 59.64/59.86 Found (fun (x00:a)=> ((eq_ref Prop) (f x00))) as proof of (((eq Prop) (f x00)) (((eq a) x) x00))
% 59.64/59.86 Found (fun (x00:a)=> ((eq_ref Prop) (f x00))) as proof of (forall (x0:a), (((eq Prop) (f x0)) (((eq a) x) x0)))
% 59.64/59.86 Found x0:(P (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 59.64/59.86 Instantiate: f:=(fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))):(a->Prop)
% 59.64/59.86 Found x0 as proof of (P0 f)
% 59.64/59.86 Found eq_ref00:=(eq_ref0 (f x00)):(((eq Prop) (f x00)) (f x00))
% 59.64/59.86 Found (eq_ref0 (f x00)) as proof of (((eq Prop) (f x00)) (((eq a) x) x00))
% 59.64/59.86 Found ((eq_ref Prop) (f x00)) as proof of (((eq Prop) (f x00)) (((eq a) x) x00))
% 59.64/59.86 Found ((eq_ref Prop) (f x00)) as proof of (((eq Prop) (f x00)) (((eq a) x) x00))
% 59.64/59.86 Found (fun (x00:a)=> ((eq_ref Prop) (f x00))) as proof of (((eq Prop) (f x00)) (((eq a) x) x00))
% 59.64/59.86 Found (fun (x00:a)=> ((eq_ref Prop) (f x00))) as proof of (forall (x0:a), (((eq Prop) (f x0)) (((eq a) x) x0)))
% 59.64/59.86 Found eq_ref000:=(eq_ref00 P1):((P1 (((eq a) x) x0))->(P1 (((eq a) x) x0)))
% 59.64/59.86 Found (eq_ref00 P1) as proof of (P2 (((eq a) x) x0))
% 59.64/59.86 Found ((eq_ref0 (((eq a) x) x0)) P1) as proof of (P2 (((eq a) x) x0))
% 59.64/59.86 Found (((eq_ref Prop) (((eq a) x) x0)) P1) as proof of (P2 (((eq a) x) x0))
% 59.64/59.86 Found (((eq_ref Prop) (((eq a) x) x0)) P1) as proof of (P2 (((eq a) x) x0))
% 59.64/59.86 Found eq_ref000:=(eq_ref00 P1):((P1 (((eq a) x) x0))->(P1 (((eq a) x) x0)))
% 59.64/59.86 Found (eq_ref00 P1) as proof of (P2 (((eq a) x) x0))
% 59.64/59.86 Found ((eq_ref0 (((eq a) x) x0)) P1) as proof of (P2 (((eq a) x) x0))
% 59.64/59.86 Found (((eq_ref Prop) (((eq a) x) x0)) P1) as proof of (P2 (((eq a) x) x0))
% 59.64/59.86 Found (((eq_ref Prop) (((eq a) x) x0)) P1) as proof of (P2 (((eq a) x) x0))
% 59.64/59.86 Found eq_ref000:=(eq_ref00 P1):((P1 (((eq a) x) x0))->(P1 (((eq a) x) x0)))
% 59.64/59.86 Found (eq_ref00 P1) as proof of (P2 (((eq a) x) x0))
% 59.64/59.86 Found ((eq_ref0 (((eq a) x) x0)) P1) as proof of (P2 (((eq a) x) x0))
% 59.64/59.86 Found (((eq_ref Prop) (((eq a) x) x0)) P1) as proof of (P2 (((eq a) x) x0))
% 59.64/59.86 Found (((eq_ref Prop) (((eq a) x) x0)) P1) as proof of (P2 (((eq a) x) x0))
% 59.64/59.86 Found eq_ref000:=(eq_ref00 P1):((P1 (((eq a) x) x0))->(P1 (((eq a) x) x0)))
% 59.64/59.86 Found (eq_ref00 P1) as proof of (P2 (((eq a) x) x0))
% 59.64/59.86 Found ((eq_ref0 (((eq a) x) x0)) P1) as proof of (P2 (((eq a) x) x0))
% 59.64/59.86 Found (((eq_ref Prop) (((eq a) x) x0)) P1) as proof of (P2 (((eq a) x) x0))
% 59.64/59.86 Found (((eq_ref Prop) (((eq a) x) x0)) P1) as proof of (P2 (((eq a) x) x0))
% 59.64/59.86 Found x1:(P (((eq a) x) x0))
% 59.64/59.86 Instantiate: b:=(((eq a) x) x0):Prop
% 59.64/59.86 Found x1 as proof of (P0 b)
% 59.64/59.86 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 59.64/59.86 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 59.64/59.86 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 59.64/59.86 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 61.09/61.33 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 61.09/61.33 Found x1:(P (((eq a) x) x0))
% 61.09/61.33 Instantiate: b:=(((eq a) x) x0):Prop
% 61.09/61.33 Found x1 as proof of (P0 b)
% 61.09/61.33 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 61.09/61.33 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 61.09/61.33 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 61.09/61.33 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 61.09/61.33 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 61.09/61.33 Found eq_ref00:=(eq_ref0 (((eq a) x) x0)):(((eq Prop) (((eq a) x) x0)) (((eq a) x) x0))
% 61.09/61.33 Found (eq_ref0 (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 61.09/61.33 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 61.09/61.33 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 61.09/61.33 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 61.09/61.33 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 61.09/61.33 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 61.09/61.33 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 61.09/61.33 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 61.09/61.33 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 61.09/61.33 Found eq_ref00:=(eq_ref0 (((eq a) x) x0)):(((eq Prop) (((eq a) x) x0)) (((eq a) x) x0))
% 61.09/61.33 Found (eq_ref0 (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 61.09/61.33 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 61.09/61.33 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 61.09/61.33 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 61.09/61.33 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 61.09/61.33 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 61.09/61.33 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 61.09/61.33 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 61.09/61.33 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 61.09/61.33 Found eq_ref00:=(eq_ref0 (((eq a) x) x0)):(((eq Prop) (((eq a) x) x0)) (((eq a) x) x0))
% 61.09/61.33 Found (eq_ref0 (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 61.09/61.33 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 61.09/61.33 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 61.09/61.33 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 61.09/61.33 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 61.09/61.33 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 61.09/61.33 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 61.09/61.33 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 61.09/61.33 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 61.09/61.33 Found eq_ref00:=(eq_ref0 (((eq a) x) x0)):(((eq Prop) (((eq a) x) x0)) (((eq a) x) x0))
% 61.09/61.33 Found (eq_ref0 (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 62.17/62.41 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 62.17/62.41 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 62.17/62.41 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 62.17/62.41 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 62.17/62.41 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 62.17/62.41 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 62.17/62.41 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 62.17/62.41 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 62.17/62.41 Found eq_ref00:=(eq_ref0 (((eq a) x) x0)):(((eq Prop) (((eq a) x) x0)) (((eq a) x) x0))
% 62.17/62.41 Found (eq_ref0 (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 62.17/62.41 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 62.17/62.41 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 62.17/62.41 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 62.17/62.41 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 62.17/62.41 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 62.17/62.41 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 62.17/62.41 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 62.17/62.41 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 62.17/62.41 Found eq_ref00:=(eq_ref0 (((eq a) x) x0)):(((eq Prop) (((eq a) x) x0)) (((eq a) x) x0))
% 62.17/62.41 Found (eq_ref0 (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 62.17/62.41 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 62.17/62.41 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 62.17/62.41 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 62.17/62.41 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 62.17/62.41 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 62.17/62.41 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 62.17/62.41 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 62.17/62.41 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 62.17/62.41 Found x01:(P b)
% 62.17/62.41 Found (fun (x01:(P b))=> x01) as proof of (P b)
% 62.17/62.41 Found (fun (x01:(P b))=> x01) as proof of (P0 b)
% 62.17/62.41 Found x01:(P b)
% 62.17/62.41 Found (fun (x01:(P b))=> x01) as proof of (P b)
% 62.17/62.41 Found (fun (x01:(P b))=> x01) as proof of (P0 b)
% 62.17/62.41 Found eq_ref000:=(eq_ref00 P):((P (((eq a) x) x0))->(P (((eq a) x) x0)))
% 62.17/62.41 Found (eq_ref00 P) as proof of (P0 (((eq a) x) x0))
% 62.17/62.41 Found ((eq_ref0 (((eq a) x) x0)) P) as proof of (P0 (((eq a) x) x0))
% 62.17/62.41 Found (((eq_ref Prop) (((eq a) x) x0)) P) as proof of (P0 (((eq a) x) x0))
% 62.17/62.41 Found (((eq_ref Prop) (((eq a) x) x0)) P) as proof of (P0 (((eq a) x) x0))
% 62.17/62.41 Found eq_ref00:=(eq_ref0 (((eq a) x) x0)):(((eq Prop) (((eq a) x) x0)) (((eq a) x) x0))
% 62.17/62.41 Found (eq_ref0 (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 62.17/62.41 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 62.17/62.41 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 62.17/62.41 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 62.17/62.41 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 62.17/62.41 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 62.17/62.41 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 62.17/62.41 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 62.17/62.41 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 67.14/67.38 Found eq_ref000:=(eq_ref00 P):((P (((eq a) x) x0))->(P (((eq a) x) x0)))
% 67.14/67.38 Found (eq_ref00 P) as proof of (P0 (((eq a) x) x0))
% 67.14/67.38 Found ((eq_ref0 (((eq a) x) x0)) P) as proof of (P0 (((eq a) x) x0))
% 67.14/67.38 Found (((eq_ref Prop) (((eq a) x) x0)) P) as proof of (P0 (((eq a) x) x0))
% 67.14/67.38 Found (((eq_ref Prop) (((eq a) x) x0)) P) as proof of (P0 (((eq a) x) x0))
% 67.14/67.38 Found eq_ref00:=(eq_ref0 (((eq a) x) x0)):(((eq Prop) (((eq a) x) x0)) (((eq a) x) x0))
% 67.14/67.38 Found (eq_ref0 (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 67.14/67.38 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 67.14/67.38 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 67.14/67.38 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 67.14/67.38 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 67.14/67.38 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 67.14/67.38 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 67.14/67.38 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 67.14/67.38 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 67.14/67.38 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))):(((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) (fun (x0:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))))
% 67.14/67.38 Found (eta_expansion_dep00 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 67.14/67.38 Found ((eta_expansion_dep0 (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 67.14/67.38 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 67.14/67.38 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 67.14/67.38 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 67.14/67.38 Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq (a->Prop)) b) (fun (x:a)=> (b x)))
% 67.14/67.38 Found (eta_expansion_dep00 b) as proof of (((eq (a->Prop)) b) ((eq a) x))
% 67.14/67.38 Found ((eta_expansion_dep0 (fun (x1:a)=> Prop)) b) as proof of (((eq (a->Prop)) b) ((eq a) x))
% 67.14/67.38 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) b) as proof of (((eq (a->Prop)) b) ((eq a) x))
% 67.14/67.38 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) b) as proof of (((eq (a->Prop)) b) ((eq a) x))
% 67.14/67.38 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) b) as proof of (((eq (a->Prop)) b) ((eq a) x))
% 67.14/67.38 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))->(P (fun (x0:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))))
% 67.14/67.38 Found (eta_expansion_dep000 P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 67.14/67.38 Found ((eta_expansion_dep00 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 67.14/67.38 Found (((eta_expansion_dep0 (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 67.65/67.88 Found ((((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 67.65/67.88 Found ((((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 67.65/67.88 Found eta_expansion000:=(eta_expansion00 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))):(((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) (fun (x0:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))))
% 67.65/67.88 Found (eta_expansion00 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 67.65/67.88 Found ((eta_expansion0 Prop) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 67.65/67.88 Found (((eta_expansion a) Prop) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 67.65/67.88 Found (((eta_expansion a) Prop) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 67.65/67.88 Found (((eta_expansion a) Prop) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 67.65/67.88 Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq (a->Prop)) b) (fun (x:a)=> (b x)))
% 67.65/67.88 Found (eta_expansion_dep00 b) as proof of (((eq (a->Prop)) b) ((eq a) x))
% 67.65/67.88 Found ((eta_expansion_dep0 (fun (x1:a)=> Prop)) b) as proof of (((eq (a->Prop)) b) ((eq a) x))
% 67.65/67.88 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) b) as proof of (((eq (a->Prop)) b) ((eq a) x))
% 67.65/67.88 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) b) as proof of (((eq (a->Prop)) b) ((eq a) x))
% 67.65/67.88 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) b) as proof of (((eq (a->Prop)) b) ((eq a) x))
% 67.65/67.88 Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq (a->Prop)) b) (fun (x:a)=> (b x)))
% 67.65/67.88 Found (eta_expansion_dep00 b) as proof of (((eq (a->Prop)) b) ((eq a) x))
% 67.65/67.88 Found ((eta_expansion_dep0 (fun (x1:a)=> Prop)) b) as proof of (((eq (a->Prop)) b) ((eq a) x))
% 67.65/67.88 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) b) as proof of (((eq (a->Prop)) b) ((eq a) x))
% 67.65/67.88 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) b) as proof of (((eq (a->Prop)) b) ((eq a) x))
% 67.65/67.88 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) b) as proof of (((eq (a->Prop)) b) ((eq a) x))
% 67.65/67.88 Found eq_ref00:=(eq_ref0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))):(((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 67.65/67.88 Found (eq_ref0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 67.65/67.88 Found ((eq_ref (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 67.65/67.88 Found ((eq_ref (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 67.65/67.88 Found ((eq_ref (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 69.78/70.01 Found eta_expansion000:=(eta_expansion00 b):(((eq (a->Prop)) b) (fun (x:a)=> (b x)))
% 69.78/70.01 Found (eta_expansion00 b) as proof of (((eq (a->Prop)) b) ((eq a) x))
% 69.78/70.01 Found ((eta_expansion0 Prop) b) as proof of (((eq (a->Prop)) b) ((eq a) x))
% 69.78/70.01 Found (((eta_expansion a) Prop) b) as proof of (((eq (a->Prop)) b) ((eq a) x))
% 69.78/70.01 Found (((eta_expansion a) Prop) b) as proof of (((eq (a->Prop)) b) ((eq a) x))
% 69.78/70.01 Found (((eta_expansion a) Prop) b) as proof of (((eq (a->Prop)) b) ((eq a) x))
% 69.78/70.01 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))):(((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) (fun (x0:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))))
% 69.78/70.01 Found (eta_expansion_dep00 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 69.78/70.01 Found ((eta_expansion_dep0 (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 69.78/70.01 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 69.78/70.01 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 69.78/70.01 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 69.78/70.01 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))->(P1 (fun (x0:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))))
% 69.78/70.01 Found (eta_expansion_dep000 P1) as proof of (P2 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 69.78/70.01 Found ((eta_expansion_dep00 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P1) as proof of (P2 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 69.78/70.01 Found (((eta_expansion_dep0 (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P1) as proof of (P2 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 69.78/70.01 Found ((((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P1) as proof of (P2 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 69.78/70.01 Found ((((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P1) as proof of (P2 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 69.78/70.01 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))->(P1 (fun (x0:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))))
% 69.78/70.01 Found (eta_expansion_dep000 P1) as proof of (P2 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 69.78/70.01 Found ((eta_expansion_dep00 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P1) as proof of (P2 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 69.78/70.01 Found (((eta_expansion_dep0 (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P1) as proof of (P2 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 73.36/73.64 Found ((((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P1) as proof of (P2 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 73.36/73.64 Found ((((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P1) as proof of (P2 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 73.36/73.64 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))->(P1 (fun (x0:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))))
% 73.36/73.64 Found (eta_expansion_dep000 P1) as proof of (P2 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 73.36/73.64 Found ((eta_expansion_dep00 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P1) as proof of (P2 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 73.36/73.64 Found (((eta_expansion_dep0 (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P1) as proof of (P2 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 73.36/73.64 Found ((((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P1) as proof of (P2 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 73.36/73.64 Found ((((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P1) as proof of (P2 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 73.36/73.64 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))->(P1 (fun (x0:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))))
% 73.36/73.64 Found (eta_expansion_dep000 P1) as proof of (P2 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 73.36/73.64 Found ((eta_expansion_dep00 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P1) as proof of (P2 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 73.36/73.64 Found (((eta_expansion_dep0 (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P1) as proof of (P2 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 73.36/73.64 Found ((((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P1) as proof of (P2 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 73.36/73.64 Found ((((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P1) as proof of (P2 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 73.36/73.64 Found x01:(P b)
% 73.36/73.64 Found (fun (x01:(P b))=> x01) as proof of (P b)
% 73.36/73.64 Found (fun (x01:(P b))=> x01) as proof of (P0 b)
% 73.36/73.64 Found eq_ref000:=(eq_ref00 P1):((P1 (((eq a) x) x0))->(P1 (((eq a) x) x0)))
% 73.36/73.64 Found (eq_ref00 P1) as proof of (P2 (((eq a) x) x0))
% 73.36/73.64 Found ((eq_ref0 (((eq a) x) x0)) P1) as proof of (P2 (((eq a) x) x0))
% 73.36/73.64 Found (((eq_ref Prop) (((eq a) x) x0)) P1) as proof of (P2 (((eq a) x) x0))
% 73.36/73.64 Found (((eq_ref Prop) (((eq a) x) x0)) P1) as proof of (P2 (((eq a) x) x0))
% 73.36/73.64 Found eq_ref000:=(eq_ref00 P1):((P1 (((eq a) x) x0))->(P1 (((eq a) x) x0)))
% 73.36/73.64 Found (eq_ref00 P1) as proof of (P2 (((eq a) x) x0))
% 73.36/73.64 Found ((eq_ref0 (((eq a) x) x0)) P1) as proof of (P2 (((eq a) x) x0))
% 73.36/73.64 Found (((eq_ref Prop) (((eq a) x) x0)) P1) as proof of (P2 (((eq a) x) x0))
% 73.36/73.64 Found (((eq_ref Prop) (((eq a) x) x0)) P1) as proof of (P2 (((eq a) x) x0))
% 73.36/73.64 Found eq_ref000:=(eq_ref00 P1):((P1 (((eq a) x) x0))->(P1 (((eq a) x) x0)))
% 73.36/73.64 Found (eq_ref00 P1) as proof of (P2 (((eq a) x) x0))
% 73.36/73.64 Found ((eq_ref0 (((eq a) x) x0)) P1) as proof of (P2 (((eq a) x) x0))
% 73.36/73.64 Found (((eq_ref Prop) (((eq a) x) x0)) P1) as proof of (P2 (((eq a) x) x0))
% 76.63/76.85 Found (((eq_ref Prop) (((eq a) x) x0)) P1) as proof of (P2 (((eq a) x) x0))
% 76.63/76.85 Found eq_ref000:=(eq_ref00 P1):((P1 (((eq a) x) x0))->(P1 (((eq a) x) x0)))
% 76.63/76.85 Found (eq_ref00 P1) as proof of (P2 (((eq a) x) x0))
% 76.63/76.85 Found ((eq_ref0 (((eq a) x) x0)) P1) as proof of (P2 (((eq a) x) x0))
% 76.63/76.85 Found (((eq_ref Prop) (((eq a) x) x0)) P1) as proof of (P2 (((eq a) x) x0))
% 76.63/76.85 Found (((eq_ref Prop) (((eq a) x) x0)) P1) as proof of (P2 (((eq a) x) x0))
% 76.63/76.85 Found eq_ref00:=(eq_ref0 (((eq a) x) x0)):(((eq Prop) (((eq a) x) x0)) (((eq a) x) x0))
% 76.63/76.85 Found (eq_ref0 (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 76.63/76.85 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 76.63/76.85 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 76.63/76.85 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 76.63/76.85 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 76.63/76.85 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 76.63/76.85 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 76.63/76.85 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 76.63/76.85 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 76.63/76.85 Found eq_ref00:=(eq_ref0 (((eq a) x) x0)):(((eq Prop) (((eq a) x) x0)) (((eq a) x) x0))
% 76.63/76.85 Found (eq_ref0 (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 76.63/76.85 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 76.63/76.85 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 76.63/76.85 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 76.63/76.85 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 76.63/76.85 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 76.63/76.85 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 76.63/76.85 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 76.63/76.85 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 76.63/76.85 Found x01:(P b)
% 76.63/76.85 Found (fun (x01:(P b))=> x01) as proof of (P b)
% 76.63/76.85 Found (fun (x01:(P b))=> x01) as proof of (P0 b)
% 76.63/76.85 Found eq_ref00:=(eq_ref0 (((eq a) x) x0)):(((eq Prop) (((eq a) x) x0)) (((eq a) x) x0))
% 76.63/76.85 Found (eq_ref0 (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 76.63/76.85 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 76.63/76.85 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 76.63/76.85 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 76.63/76.85 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 76.63/76.85 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 76.63/76.85 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 76.63/76.85 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 76.63/76.85 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 76.63/76.85 Found x01:(P b)
% 76.63/76.85 Found (fun (x01:(P b))=> x01) as proof of (P b)
% 76.63/76.85 Found (fun (x01:(P b))=> x01) as proof of (P0 b)
% 76.63/76.85 Found eq_ref00:=(eq_ref0 (((eq a) x) x0)):(((eq Prop) (((eq a) x) x0)) (((eq a) x) x0))
% 76.63/76.85 Found (eq_ref0 (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 76.63/76.85 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 76.63/76.85 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 76.63/76.85 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 76.63/76.85 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 76.63/76.85 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 76.63/76.85 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 77.55/77.80 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 77.55/77.80 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 77.55/77.80 Found eq_ref00:=(eq_ref0 (((eq a) x) x0)):(((eq Prop) (((eq a) x) x0)) (((eq a) x) x0))
% 77.55/77.80 Found (eq_ref0 (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 77.55/77.80 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 77.55/77.80 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 77.55/77.80 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 77.55/77.80 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 77.55/77.80 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 77.55/77.80 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 77.55/77.80 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 77.55/77.80 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 77.55/77.80 Found eq_ref00:=(eq_ref0 (((eq a) x) x0)):(((eq Prop) (((eq a) x) x0)) (((eq a) x) x0))
% 77.55/77.80 Found (eq_ref0 (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 77.55/77.80 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 77.55/77.80 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 77.55/77.80 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 77.55/77.80 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 77.55/77.80 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 77.55/77.80 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 77.55/77.80 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 77.55/77.80 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 77.55/77.80 Found eq_ref000:=(eq_ref00 P):((P (((eq a) x) x0))->(P (((eq a) x) x0)))
% 77.55/77.80 Found (eq_ref00 P) as proof of (P0 (((eq a) x) x0))
% 77.55/77.80 Found ((eq_ref0 (((eq a) x) x0)) P) as proof of (P0 (((eq a) x) x0))
% 77.55/77.80 Found (((eq_ref Prop) (((eq a) x) x0)) P) as proof of (P0 (((eq a) x) x0))
% 77.55/77.80 Found (((eq_ref Prop) (((eq a) x) x0)) P) as proof of (P0 (((eq a) x) x0))
% 77.55/77.80 Found eq_ref00:=(eq_ref0 (((eq a) x) x0)):(((eq Prop) (((eq a) x) x0)) (((eq a) x) x0))
% 77.55/77.80 Found (eq_ref0 (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 77.55/77.80 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 77.55/77.80 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 77.55/77.80 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 77.55/77.80 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 77.55/77.80 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 77.55/77.80 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 77.55/77.80 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 77.55/77.80 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 77.55/77.80 Found eq_ref000:=(eq_ref00 P):((P (((eq a) x) x0))->(P (((eq a) x) x0)))
% 77.55/77.80 Found (eq_ref00 P) as proof of (P0 (((eq a) x) x0))
% 77.55/77.80 Found ((eq_ref0 (((eq a) x) x0)) P) as proof of (P0 (((eq a) x) x0))
% 77.55/77.80 Found (((eq_ref Prop) (((eq a) x) x0)) P) as proof of (P0 (((eq a) x) x0))
% 77.55/77.80 Found (((eq_ref Prop) (((eq a) x) x0)) P) as proof of (P0 (((eq a) x) x0))
% 77.55/77.80 Found eq_ref00:=(eq_ref0 (((eq a) x) x0)):(((eq Prop) (((eq a) x) x0)) (((eq a) x) x0))
% 77.55/77.80 Found (eq_ref0 (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 77.55/77.80 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 77.55/77.80 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 77.55/77.80 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 81.53/81.81 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 81.53/81.81 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 81.53/81.81 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 81.53/81.81 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 81.53/81.81 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 81.53/81.81 Found eta_expansion_dep000:=(eta_expansion_dep00 a0):(((eq (a->Prop)) a0) (fun (x:a)=> (a0 x)))
% 81.53/81.81 Found (eta_expansion_dep00 a0) as proof of (((eq (a->Prop)) a0) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))
% 81.53/81.81 Found ((eta_expansion_dep0 (fun (x3:a)=> Prop)) a0) as proof of (((eq (a->Prop)) a0) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))
% 81.53/81.81 Found (((eta_expansion_dep a) (fun (x3:a)=> Prop)) a0) as proof of (((eq (a->Prop)) a0) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))
% 81.53/81.81 Found (((eta_expansion_dep a) (fun (x3:a)=> Prop)) a0) as proof of (((eq (a->Prop)) a0) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))
% 81.53/81.81 Found (((eta_expansion_dep a) (fun (x3:a)=> Prop)) a0) as proof of (((eq (a->Prop)) a0) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))
% 81.53/81.81 Found eta_expansion000:=(eta_expansion00 a0):(((eq (a->Prop)) a0) (fun (x:a)=> (a0 x)))
% 81.53/81.81 Found (eta_expansion00 a0) as proof of (((eq (a->Prop)) a0) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))
% 81.53/81.81 Found ((eta_expansion0 Prop) a0) as proof of (((eq (a->Prop)) a0) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))
% 81.53/81.81 Found (((eta_expansion a) Prop) a0) as proof of (((eq (a->Prop)) a0) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))
% 81.53/81.81 Found (((eta_expansion a) Prop) a0) as proof of (((eq (a->Prop)) a0) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))
% 81.53/81.81 Found (((eta_expansion a) Prop) a0) as proof of (((eq (a->Prop)) a0) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))
% 81.53/81.81 Found eta_expansion_dep000:=(eta_expansion_dep00 a0):(((eq (a->Prop)) a0) (fun (x:a)=> (a0 x)))
% 81.53/81.81 Found (eta_expansion_dep00 a0) as proof of (((eq (a->Prop)) a0) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))
% 81.53/81.81 Found ((eta_expansion_dep0 (fun (x3:a)=> Prop)) a0) as proof of (((eq (a->Prop)) a0) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))
% 81.53/81.81 Found (((eta_expansion_dep a) (fun (x3:a)=> Prop)) a0) as proof of (((eq (a->Prop)) a0) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))
% 81.53/81.81 Found (((eta_expansion_dep a) (fun (x3:a)=> Prop)) a0) as proof of (((eq (a->Prop)) a0) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))
% 81.53/81.81 Found (((eta_expansion_dep a) (fun (x3:a)=> Prop)) a0) as proof of (((eq (a->Prop)) a0) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))
% 81.53/81.81 Found eta_expansion_dep000:=(eta_expansion_dep00 a0):(((eq (a->Prop)) a0) (fun (x:a)=> (a0 x)))
% 81.53/81.81 Found (eta_expansion_dep00 a0) as proof of (((eq (a->Prop)) a0) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))
% 81.53/81.81 Found ((eta_expansion_dep0 (fun (x3:a)=> Prop)) a0) as proof of (((eq (a->Prop)) a0) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))
% 81.53/81.81 Found (((eta_expansion_dep a) (fun (x3:a)=> Prop)) a0) as proof of (((eq (a->Prop)) a0) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))
% 81.53/81.81 Found (((eta_expansion_dep a) (fun (x3:a)=> Prop)) a0) as proof of (((eq (a->Prop)) a0) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))
% 81.53/81.81 Found (((eta_expansion_dep a) (fun (x3:a)=> Prop)) a0) as proof of (((eq (a->Prop)) a0) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))
% 81.53/81.81 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 81.53/81.81 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 81.53/81.81 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 86.20/86.49 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 86.20/86.49 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 86.20/86.49 Found x1:(P0 b)
% 86.20/86.49 Instantiate: b:=(forall (P:(a->Prop)), ((P x)->(P x0))):Prop
% 86.20/86.49 Found (fun (x1:(P0 b))=> x1) as proof of (P0 (((eq a) x) x0))
% 86.20/86.49 Found (fun (P0:(Prop->Prop)) (x1:(P0 b))=> x1) as proof of ((P0 b)->(P0 (((eq a) x) x0)))
% 86.20/86.49 Found (fun (P0:(Prop->Prop)) (x1:(P0 b))=> x1) as proof of (P b)
% 86.20/86.49 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 86.20/86.49 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 86.20/86.49 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 86.20/86.49 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 86.20/86.49 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 86.20/86.49 Found x1:(P0 b)
% 86.20/86.49 Instantiate: b:=(forall (P:(a->Prop)), ((P x)->(P x0))):Prop
% 86.20/86.49 Found (fun (x1:(P0 b))=> x1) as proof of (P0 (((eq a) x) x0))
% 86.20/86.49 Found (fun (P0:(Prop->Prop)) (x1:(P0 b))=> x1) as proof of ((P0 b)->(P0 (((eq a) x) x0)))
% 86.20/86.49 Found (fun (P0:(Prop->Prop)) (x1:(P0 b))=> x1) as proof of (P b)
% 86.20/86.49 Found x1:(P ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 86.20/86.49 Instantiate: b:=((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))):Prop
% 86.20/86.49 Found x1 as proof of (P0 b)
% 86.20/86.49 Found eq_ref00:=(eq_ref0 (((eq a) x) x0)):(((eq Prop) (((eq a) x) x0)) (((eq a) x) x0))
% 86.20/86.49 Found (eq_ref0 (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 86.20/86.49 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 86.20/86.49 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 86.20/86.49 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 86.20/86.49 Found x1:(P ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 86.20/86.49 Instantiate: b:=((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))):Prop
% 86.20/86.49 Found x1 as proof of (P0 b)
% 86.20/86.49 Found eq_ref00:=(eq_ref0 (((eq a) x) x0)):(((eq Prop) (((eq a) x) x0)) (((eq a) x) x0))
% 86.20/86.49 Found (eq_ref0 (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 86.20/86.49 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 86.20/86.49 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 86.20/86.49 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 86.20/86.49 Found eta_expansion000:=(eta_expansion00 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))):(((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) (fun (x0:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))))
% 86.20/86.49 Found (eta_expansion00 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b0)
% 86.20/86.49 Found ((eta_expansion0 Prop) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b0)
% 86.20/86.49 Found (((eta_expansion a) Prop) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b0)
% 95.97/96.21 Found (((eta_expansion a) Prop) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b0)
% 95.97/96.21 Found (((eta_expansion a) Prop) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b0)
% 95.97/96.21 Found eq_ref00:=(eq_ref0 b0):(((eq (a->Prop)) b0) b0)
% 95.97/96.21 Found (eq_ref0 b0) as proof of (((eq (a->Prop)) b0) b)
% 95.97/96.21 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) b)
% 95.97/96.21 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) b)
% 95.97/96.21 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) b)
% 95.97/96.21 Found eq_ref00:=(eq_ref0 (((eq a) x) x0)):(((eq Prop) (((eq a) x) x0)) (((eq a) x) x0))
% 95.97/96.21 Found (eq_ref0 (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b0)
% 95.97/96.21 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b0)
% 95.97/96.21 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b0)
% 95.97/96.21 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b0)
% 95.97/96.21 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 95.97/96.21 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 95.97/96.21 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 95.97/96.21 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 95.97/96.21 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 95.97/96.21 Found eq_ref00:=(eq_ref0 (((eq a) x) x0)):(((eq Prop) (((eq a) x) x0)) (((eq a) x) x0))
% 95.97/96.21 Found (eq_ref0 (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b0)
% 95.97/96.21 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b0)
% 95.97/96.21 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b0)
% 95.97/96.21 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b0)
% 95.97/96.21 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 95.97/96.21 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 95.97/96.21 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 95.97/96.21 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 95.97/96.21 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 95.97/96.21 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (Xy:a)=> (((eq a) x) Xy)))->(P (fun (x0:a)=> (((eq a) x) x0))))
% 95.97/96.21 Found (eta_expansion_dep000 P) as proof of (P0 (fun (Xy:a)=> (((eq a) x) Xy)))
% 95.97/96.21 Found ((eta_expansion_dep00 (fun (Xy:a)=> (((eq a) x) Xy))) P) as proof of (P0 (fun (Xy:a)=> (((eq a) x) Xy)))
% 95.97/96.21 Found (((eta_expansion_dep0 (fun (x1:a)=> Prop)) (fun (Xy:a)=> (((eq a) x) Xy))) P) as proof of (P0 (fun (Xy:a)=> (((eq a) x) Xy)))
% 95.97/96.21 Found ((((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xy:a)=> (((eq a) x) Xy))) P) as proof of (P0 (fun (Xy:a)=> (((eq a) x) Xy)))
% 95.97/96.21 Found ((((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xy:a)=> (((eq a) x) Xy))) P) as proof of (P0 (fun (Xy:a)=> (((eq a) x) Xy)))
% 95.97/96.21 Found eq_ref00:=(eq_ref0 a0):(((eq (a->Prop)) a0) a0)
% 95.97/96.21 Found (eq_ref0 a0) as proof of (((eq (a->Prop)) a0) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))
% 95.97/96.21 Found ((eq_ref (a->Prop)) a0) as proof of (((eq (a->Prop)) a0) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))
% 95.97/96.21 Found ((eq_ref (a->Prop)) a0) as proof of (((eq (a->Prop)) a0) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))
% 95.97/96.21 Found ((eq_ref (a->Prop)) a0) as proof of (((eq (a->Prop)) a0) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))
% 95.97/96.21 Found eta_expansion_dep000:=(eta_expansion_dep00 a0):(((eq (a->Prop)) a0) (fun (x:a)=> (a0 x)))
% 95.97/96.21 Found (eta_expansion_dep00 a0) as proof of (((eq (a->Prop)) a0) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))
% 102.16/102.40 Found ((eta_expansion_dep0 (fun (x3:a)=> Prop)) a0) as proof of (((eq (a->Prop)) a0) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))
% 102.16/102.40 Found (((eta_expansion_dep a) (fun (x3:a)=> Prop)) a0) as proof of (((eq (a->Prop)) a0) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))
% 102.16/102.40 Found (((eta_expansion_dep a) (fun (x3:a)=> Prop)) a0) as proof of (((eq (a->Prop)) a0) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))
% 102.16/102.40 Found (((eta_expansion_dep a) (fun (x3:a)=> Prop)) a0) as proof of (((eq (a->Prop)) a0) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))
% 102.16/102.40 Found eta_expansion000:=(eta_expansion00 a0):(((eq (a->Prop)) a0) (fun (x:a)=> (a0 x)))
% 102.16/102.40 Found (eta_expansion00 a0) as proof of (((eq (a->Prop)) a0) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))
% 102.16/102.40 Found ((eta_expansion0 Prop) a0) as proof of (((eq (a->Prop)) a0) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))
% 102.16/102.40 Found (((eta_expansion a) Prop) a0) as proof of (((eq (a->Prop)) a0) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))
% 102.16/102.40 Found (((eta_expansion a) Prop) a0) as proof of (((eq (a->Prop)) a0) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))
% 102.16/102.40 Found (((eta_expansion a) Prop) a0) as proof of (((eq (a->Prop)) a0) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))
% 102.16/102.40 Found eta_expansion000:=(eta_expansion00 a0):(((eq (a->Prop)) a0) (fun (x:a)=> (a0 x)))
% 102.16/102.40 Found (eta_expansion00 a0) as proof of (((eq (a->Prop)) a0) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))
% 102.16/102.40 Found ((eta_expansion0 Prop) a0) as proof of (((eq (a->Prop)) a0) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))
% 102.16/102.40 Found (((eta_expansion a) Prop) a0) as proof of (((eq (a->Prop)) a0) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))
% 102.16/102.40 Found (((eta_expansion a) Prop) a0) as proof of (((eq (a->Prop)) a0) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))
% 102.16/102.40 Found (((eta_expansion a) Prop) a0) as proof of (((eq (a->Prop)) a0) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))
% 102.16/102.40 Found x1:(P ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 102.16/102.40 Instantiate: b:=((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))):Prop
% 102.16/102.40 Found x1 as proof of (P0 b)
% 102.16/102.40 Found eq_ref00:=(eq_ref0 (((eq a) x) x0)):(((eq Prop) (((eq a) x) x0)) (((eq a) x) x0))
% 102.16/102.40 Found (eq_ref0 (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 102.16/102.40 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 102.16/102.40 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 102.16/102.40 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 102.16/102.40 Found x1:(P ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 102.16/102.40 Instantiate: b:=((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))):Prop
% 102.16/102.40 Found x1 as proof of (P0 b)
% 102.16/102.40 Found eq_ref00:=(eq_ref0 (((eq a) x) x0)):(((eq Prop) (((eq a) x) x0)) (((eq a) x) x0))
% 102.16/102.40 Found (eq_ref0 (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 102.16/102.40 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 102.16/102.40 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 102.16/102.40 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 102.16/102.40 Found x01:(P b)
% 102.16/102.40 Found (fun (x01:(P b))=> x01) as proof of (P b)
% 102.16/102.40 Found (fun (x01:(P b))=> x01) as proof of (P0 b)
% 102.16/102.40 Found eta_expansion0000:=(eta_expansion000 P):((P (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))->(P (fun (x0:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))))
% 102.16/102.40 Found (eta_expansion000 P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 102.16/102.40 Found ((eta_expansion00 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 102.16/102.40 Found (((eta_expansion0 Prop) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 104.21/104.45 Found ((((eta_expansion a) Prop) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 104.21/104.45 Found ((((eta_expansion a) Prop) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 104.21/104.45 Found eta_expansion0000:=(eta_expansion000 P):((P (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))->(P (fun (x0:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))))
% 104.21/104.45 Found (eta_expansion000 P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 104.21/104.45 Found ((eta_expansion00 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 104.21/104.45 Found (((eta_expansion0 Prop) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 104.21/104.45 Found ((((eta_expansion a) Prop) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 104.21/104.45 Found ((((eta_expansion a) Prop) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 104.21/104.45 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 104.21/104.45 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 104.21/104.45 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 104.21/104.45 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 104.21/104.45 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 104.21/104.45 Found x1:(P0 b)
% 104.21/104.45 Instantiate: b:=(forall (P:(a->Prop)), ((P x)->(P x0))):Prop
% 104.21/104.45 Found (fun (x1:(P0 b))=> x1) as proof of (P0 (((eq a) x) x0))
% 104.21/104.45 Found (fun (P0:(Prop->Prop)) (x1:(P0 b))=> x1) as proof of ((P0 b)->(P0 (((eq a) x) x0)))
% 104.21/104.45 Found (fun (P0:(Prop->Prop)) (x1:(P0 b))=> x1) as proof of (P b)
% 104.21/104.45 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 104.21/104.45 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 104.21/104.45 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 104.21/104.45 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 104.21/104.45 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 104.21/104.45 Found x1:(P0 b)
% 104.21/104.45 Instantiate: b:=(forall (P:(a->Prop)), ((P x)->(P x0))):Prop
% 104.21/104.45 Found (fun (x1:(P0 b))=> x1) as proof of (P0 (((eq a) x) x0))
% 104.21/104.45 Found (fun (P0:(Prop->Prop)) (x1:(P0 b))=> x1) as proof of ((P0 b)->(P0 (((eq a) x) x0)))
% 109.86/110.10 Found (fun (P0:(Prop->Prop)) (x1:(P0 b))=> x1) as proof of (P b)
% 109.86/110.10 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (Xy:a)=> (((eq a) x) Xy)))->(P (fun (x0:a)=> (((eq a) x) x0))))
% 109.86/110.10 Found (eta_expansion_dep000 P) as proof of (P0 (fun (Xy:a)=> (((eq a) x) Xy)))
% 109.86/110.10 Found ((eta_expansion_dep00 (fun (Xy:a)=> (((eq a) x) Xy))) P) as proof of (P0 (fun (Xy:a)=> (((eq a) x) Xy)))
% 109.86/110.10 Found (((eta_expansion_dep0 (fun (x1:a)=> Prop)) (fun (Xy:a)=> (((eq a) x) Xy))) P) as proof of (P0 (fun (Xy:a)=> (((eq a) x) Xy)))
% 109.86/110.10 Found ((((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xy:a)=> (((eq a) x) Xy))) P) as proof of (P0 (fun (Xy:a)=> (((eq a) x) Xy)))
% 109.86/110.10 Found ((((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xy:a)=> (((eq a) x) Xy))) P) as proof of (P0 (fun (Xy:a)=> (((eq a) x) Xy)))
% 109.86/110.10 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (Xy:a)=> (((eq a) x) Xy)))->(P (fun (x0:a)=> (((eq a) x) x0))))
% 109.86/110.10 Found (eta_expansion_dep000 P) as proof of (P0 (fun (Xy:a)=> (((eq a) x) Xy)))
% 109.86/110.10 Found ((eta_expansion_dep00 (fun (Xy:a)=> (((eq a) x) Xy))) P) as proof of (P0 (fun (Xy:a)=> (((eq a) x) Xy)))
% 109.86/110.10 Found (((eta_expansion_dep0 (fun (x1:a)=> Prop)) (fun (Xy:a)=> (((eq a) x) Xy))) P) as proof of (P0 (fun (Xy:a)=> (((eq a) x) Xy)))
% 109.86/110.10 Found ((((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xy:a)=> (((eq a) x) Xy))) P) as proof of (P0 (fun (Xy:a)=> (((eq a) x) Xy)))
% 109.86/110.10 Found ((((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xy:a)=> (((eq a) x) Xy))) P) as proof of (P0 (fun (Xy:a)=> (((eq a) x) Xy)))
% 109.86/110.10 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xy:a)=> (((eq a) x) Xy))):(((eq (a->Prop)) (fun (Xy:a)=> (((eq a) x) Xy))) (fun (x0:a)=> (((eq a) x) x0)))
% 109.86/110.10 Found (eta_expansion_dep00 (fun (Xy:a)=> (((eq a) x) Xy))) as proof of (((eq (a->Prop)) (fun (Xy:a)=> (((eq a) x) Xy))) b)
% 109.86/110.10 Found ((eta_expansion_dep0 (fun (x1:a)=> Prop)) (fun (Xy:a)=> (((eq a) x) Xy))) as proof of (((eq (a->Prop)) (fun (Xy:a)=> (((eq a) x) Xy))) b)
% 109.86/110.10 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xy:a)=> (((eq a) x) Xy))) as proof of (((eq (a->Prop)) (fun (Xy:a)=> (((eq a) x) Xy))) b)
% 109.86/110.10 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xy:a)=> (((eq a) x) Xy))) as proof of (((eq (a->Prop)) (fun (Xy:a)=> (((eq a) x) Xy))) b)
% 109.86/110.10 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xy:a)=> (((eq a) x) Xy))) as proof of (((eq (a->Prop)) (fun (Xy:a)=> (((eq a) x) Xy))) b)
% 109.86/110.10 Found eta_expansion000:=(eta_expansion00 b):(((eq (a->Prop)) b) (fun (x:a)=> (b x)))
% 109.86/110.10 Found (eta_expansion00 b) as proof of (((eq (a->Prop)) b) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 109.86/110.10 Found ((eta_expansion0 Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 109.86/110.10 Found (((eta_expansion a) Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 109.86/110.10 Found (((eta_expansion a) Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 109.86/110.10 Found (((eta_expansion a) Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 109.86/110.10 Found x1:(P ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 109.86/110.10 Instantiate: b:=((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))):Prop
% 109.86/110.10 Found x1 as proof of (P0 b)
% 109.86/110.10 Found eq_ref00:=(eq_ref0 (((eq a) x) x0)):(((eq Prop) (((eq a) x) x0)) (((eq a) x) x0))
% 109.86/110.10 Found (eq_ref0 (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 109.86/110.10 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 109.86/110.10 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 109.86/110.10 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 109.86/110.10 Found x1:(P ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 109.86/110.10 Instantiate: b:=((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))):Prop
% 109.86/110.10 Found x1 as proof of (P0 b)
% 109.86/110.10 Found eq_ref00:=(eq_ref0 (((eq a) x) x0)):(((eq Prop) (((eq a) x) x0)) (((eq a) x) x0))
% 109.86/110.10 Found (eq_ref0 (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 116.38/116.65 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 116.38/116.65 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 116.38/116.65 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 116.38/116.65 Found eta_expansion000:=(eta_expansion00 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))):(((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) (fun (x0:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))))
% 116.38/116.65 Found (eta_expansion00 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b0)
% 116.38/116.65 Found ((eta_expansion0 Prop) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b0)
% 116.38/116.65 Found (((eta_expansion a) Prop) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b0)
% 116.38/116.65 Found (((eta_expansion a) Prop) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b0)
% 116.38/116.65 Found (((eta_expansion a) Prop) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b0)
% 116.38/116.65 Found eq_ref00:=(eq_ref0 b0):(((eq (a->Prop)) b0) b0)
% 116.38/116.65 Found (eq_ref0 b0) as proof of (((eq (a->Prop)) b0) b)
% 116.38/116.65 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) b)
% 116.38/116.65 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) b)
% 116.38/116.65 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) b)
% 116.38/116.65 Found eq_ref00:=(eq_ref0 (b x0)):(((eq Prop) (b x0)) (b x0))
% 116.38/116.65 Found (eq_ref0 (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 116.38/116.65 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 116.38/116.65 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 116.38/116.65 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 116.38/116.65 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 116.38/116.65 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 116.38/116.65 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 116.38/116.65 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 116.38/116.65 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 116.38/116.65 Found eq_ref00:=(eq_ref0 (((eq a) x) x0)):(((eq Prop) (((eq a) x) x0)) (((eq a) x) x0))
% 116.38/116.65 Found (eq_ref0 (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b0)
% 116.38/116.65 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b0)
% 116.38/116.65 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b0)
% 116.38/116.65 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b0)
% 116.38/116.65 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 116.38/116.65 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 116.38/116.65 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 116.38/116.65 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 116.38/116.65 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 116.38/116.65 Found eq_ref00:=(eq_ref0 (((eq a) x) x0)):(((eq Prop) (((eq a) x) x0)) (((eq a) x) x0))
% 116.38/116.65 Found (eq_ref0 (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b0)
% 116.38/116.65 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b0)
% 116.38/116.65 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b0)
% 120.29/120.59 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b0)
% 120.29/120.59 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 120.29/120.59 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 120.29/120.59 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 120.29/120.59 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 120.29/120.59 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 120.29/120.59 Found eq_ref00:=(eq_ref0 (b x0)):(((eq Prop) (b x0)) (b x0))
% 120.29/120.59 Found (eq_ref0 (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 120.29/120.59 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 120.29/120.59 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 120.29/120.59 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 120.29/120.59 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 120.29/120.59 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 120.29/120.59 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 120.29/120.59 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 120.29/120.59 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 120.29/120.59 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P ((eq a) x))->(P (fun (x0:a)=> (((eq a) x) x0))))
% 120.29/120.59 Found (eta_expansion_dep000 P) as proof of (P0 ((eq a) x))
% 120.29/120.59 Found ((eta_expansion_dep00 ((eq a) x)) P) as proof of (P0 ((eq a) x))
% 120.29/120.59 Found (((eta_expansion_dep0 (fun (x1:a)=> Prop)) ((eq a) x)) P) as proof of (P0 ((eq a) x))
% 120.29/120.59 Found ((((eta_expansion_dep a) (fun (x1:a)=> Prop)) ((eq a) x)) P) as proof of (P0 ((eq a) x))
% 120.29/120.59 Found ((((eta_expansion_dep a) (fun (x1:a)=> Prop)) ((eq a) x)) P) as proof of (P0 ((eq a) x))
% 120.29/120.59 Found eq_ref000:=(eq_ref00 P1):((P1 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))->(P1 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))))
% 120.29/120.59 Found (eq_ref00 P1) as proof of (P2 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 120.29/120.59 Found ((eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P1) as proof of (P2 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 120.29/120.59 Found (((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P1) as proof of (P2 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 120.29/120.59 Found (((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P1) as proof of (P2 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 120.29/120.59 Found eq_ref000:=(eq_ref00 P1):((P1 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))->(P1 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))))
% 120.29/120.59 Found (eq_ref00 P1) as proof of (P2 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 120.29/120.59 Found ((eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P1) as proof of (P2 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 120.29/120.59 Found (((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P1) as proof of (P2 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 120.29/120.59 Found (((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P1) as proof of (P2 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 120.29/120.59 Found eq_ref000:=(eq_ref00 P1):((P1 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))->(P1 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))))
% 120.29/120.59 Found (eq_ref00 P1) as proof of (P2 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 120.29/120.59 Found ((eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P1) as proof of (P2 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 120.29/120.59 Found (((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P1) as proof of (P2 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 121.79/122.08 Found (((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P1) as proof of (P2 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 121.79/122.08 Found eq_ref000:=(eq_ref00 P1):((P1 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))->(P1 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))))
% 121.79/122.08 Found (eq_ref00 P1) as proof of (P2 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 121.79/122.08 Found ((eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P1) as proof of (P2 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 121.79/122.08 Found (((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P1) as proof of (P2 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 121.79/122.08 Found (((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P1) as proof of (P2 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 121.79/122.08 Found eq_ref000:=(eq_ref00 P1):((P1 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))->(P1 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))))
% 121.79/122.08 Found (eq_ref00 P1) as proof of (P2 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 121.79/122.08 Found ((eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P1) as proof of (P2 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 121.79/122.08 Found (((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P1) as proof of (P2 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 121.79/122.08 Found (((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P1) as proof of (P2 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 121.79/122.08 Found eq_ref000:=(eq_ref00 P1):((P1 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))->(P1 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))))
% 121.79/122.08 Found (eq_ref00 P1) as proof of (P2 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 121.79/122.08 Found ((eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P1) as proof of (P2 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 121.79/122.08 Found (((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P1) as proof of (P2 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 121.79/122.08 Found (((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P1) as proof of (P2 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 121.79/122.08 Found eq_ref000:=(eq_ref00 P1):((P1 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))->(P1 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))))
% 121.79/122.08 Found (eq_ref00 P1) as proof of (P2 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 121.79/122.08 Found ((eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P1) as proof of (P2 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 121.79/122.08 Found (((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P1) as proof of (P2 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 121.79/122.08 Found (((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P1) as proof of (P2 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 121.79/122.08 Found eq_ref000:=(eq_ref00 P1):((P1 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))->(P1 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))))
% 121.79/122.08 Found (eq_ref00 P1) as proof of (P2 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 121.79/122.08 Found ((eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P1) as proof of (P2 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 121.79/122.08 Found (((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P1) as proof of (P2 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 121.79/122.08 Found (((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P1) as proof of (P2 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 125.49/125.74 Found x1:(P ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 125.49/125.74 Instantiate: b:=((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))):Prop
% 125.49/125.74 Found x1 as proof of (P0 b)
% 125.49/125.74 Found eq_ref00:=(eq_ref0 (((eq a) x) x0)):(((eq Prop) (((eq a) x) x0)) (((eq a) x) x0))
% 125.49/125.74 Found (eq_ref0 (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 125.49/125.74 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 125.49/125.74 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 125.49/125.74 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 125.49/125.74 Found x1:(P ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 125.49/125.74 Instantiate: b:=((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))):Prop
% 125.49/125.74 Found x1 as proof of (P0 b)
% 125.49/125.74 Found eq_ref00:=(eq_ref0 (((eq a) x) x0)):(((eq Prop) (((eq a) x) x0)) (((eq a) x) x0))
% 125.49/125.74 Found (eq_ref0 (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 125.49/125.74 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 125.49/125.74 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 125.49/125.74 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 125.49/125.74 Found eq_ref000:=(eq_ref00 P):((P ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))->(P ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))))
% 125.49/125.74 Found (eq_ref00 P) as proof of (P0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 125.49/125.74 Found ((eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P) as proof of (P0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 125.49/125.74 Found (((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P) as proof of (P0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 125.49/125.74 Found (((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P) as proof of (P0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 125.49/125.74 Found eq_ref000:=(eq_ref00 P):((P ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))->(P ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))))
% 125.49/125.74 Found (eq_ref00 P) as proof of (P0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 125.49/125.74 Found ((eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P) as proof of (P0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 125.49/125.74 Found (((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P) as proof of (P0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 125.49/125.74 Found (((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P) as proof of (P0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 125.49/125.74 Found x01:(P b)
% 125.49/125.74 Found (fun (x01:(P b))=> x01) as proof of (P b)
% 125.49/125.74 Found (fun (x01:(P b))=> x01) as proof of (P0 b)
% 125.49/125.74 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 125.49/125.74 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 125.49/125.74 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 125.49/125.74 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 125.49/125.74 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 125.49/125.74 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 125.49/125.74 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 125.49/125.74 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 127.08/127.34 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 127.08/127.34 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 127.08/127.34 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 127.08/127.34 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 127.08/127.34 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 127.08/127.34 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 127.08/127.34 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 127.08/127.34 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 127.08/127.34 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 127.08/127.34 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 127.08/127.34 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 127.08/127.34 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 127.08/127.34 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 127.08/127.34 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 127.08/127.34 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 127.08/127.34 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 127.08/127.34 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 127.08/127.34 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 127.08/127.34 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 127.08/127.34 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 127.08/127.34 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 127.08/127.34 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 127.08/127.34 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 127.08/127.34 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 127.08/127.34 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 127.08/127.34 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 127.08/127.34 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 127.08/127.34 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 127.08/127.34 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 127.08/127.34 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 127.08/127.34 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 127.08/127.34 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 127.08/127.34 Found x01:(P b)
% 127.08/127.34 Found (fun (x01:(P b))=> x01) as proof of (P b)
% 127.08/127.34 Found (fun (x01:(P b))=> x01) as proof of (P0 b)
% 127.08/127.34 Found x01:(P b)
% 127.83/128.08 Found (fun (x01:(P b))=> x01) as proof of (P b)
% 127.83/128.08 Found (fun (x01:(P b))=> x01) as proof of (P0 b)
% 127.83/128.08 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 127.83/128.08 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 127.83/128.08 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 127.83/128.08 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 127.83/128.08 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 127.83/128.08 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 127.83/128.08 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 127.83/128.08 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 127.83/128.08 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 127.83/128.08 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 127.83/128.08 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 127.83/128.08 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 127.83/128.08 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 127.83/128.08 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 127.83/128.08 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 127.83/128.08 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 127.83/128.08 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 127.83/128.08 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 127.83/128.08 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 127.83/128.08 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 127.83/128.08 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 127.83/128.08 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 127.83/128.08 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 127.83/128.08 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 127.83/128.08 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 127.83/128.08 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 127.83/128.08 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 127.83/128.08 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 127.83/128.08 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 127.83/128.08 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 127.83/128.08 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 127.83/128.08 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 127.83/128.08 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 127.83/128.08 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 130.35/130.61 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 130.35/130.61 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 130.35/130.61 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 130.35/130.61 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 130.35/130.61 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 130.35/130.61 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 130.35/130.61 Found eq_ref000:=(eq_ref00 P):((P ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))->(P ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))))
% 130.35/130.61 Found (eq_ref00 P) as proof of (P0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 130.35/130.61 Found ((eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P) as proof of (P0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 130.35/130.61 Found (((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P) as proof of (P0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 130.35/130.61 Found (((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P) as proof of (P0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 130.35/130.61 Found eq_ref000:=(eq_ref00 P):((P ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))->(P ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))))
% 130.35/130.61 Found (eq_ref00 P) as proof of (P0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 130.35/130.61 Found ((eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P) as proof of (P0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 130.35/130.61 Found (((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P) as proof of (P0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 130.35/130.61 Found (((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P) as proof of (P0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 130.35/130.61 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 130.35/130.61 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 130.35/130.61 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 130.35/130.61 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 130.35/130.61 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 130.35/130.61 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 130.35/130.61 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 130.35/130.61 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 130.35/130.61 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 130.35/130.61 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 130.35/130.61 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 130.35/130.61 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 130.35/130.61 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 130.35/130.61 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 131.24/131.55 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 131.24/131.55 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 131.24/131.55 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 131.24/131.55 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 131.24/131.55 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 131.24/131.55 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 131.24/131.55 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 131.24/131.55 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 131.24/131.55 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 131.24/131.55 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 131.24/131.55 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 131.24/131.55 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 131.24/131.55 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 131.24/131.55 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 131.24/131.55 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 131.24/131.55 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 131.24/131.55 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 131.24/131.55 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 131.24/131.55 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 131.24/131.55 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 131.24/131.55 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 131.24/131.55 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 131.24/131.55 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 131.24/131.55 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 131.24/131.55 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 131.24/131.55 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 131.24/131.55 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 131.24/131.55 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 131.24/131.55 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 131.24/131.55 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 131.24/131.55 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 131.24/131.55 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 131.98/132.29 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 131.98/132.29 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 131.98/132.29 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 131.98/132.29 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 131.98/132.29 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 131.98/132.29 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 131.98/132.29 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 131.98/132.29 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 131.98/132.29 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 131.98/132.29 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 131.98/132.29 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 131.98/132.29 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 131.98/132.29 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 131.98/132.29 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 131.98/132.29 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 131.98/132.29 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 131.98/132.29 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 131.98/132.29 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 131.98/132.29 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 131.98/132.29 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 131.98/132.29 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 131.98/132.29 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 131.98/132.29 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 131.98/132.29 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 131.98/132.29 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 131.98/132.29 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 131.98/132.29 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 131.98/132.29 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 131.98/132.29 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 132.56/132.88 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 132.56/132.88 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 132.56/132.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 132.56/132.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 132.56/132.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 132.56/132.88 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 132.56/132.88 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 132.56/132.88 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 132.56/132.88 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 132.56/132.88 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 132.56/132.88 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 132.56/132.88 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 132.56/132.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 132.56/132.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 132.56/132.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 132.56/132.88 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 132.56/132.88 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 132.56/132.88 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 132.56/132.88 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 132.56/132.88 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 132.56/132.88 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 132.56/132.88 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 132.56/132.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 132.56/132.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 132.56/132.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 132.56/132.88 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 132.56/132.88 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 132.56/132.88 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 132.56/132.88 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 132.56/132.88 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 132.56/132.88 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 132.56/132.88 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 132.56/132.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 132.56/132.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 134.08/134.33 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 134.08/134.33 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 134.08/134.33 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 134.08/134.33 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 134.08/134.33 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 134.08/134.33 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 134.08/134.33 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 134.08/134.33 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 134.08/134.33 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 134.08/134.33 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 134.08/134.33 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 134.08/134.33 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 134.08/134.33 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 134.08/134.33 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 134.08/134.33 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 134.08/134.33 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 134.08/134.33 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 134.08/134.33 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 134.08/134.33 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 134.08/134.33 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 134.08/134.33 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 134.08/134.33 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 134.08/134.33 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 134.08/134.33 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 134.08/134.33 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 134.08/134.33 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 134.08/134.33 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 134.08/134.33 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 134.08/134.33 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 134.08/134.33 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 134.08/134.33 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 134.08/134.33 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 136.05/136.32 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 136.05/136.32 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 136.05/136.32 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 136.05/136.32 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 136.05/136.32 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 136.05/136.32 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 136.05/136.32 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 136.05/136.32 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 136.05/136.32 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 136.05/136.32 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 136.05/136.32 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 136.05/136.32 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 136.05/136.32 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 136.05/136.32 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 136.05/136.32 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 136.05/136.32 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 136.05/136.32 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 136.05/136.32 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 136.05/136.32 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 136.05/136.32 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P ((eq a) x))->(P (fun (x0:a)=> (((eq a) x) x0))))
% 136.05/136.32 Found (eta_expansion_dep000 P) as proof of (P0 ((eq a) x))
% 136.05/136.32 Found ((eta_expansion_dep00 ((eq a) x)) P) as proof of (P0 ((eq a) x))
% 136.05/136.32 Found (((eta_expansion_dep0 (fun (x1:a)=> Prop)) ((eq a) x)) P) as proof of (P0 ((eq a) x))
% 136.05/136.32 Found ((((eta_expansion_dep a) (fun (x1:a)=> Prop)) ((eq a) x)) P) as proof of (P0 ((eq a) x))
% 136.05/136.32 Found ((((eta_expansion_dep a) (fun (x1:a)=> Prop)) ((eq a) x)) P) as proof of (P0 ((eq a) x))
% 136.05/136.32 Found eta_expansion0000:=(eta_expansion000 P):((P (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))->(P (fun (x0:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))))
% 136.05/136.32 Found (eta_expansion000 P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 136.05/136.32 Found ((eta_expansion00 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 136.05/136.32 Found (((eta_expansion0 Prop) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 136.05/136.32 Found ((((eta_expansion a) Prop) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 136.05/136.32 Found ((((eta_expansion a) Prop) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 136.05/136.32 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P ((eq a) x))->(P (fun (x0:a)=> (((eq a) x) x0))))
% 139.66/139.91 Found (eta_expansion_dep000 P) as proof of (P0 ((eq a) x))
% 139.66/139.91 Found ((eta_expansion_dep00 ((eq a) x)) P) as proof of (P0 ((eq a) x))
% 139.66/139.91 Found (((eta_expansion_dep0 (fun (x1:a)=> Prop)) ((eq a) x)) P) as proof of (P0 ((eq a) x))
% 139.66/139.91 Found ((((eta_expansion_dep a) (fun (x1:a)=> Prop)) ((eq a) x)) P) as proof of (P0 ((eq a) x))
% 139.66/139.91 Found ((((eta_expansion_dep a) (fun (x1:a)=> Prop)) ((eq a) x)) P) as proof of (P0 ((eq a) x))
% 139.66/139.91 Found eta_expansion0000:=(eta_expansion000 P):((P (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))->(P (fun (x0:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))))
% 139.66/139.91 Found (eta_expansion000 P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 139.66/139.91 Found ((eta_expansion00 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 139.66/139.91 Found (((eta_expansion0 Prop) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 139.66/139.91 Found ((((eta_expansion a) Prop) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 139.66/139.91 Found ((((eta_expansion a) Prop) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 139.66/139.91 Found eta_expansion000:=(eta_expansion00 ((eq a) x)):(((eq (a->Prop)) ((eq a) x)) (fun (x0:a)=> (((eq a) x) x0)))
% 139.66/139.91 Found (eta_expansion00 ((eq a) x)) as proof of (((eq (a->Prop)) ((eq a) x)) b)
% 139.66/139.91 Found ((eta_expansion0 Prop) ((eq a) x)) as proof of (((eq (a->Prop)) ((eq a) x)) b)
% 139.66/139.91 Found (((eta_expansion a) Prop) ((eq a) x)) as proof of (((eq (a->Prop)) ((eq a) x)) b)
% 139.66/139.91 Found (((eta_expansion a) Prop) ((eq a) x)) as proof of (((eq (a->Prop)) ((eq a) x)) b)
% 139.66/139.91 Found (((eta_expansion a) Prop) ((eq a) x)) as proof of (((eq (a->Prop)) ((eq a) x)) b)
% 139.66/139.91 Found eta_expansion000:=(eta_expansion00 b):(((eq (a->Prop)) b) (fun (x:a)=> (b x)))
% 139.66/139.91 Found (eta_expansion00 b) as proof of (((eq (a->Prop)) b) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 139.66/139.91 Found ((eta_expansion0 Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 139.66/139.91 Found (((eta_expansion a) Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 139.66/139.91 Found (((eta_expansion a) Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 139.66/139.91 Found (((eta_expansion a) Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 139.66/139.91 Found eq_ref00:=(eq_ref0 b0):(((eq (a->Prop)) b0) b0)
% 139.66/139.91 Found (eq_ref0 b0) as proof of (((eq (a->Prop)) b0) (fun (Xy:a)=> (((eq a) x) Xy)))
% 139.66/139.91 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (fun (Xy:a)=> (((eq a) x) Xy)))
% 139.66/139.91 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (fun (Xy:a)=> (((eq a) x) Xy)))
% 139.66/139.91 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (fun (Xy:a)=> (((eq a) x) Xy)))
% 139.66/139.91 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))):(((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) (fun (x0:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))))
% 139.66/139.91 Found (eta_expansion_dep00 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b0)
% 139.66/139.91 Found ((eta_expansion_dep0 (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b0)
% 154.26/154.52 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b0)
% 154.26/154.52 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b0)
% 154.26/154.52 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b0)
% 154.26/154.52 Found x11:(P b)
% 154.26/154.52 Found (fun (x11:(P b))=> x11) as proof of (P b)
% 154.26/154.52 Found (fun (x11:(P b))=> x11) as proof of (P0 b)
% 154.26/154.52 Found x11:(P b)
% 154.26/154.52 Found (fun (x11:(P b))=> x11) as proof of (P b)
% 154.26/154.52 Found (fun (x11:(P b))=> x11) as proof of (P0 b)
% 154.26/154.52 Found x11:(P (b x0))
% 154.26/154.52 Found (fun (x11:(P (b x0)))=> x11) as proof of (P (b x0))
% 154.26/154.52 Found (fun (x11:(P (b x0)))=> x11) as proof of (P0 (b x0))
% 154.26/154.52 Found x11:(P (b x0))
% 154.26/154.52 Found (fun (x11:(P (b x0)))=> x11) as proof of (P (b x0))
% 154.26/154.52 Found (fun (x11:(P (b x0)))=> x11) as proof of (P0 (b x0))
% 154.26/154.52 Found eq_ref00:=(eq_ref0 (b x0)):(((eq Prop) (b x0)) (b x0))
% 154.26/154.52 Found (eq_ref0 (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 154.26/154.52 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 154.26/154.52 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 154.26/154.52 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 154.26/154.52 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 154.26/154.52 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 154.26/154.52 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 154.26/154.52 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 154.26/154.52 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 154.26/154.52 Found eq_ref00:=(eq_ref0 (b x0)):(((eq Prop) (b x0)) (b x0))
% 154.26/154.52 Found (eq_ref0 (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 154.26/154.52 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 154.26/154.52 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 154.26/154.52 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 154.26/154.52 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 154.26/154.52 Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 154.26/154.52 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 154.26/154.52 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 154.26/154.52 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 154.26/154.52 Found eq_ref000:=(eq_ref00 P1):((P1 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))->(P1 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))))
% 154.26/154.52 Found (eq_ref00 P1) as proof of (P2 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 154.26/154.52 Found ((eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P1) as proof of (P2 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 154.26/154.52 Found (((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P1) as proof of (P2 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 154.26/154.52 Found (((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P1) as proof of (P2 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 154.26/154.52 Found eq_ref000:=(eq_ref00 P1):((P1 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))->(P1 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))))
% 154.26/154.52 Found (eq_ref00 P1) as proof of (P2 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 154.26/154.52 Found ((eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P1) as proof of (P2 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 155.46/155.74 Found (((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P1) as proof of (P2 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 155.46/155.74 Found (((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P1) as proof of (P2 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 155.46/155.74 Found eq_ref000:=(eq_ref00 P1):((P1 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))->(P1 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))))
% 155.46/155.74 Found (eq_ref00 P1) as proof of (P2 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 155.46/155.74 Found ((eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P1) as proof of (P2 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 155.46/155.74 Found (((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P1) as proof of (P2 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 155.46/155.74 Found (((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P1) as proof of (P2 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 155.46/155.74 Found eq_ref000:=(eq_ref00 P1):((P1 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))->(P1 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))))
% 155.46/155.74 Found (eq_ref00 P1) as proof of (P2 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 155.46/155.74 Found ((eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P1) as proof of (P2 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 155.46/155.74 Found (((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P1) as proof of (P2 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 155.46/155.74 Found (((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P1) as proof of (P2 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 155.46/155.74 Found eq_ref000:=(eq_ref00 P1):((P1 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))->(P1 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))))
% 155.46/155.74 Found (eq_ref00 P1) as proof of (P2 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 155.46/155.74 Found ((eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P1) as proof of (P2 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 155.46/155.74 Found (((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P1) as proof of (P2 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 155.46/155.74 Found (((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P1) as proof of (P2 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 155.46/155.74 Found eq_ref000:=(eq_ref00 P1):((P1 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))->(P1 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))))
% 155.46/155.74 Found (eq_ref00 P1) as proof of (P2 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 155.46/155.74 Found ((eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P1) as proof of (P2 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 155.46/155.74 Found (((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P1) as proof of (P2 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 155.46/155.74 Found (((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P1) as proof of (P2 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 155.46/155.74 Found eq_ref000:=(eq_ref00 P1):((P1 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))->(P1 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))))
% 155.46/155.74 Found (eq_ref00 P1) as proof of (P2 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 155.46/155.74 Found ((eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P1) as proof of (P2 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 155.46/155.74 Found (((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P1) as proof of (P2 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 159.53/159.85 Found (((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P1) as proof of (P2 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 159.53/159.85 Found eq_ref000:=(eq_ref00 P1):((P1 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))->(P1 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))))
% 159.53/159.85 Found (eq_ref00 P1) as proof of (P2 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 159.53/159.85 Found ((eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P1) as proof of (P2 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 159.53/159.85 Found (((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P1) as proof of (P2 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 159.53/159.85 Found (((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P1) as proof of (P2 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 159.53/159.85 Found eq_ref000:=(eq_ref00 P):((P ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))->(P ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))))
% 159.53/159.85 Found (eq_ref00 P) as proof of (P0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 159.53/159.85 Found ((eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P) as proof of (P0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 159.53/159.85 Found (((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P) as proof of (P0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 159.53/159.85 Found (((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P) as proof of (P0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 159.53/159.85 Found eq_ref000:=(eq_ref00 P):((P ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))->(P ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))))
% 159.53/159.85 Found (eq_ref00 P) as proof of (P0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 159.53/159.85 Found ((eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P) as proof of (P0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 159.53/159.85 Found (((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P) as proof of (P0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 159.53/159.85 Found (((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P) as proof of (P0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 159.53/159.85 Found eq_ref000:=(eq_ref00 P):((P ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))->(P ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))))
% 159.53/159.85 Found (eq_ref00 P) as proof of (P0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 159.53/159.85 Found ((eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P) as proof of (P0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 159.53/159.85 Found (((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P) as proof of (P0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 159.53/159.85 Found (((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P) as proof of (P0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 159.53/159.85 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 159.53/159.85 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 159.53/159.85 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 159.53/159.85 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 160.37/160.68 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 160.37/160.68 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 160.37/160.68 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 160.37/160.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 160.37/160.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 160.37/160.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 160.37/160.68 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 160.37/160.68 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 160.37/160.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 160.37/160.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 160.37/160.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 160.37/160.68 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 160.37/160.68 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 160.37/160.68 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 160.37/160.68 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 160.37/160.68 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 160.37/160.68 Found x01:(P b)
% 160.37/160.68 Found (fun (x01:(P b))=> x01) as proof of (P b)
% 160.37/160.68 Found (fun (x01:(P b))=> x01) as proof of (P0 b)
% 160.37/160.68 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 160.37/160.68 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 160.37/160.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 160.37/160.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 160.37/160.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 160.37/160.68 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 160.37/160.68 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 160.37/160.68 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 160.37/160.68 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 160.37/160.68 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 160.37/160.68 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 160.37/160.68 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 160.37/160.68 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 160.37/160.68 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 160.37/160.68 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 161.70/162.01 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 161.70/162.01 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 161.70/162.01 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 161.70/162.01 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 161.70/162.01 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 161.70/162.01 Found x01:(P b)
% 161.70/162.01 Found (fun (x01:(P b))=> x01) as proof of (P b)
% 161.70/162.01 Found (fun (x01:(P b))=> x01) as proof of (P0 b)
% 161.70/162.01 Found eq_ref000:=(eq_ref00 P):((P ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))->(P ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))))
% 161.70/162.01 Found (eq_ref00 P) as proof of (P0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 161.70/162.01 Found ((eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P) as proof of (P0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 161.70/162.01 Found (((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P) as proof of (P0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 161.70/162.01 Found (((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P) as proof of (P0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 161.70/162.01 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 161.70/162.01 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 161.70/162.01 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 161.70/162.01 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 161.70/162.01 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 161.70/162.01 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 161.70/162.01 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 161.70/162.01 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 161.70/162.01 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 161.70/162.01 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 161.70/162.01 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 161.70/162.01 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 161.70/162.01 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 161.70/162.01 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 161.70/162.01 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 161.70/162.01 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 161.70/162.01 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 161.70/162.01 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 161.70/162.01 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 161.70/162.01 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 161.70/162.01 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 162.64/162.98 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 162.64/162.98 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 162.64/162.98 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 162.64/162.98 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 162.64/162.98 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 162.64/162.98 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 162.64/162.98 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 162.64/162.98 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 162.64/162.98 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 162.64/162.98 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 162.64/162.98 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 162.64/162.98 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 162.64/162.98 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 162.64/162.98 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 162.64/162.98 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 162.64/162.98 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 162.64/162.98 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 162.64/162.98 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 162.64/162.98 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 162.64/162.98 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 162.64/162.98 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 162.64/162.98 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 162.64/162.98 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 162.64/162.98 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 162.64/162.98 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 162.64/162.98 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 162.64/162.98 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 162.64/162.98 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 162.64/162.98 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 162.64/162.98 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 162.64/162.98 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 162.64/162.98 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 163.34/163.60 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 163.34/163.60 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 163.34/163.60 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 163.34/163.60 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 163.34/163.60 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 163.34/163.60 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 163.34/163.60 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 163.34/163.60 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 163.34/163.60 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 163.34/163.60 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 163.34/163.60 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 163.34/163.60 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 163.34/163.60 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 163.34/163.60 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 163.34/163.60 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 163.34/163.60 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 163.34/163.60 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 163.34/163.60 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 163.34/163.60 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 163.34/163.60 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 163.34/163.60 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 163.34/163.60 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 163.34/163.60 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 163.34/163.60 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 163.34/163.60 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 163.34/163.60 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 163.34/163.60 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 163.34/163.60 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 163.34/163.60 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 163.34/163.60 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 163.34/163.60 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 163.34/163.60 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 163.34/163.60 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 163.34/163.60 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 163.34/163.60 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 164.01/164.36 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 164.01/164.36 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 164.01/164.36 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 164.01/164.36 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 164.01/164.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 164.01/164.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 164.01/164.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 164.01/164.36 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 164.01/164.36 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 164.01/164.36 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 164.01/164.36 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 164.01/164.36 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 164.01/164.36 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 164.01/164.36 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 164.01/164.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 164.01/164.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 164.01/164.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 164.01/164.36 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 164.01/164.36 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 164.01/164.36 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 164.01/164.36 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 164.01/164.36 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 164.01/164.36 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 164.01/164.36 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 164.01/164.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 164.01/164.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 164.01/164.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 164.01/164.36 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 164.01/164.36 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 164.01/164.36 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 164.01/164.36 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 164.01/164.36 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 165.07/165.36 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 165.07/165.36 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 165.07/165.36 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 165.07/165.36 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 165.07/165.36 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 165.07/165.36 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 165.07/165.36 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 165.07/165.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 165.07/165.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 165.07/165.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 165.07/165.36 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 165.07/165.36 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 165.07/165.36 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 165.07/165.36 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 165.07/165.36 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 165.07/165.36 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 165.07/165.36 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 165.07/165.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 165.07/165.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 165.07/165.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 165.07/165.36 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 165.07/165.36 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 165.07/165.36 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 165.07/165.36 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 165.07/165.36 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 165.07/165.36 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 165.07/165.36 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 165.07/165.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 165.07/165.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 165.07/165.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 165.07/165.36 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 166.25/166.53 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 166.25/166.53 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 166.25/166.53 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 166.25/166.53 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 166.25/166.53 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 166.25/166.53 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 166.25/166.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 166.25/166.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 166.25/166.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 166.25/166.53 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 166.25/166.53 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 166.25/166.53 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 166.25/166.53 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 166.25/166.53 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 166.25/166.53 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 166.25/166.53 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 166.25/166.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 166.25/166.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 166.25/166.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 166.25/166.53 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 166.25/166.53 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 166.25/166.53 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 166.25/166.53 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 166.25/166.53 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 166.25/166.53 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 166.25/166.53 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 166.25/166.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 166.25/166.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 166.25/166.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 166.25/166.53 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 166.25/166.53 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 166.25/166.53 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 169.11/169.39 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 169.11/169.39 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 169.11/169.39 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 169.11/169.39 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 169.11/169.39 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 169.11/169.39 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 169.11/169.39 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 169.11/169.39 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 169.11/169.39 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 169.11/169.39 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 169.11/169.39 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 169.11/169.39 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 169.11/169.39 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 169.11/169.39 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 169.11/169.39 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 169.11/169.39 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 169.11/169.39 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq a) x) x0))
% 169.11/169.39 Found eta_expansion_dep000:=(eta_expansion_dep00 b0):(((eq (a->Prop)) b0) (fun (x:a)=> (b0 x)))
% 169.11/169.39 Found (eta_expansion_dep00 b0) as proof of (((eq (a->Prop)) b0) ((eq a) x))
% 169.11/169.39 Found ((eta_expansion_dep0 (fun (x1:a)=> Prop)) b0) as proof of (((eq (a->Prop)) b0) ((eq a) x))
% 169.11/169.39 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) b0) as proof of (((eq (a->Prop)) b0) ((eq a) x))
% 169.11/169.39 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) b0) as proof of (((eq (a->Prop)) b0) ((eq a) x))
% 169.11/169.39 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) b0) as proof of (((eq (a->Prop)) b0) ((eq a) x))
% 169.11/169.39 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))):(((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) (fun (x0:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))))
% 169.11/169.39 Found (eta_expansion_dep00 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b0)
% 169.11/169.39 Found ((eta_expansion_dep0 (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b0)
% 169.11/169.39 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b0)
% 169.11/169.39 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b0)
% 169.11/169.39 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b0)
% 169.11/169.39 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xy:a)=> (((eq a) x) Xy))):(((eq (a->Prop)) (fun (Xy:a)=> (((eq a) x) Xy))) (fun (x0:a)=> (((eq a) x) x0)))
% 185.46/185.78 Found (eta_expansion_dep00 (fun (Xy:a)=> (((eq a) x) Xy))) as proof of (((eq (a->Prop)) (fun (Xy:a)=> (((eq a) x) Xy))) b0)
% 185.46/185.78 Found ((eta_expansion_dep0 (fun (x1:a)=> Prop)) (fun (Xy:a)=> (((eq a) x) Xy))) as proof of (((eq (a->Prop)) (fun (Xy:a)=> (((eq a) x) Xy))) b0)
% 185.46/185.78 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xy:a)=> (((eq a) x) Xy))) as proof of (((eq (a->Prop)) (fun (Xy:a)=> (((eq a) x) Xy))) b0)
% 185.46/185.78 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xy:a)=> (((eq a) x) Xy))) as proof of (((eq (a->Prop)) (fun (Xy:a)=> (((eq a) x) Xy))) b0)
% 185.46/185.78 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xy:a)=> (((eq a) x) Xy))) as proof of (((eq (a->Prop)) (fun (Xy:a)=> (((eq a) x) Xy))) b0)
% 185.46/185.78 Found eta_expansion_dep000:=(eta_expansion_dep00 b0):(((eq (a->Prop)) b0) (fun (x:a)=> (b0 x)))
% 185.46/185.78 Found (eta_expansion_dep00 b0) as proof of (((eq (a->Prop)) b0) b)
% 185.46/185.78 Found ((eta_expansion_dep0 (fun (x1:a)=> Prop)) b0) as proof of (((eq (a->Prop)) b0) b)
% 185.46/185.78 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) b0) as proof of (((eq (a->Prop)) b0) b)
% 185.46/185.78 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) b0) as proof of (((eq (a->Prop)) b0) b)
% 185.46/185.78 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) b0) as proof of (((eq (a->Prop)) b0) b)
% 185.46/185.78 Found x11:(P b)
% 185.46/185.78 Found (fun (x11:(P b))=> x11) as proof of (P b)
% 185.46/185.78 Found (fun (x11:(P b))=> x11) as proof of (P0 b)
% 185.46/185.78 Found x11:(P b)
% 185.46/185.78 Found (fun (x11:(P b))=> x11) as proof of (P b)
% 185.46/185.78 Found (fun (x11:(P b))=> x11) as proof of (P0 b)
% 185.46/185.78 Found x11:(P (b x0))
% 185.46/185.78 Found (fun (x11:(P (b x0)))=> x11) as proof of (P (b x0))
% 185.46/185.78 Found (fun (x11:(P (b x0)))=> x11) as proof of (P0 (b x0))
% 185.46/185.78 Found x11:(P (b x0))
% 185.46/185.78 Found (fun (x11:(P (b x0)))=> x11) as proof of (P (b x0))
% 185.46/185.78 Found (fun (x11:(P (b x0)))=> x11) as proof of (P0 (b x0))
% 185.46/185.78 Found eq_ref00:=(eq_ref0 (((eq a) x) x0)):(((eq Prop) (((eq a) x) x0)) (((eq a) x) x0))
% 185.46/185.78 Found (eq_ref0 (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 185.46/185.78 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 185.46/185.78 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 185.46/185.78 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 185.46/185.78 Found x1:(P0 b)
% 185.46/185.78 Instantiate: b:=((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))):Prop
% 185.46/185.78 Found (fun (x1:(P0 b))=> x1) as proof of (P0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 185.46/185.78 Found (fun (P0:(Prop->Prop)) (x1:(P0 b))=> x1) as proof of ((P0 b)->(P0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))))
% 185.46/185.78 Found (fun (P0:(Prop->Prop)) (x1:(P0 b))=> x1) as proof of (P b)
% 185.46/185.78 Found eq_ref00:=(eq_ref0 (((eq a) x) x0)):(((eq Prop) (((eq a) x) x0)) (((eq a) x) x0))
% 185.46/185.78 Found (eq_ref0 (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 185.46/185.78 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 185.46/185.78 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 185.46/185.78 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 185.46/185.78 Found x1:(P0 b)
% 185.46/185.78 Instantiate: b:=((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))):Prop
% 185.46/185.78 Found (fun (x1:(P0 b))=> x1) as proof of (P0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 185.46/185.78 Found (fun (P0:(Prop->Prop)) (x1:(P0 b))=> x1) as proof of ((P0 b)->(P0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))))
% 185.46/185.78 Found (fun (P0:(Prop->Prop)) (x1:(P0 b))=> x1) as proof of (P b)
% 185.46/185.78 Found x1:(P (((eq a) x) x0))
% 185.46/185.78 Instantiate: b:=(((eq a) x) x0):Prop
% 185.46/185.78 Found x1 as proof of (P0 b)
% 185.46/185.78 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 185.46/185.78 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 185.46/185.78 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 186.84/187.12 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 186.84/187.12 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 186.84/187.12 Found x1:(P (((eq a) x) x0))
% 186.84/187.12 Instantiate: b:=(((eq a) x) x0):Prop
% 186.84/187.12 Found x1 as proof of (P0 b)
% 186.84/187.12 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 186.84/187.12 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 186.84/187.12 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 186.84/187.12 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 186.84/187.12 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 186.84/187.12 Found eta_expansion000:=(eta_expansion00 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))):(((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) (fun (x0:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))))
% 186.84/187.12 Found (eta_expansion00 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 186.84/187.12 Found ((eta_expansion0 Prop) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 186.84/187.12 Found (((eta_expansion a) Prop) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 186.84/187.12 Found (((eta_expansion a) Prop) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 186.84/187.12 Found (((eta_expansion a) Prop) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 186.84/187.12 Found eq_ref00:=(eq_ref0 b):(((eq (a->Prop)) b) b)
% 186.84/187.12 Found (eq_ref0 b) as proof of (((eq (a->Prop)) b) (fun (Xy:a)=> (((eq a) x) Xy)))
% 186.84/187.12 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xy:a)=> (((eq a) x) Xy)))
% 186.84/187.12 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xy:a)=> (((eq a) x) Xy)))
% 186.84/187.12 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xy:a)=> (((eq a) x) Xy)))
% 186.84/187.12 Found eta_expansion000:=(eta_expansion00 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))):(((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) (fun (x0:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))))
% 186.84/187.12 Found (eta_expansion00 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 186.84/187.12 Found ((eta_expansion0 Prop) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 189.74/190.06 Found (((eta_expansion a) Prop) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 189.74/190.06 Found (((eta_expansion a) Prop) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 189.74/190.06 Found (((eta_expansion a) Prop) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 189.74/190.06 Found eq_ref00:=(eq_ref0 b):(((eq (a->Prop)) b) b)
% 189.74/190.06 Found (eq_ref0 b) as proof of (((eq (a->Prop)) b) (fun (Xy:a)=> (((eq a) x) Xy)))
% 189.74/190.06 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xy:a)=> (((eq a) x) Xy)))
% 189.74/190.06 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xy:a)=> (((eq a) x) Xy)))
% 189.74/190.06 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xy:a)=> (((eq a) x) Xy)))
% 189.74/190.06 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))->(P (fun (x0:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))))
% 189.74/190.06 Found (eta_expansion_dep000 P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 189.74/190.06 Found ((eta_expansion_dep00 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 189.74/190.06 Found (((eta_expansion_dep0 (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 189.74/190.06 Found ((((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 189.74/190.06 Found ((((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 189.74/190.06 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))->(P (fun (x0:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))))
% 189.74/190.06 Found (eta_expansion_dep000 P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 189.74/190.06 Found ((eta_expansion_dep00 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 189.74/190.06 Found (((eta_expansion_dep0 (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 189.74/190.06 Found ((((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 189.74/190.06 Found ((((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 189.74/190.06 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))->(P (fun (x0:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))))
% 189.74/190.06 Found (eta_expansion_dep000 P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 189.74/190.06 Found ((eta_expansion_dep00 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 193.06/193.35 Found (((eta_expansion_dep0 (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 193.06/193.35 Found ((((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 193.06/193.35 Found ((((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 193.06/193.35 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))->(P (fun (x0:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))))
% 193.06/193.35 Found (eta_expansion_dep000 P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 193.06/193.35 Found ((eta_expansion_dep00 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 193.06/193.35 Found (((eta_expansion_dep0 (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 193.06/193.35 Found ((((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 193.06/193.35 Found ((((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 193.06/193.35 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 193.06/193.35 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b0)
% 193.06/193.35 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b0)
% 193.06/193.35 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b0)
% 193.06/193.35 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b0)
% 193.06/193.35 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 193.06/193.35 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 193.06/193.35 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 193.06/193.35 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 193.06/193.35 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 193.06/193.35 Found eq_ref000:=(eq_ref00 P):((P (fun (Xy:a)=> (((eq a) x) Xy)))->(P (fun (Xy:a)=> (((eq a) x) Xy))))
% 193.06/193.35 Found (eq_ref00 P) as proof of (P0 (fun (Xy:a)=> (((eq a) x) Xy)))
% 193.06/193.35 Found ((eq_ref0 (fun (Xy:a)=> (((eq a) x) Xy))) P) as proof of (P0 (fun (Xy:a)=> (((eq a) x) Xy)))
% 193.06/193.35 Found (((eq_ref (a->Prop)) (fun (Xy:a)=> (((eq a) x) Xy))) P) as proof of (P0 (fun (Xy:a)=> (((eq a) x) Xy)))
% 193.06/193.35 Found (((eq_ref (a->Prop)) (fun (Xy:a)=> (((eq a) x) Xy))) P) as proof of (P0 (fun (Xy:a)=> (((eq a) x) Xy)))
% 193.06/193.35 Found eta_expansion0000:=(eta_expansion000 P):((P (fun (Xy:a)=> (((eq a) x) Xy)))->(P (fun (x0:a)=> (((eq a) x) x0))))
% 193.06/193.35 Found (eta_expansion000 P) as proof of (P0 (fun (Xy:a)=> (((eq a) x) Xy)))
% 193.06/193.35 Found ((eta_expansion00 (fun (Xy:a)=> (((eq a) x) Xy))) P) as proof of (P0 (fun (Xy:a)=> (((eq a) x) Xy)))
% 193.06/193.35 Found (((eta_expansion0 Prop) (fun (Xy:a)=> (((eq a) x) Xy))) P) as proof of (P0 (fun (Xy:a)=> (((eq a) x) Xy)))
% 205.12/205.41 Found ((((eta_expansion a) Prop) (fun (Xy:a)=> (((eq a) x) Xy))) P) as proof of (P0 (fun (Xy:a)=> (((eq a) x) Xy)))
% 205.12/205.41 Found ((((eta_expansion a) Prop) (fun (Xy:a)=> (((eq a) x) Xy))) P) as proof of (P0 (fun (Xy:a)=> (((eq a) x) Xy)))
% 205.12/205.41 Found eq_ref000:=(eq_ref00 P):((P (((eq a) x) x0))->(P (((eq a) x) x0)))
% 205.12/205.41 Found (eq_ref00 P) as proof of (P0 (((eq a) x) x0))
% 205.12/205.41 Found ((eq_ref0 (((eq a) x) x0)) P) as proof of (P0 (((eq a) x) x0))
% 205.12/205.41 Found (((eq_ref Prop) (((eq a) x) x0)) P) as proof of (P0 (((eq a) x) x0))
% 205.12/205.41 Found (((eq_ref Prop) (((eq a) x) x0)) P) as proof of (P0 (((eq a) x) x0))
% 205.12/205.41 Found eq_ref000:=(eq_ref00 P):((P (((eq a) x) x0))->(P (((eq a) x) x0)))
% 205.12/205.41 Found (eq_ref00 P) as proof of (P0 (((eq a) x) x0))
% 205.12/205.41 Found ((eq_ref0 (((eq a) x) x0)) P) as proof of (P0 (((eq a) x) x0))
% 205.12/205.41 Found (((eq_ref Prop) (((eq a) x) x0)) P) as proof of (P0 (((eq a) x) x0))
% 205.12/205.41 Found (((eq_ref Prop) (((eq a) x) x0)) P) as proof of (P0 (((eq a) x) x0))
% 205.12/205.41 Found eq_ref000:=(eq_ref00 P):((P (((eq a) x) x0))->(P (((eq a) x) x0)))
% 205.12/205.41 Found (eq_ref00 P) as proof of (P0 (((eq a) x) x0))
% 205.12/205.41 Found ((eq_ref0 (((eq a) x) x0)) P) as proof of (P0 (((eq a) x) x0))
% 205.12/205.41 Found (((eq_ref Prop) (((eq a) x) x0)) P) as proof of (P0 (((eq a) x) x0))
% 205.12/205.41 Found (((eq_ref Prop) (((eq a) x) x0)) P) as proof of (P0 (((eq a) x) x0))
% 205.12/205.41 Found eq_ref000:=(eq_ref00 P):((P (((eq a) x) x0))->(P (((eq a) x) x0)))
% 205.12/205.41 Found (eq_ref00 P) as proof of (P0 (((eq a) x) x0))
% 205.12/205.41 Found ((eq_ref0 (((eq a) x) x0)) P) as proof of (P0 (((eq a) x) x0))
% 205.12/205.41 Found (((eq_ref Prop) (((eq a) x) x0)) P) as proof of (P0 (((eq a) x) x0))
% 205.12/205.41 Found (((eq_ref Prop) (((eq a) x) x0)) P) as proof of (P0 (((eq a) x) x0))
% 205.12/205.41 Found eq_ref000:=(eq_ref00 P):((P ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))->(P ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))))
% 205.12/205.41 Found (eq_ref00 P) as proof of (P0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 205.12/205.41 Found ((eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P) as proof of (P0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 205.12/205.41 Found (((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P) as proof of (P0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 205.12/205.41 Found (((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P) as proof of (P0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 205.12/205.41 Found eta_expansion_dep000:=(eta_expansion_dep00 ((eq a) x)):(((eq (a->Prop)) ((eq a) x)) (fun (x0:a)=> (((eq a) x) x0)))
% 205.12/205.41 Found (eta_expansion_dep00 ((eq a) x)) as proof of (((eq (a->Prop)) ((eq a) x)) b0)
% 205.12/205.41 Found ((eta_expansion_dep0 (fun (x1:a)=> Prop)) ((eq a) x)) as proof of (((eq (a->Prop)) ((eq a) x)) b0)
% 205.12/205.41 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) ((eq a) x)) as proof of (((eq (a->Prop)) ((eq a) x)) b0)
% 205.12/205.41 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) ((eq a) x)) as proof of (((eq (a->Prop)) ((eq a) x)) b0)
% 205.12/205.41 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) ((eq a) x)) as proof of (((eq (a->Prop)) ((eq a) x)) b0)
% 205.12/205.41 Found eq_ref00:=(eq_ref0 b0):(((eq (a->Prop)) b0) b0)
% 205.12/205.41 Found (eq_ref0 b0) as proof of (((eq (a->Prop)) b0) b)
% 205.12/205.41 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) b)
% 205.12/205.41 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) b)
% 205.12/205.41 Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) b)
% 205.12/205.41 Found eq_ref00:=(eq_ref0 (((eq a) x) x0)):(((eq Prop) (((eq a) x) x0)) (((eq a) x) x0))
% 205.12/205.41 Found (eq_ref0 (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 205.12/205.41 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 205.12/205.41 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 205.12/205.41 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 205.12/205.41 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 205.12/205.41 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 205.12/205.41 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 205.12/205.41 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 207.15/207.47 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 207.15/207.47 Found eq_ref00:=(eq_ref0 (((eq a) x) x0)):(((eq Prop) (((eq a) x) x0)) (((eq a) x) x0))
% 207.15/207.47 Found (eq_ref0 (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 207.15/207.47 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 207.15/207.47 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 207.15/207.47 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 207.15/207.47 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 207.15/207.47 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 207.15/207.47 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 207.15/207.47 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 207.15/207.47 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 207.15/207.47 Found eq_ref00:=(eq_ref0 (((eq a) x) x0)):(((eq Prop) (((eq a) x) x0)) (((eq a) x) x0))
% 207.15/207.47 Found (eq_ref0 (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 207.15/207.47 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 207.15/207.47 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 207.15/207.47 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 207.15/207.47 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 207.15/207.47 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 207.15/207.47 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 207.15/207.47 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 207.15/207.47 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 207.15/207.47 Found eq_ref00:=(eq_ref0 (((eq a) x) x0)):(((eq Prop) (((eq a) x) x0)) (((eq a) x) x0))
% 207.15/207.47 Found (eq_ref0 (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 207.15/207.47 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 207.15/207.47 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 207.15/207.47 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 207.15/207.47 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 207.15/207.47 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 207.15/207.47 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 207.15/207.47 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 207.15/207.47 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 207.15/207.47 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 207.15/207.47 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b0)
% 207.15/207.47 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b0)
% 207.15/207.47 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b0)
% 207.15/207.47 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b0)
% 207.15/207.47 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 207.15/207.47 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 207.15/207.47 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 207.15/207.47 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 220.31/220.61 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 220.31/220.61 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 220.31/220.61 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b0)
% 220.31/220.61 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b0)
% 220.31/220.61 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b0)
% 220.31/220.61 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b0)
% 220.31/220.61 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 220.31/220.61 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 220.31/220.61 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 220.31/220.61 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 220.31/220.61 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 220.31/220.61 Found eq_ref00:=(eq_ref0 (((eq a) x) x0)):(((eq Prop) (((eq a) x) x0)) (((eq a) x) x0))
% 220.31/220.61 Found (eq_ref0 (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 220.31/220.61 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 220.31/220.61 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 220.31/220.61 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 220.31/220.61 Found x1:(P0 b)
% 220.31/220.61 Instantiate: b:=((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))):Prop
% 220.31/220.61 Found (fun (x1:(P0 b))=> x1) as proof of (P0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 220.31/220.61 Found (fun (P0:(Prop->Prop)) (x1:(P0 b))=> x1) as proof of ((P0 b)->(P0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))))
% 220.31/220.61 Found (fun (P0:(Prop->Prop)) (x1:(P0 b))=> x1) as proof of (P b)
% 220.31/220.61 Found eq_ref00:=(eq_ref0 (((eq a) x) x0)):(((eq Prop) (((eq a) x) x0)) (((eq a) x) x0))
% 220.31/220.61 Found (eq_ref0 (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 220.31/220.61 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 220.31/220.61 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 220.31/220.61 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 220.31/220.61 Found x1:(P0 b)
% 220.31/220.61 Instantiate: b:=((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))):Prop
% 220.31/220.61 Found (fun (x1:(P0 b))=> x1) as proof of (P0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 220.31/220.61 Found (fun (P0:(Prop->Prop)) (x1:(P0 b))=> x1) as proof of ((P0 b)->(P0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))))
% 220.31/220.61 Found (fun (P0:(Prop->Prop)) (x1:(P0 b))=> x1) as proof of (P b)
% 220.31/220.61 Found eta_expansion000:=(eta_expansion00 b):(((eq (a->Prop)) b) (fun (x:a)=> (b x)))
% 220.31/220.61 Found (eta_expansion00 b) as proof of (((eq (a->Prop)) b) ((eq a) x))
% 220.31/220.61 Found ((eta_expansion0 Prop) b) as proof of (((eq (a->Prop)) b) ((eq a) x))
% 220.31/220.61 Found (((eta_expansion a) Prop) b) as proof of (((eq (a->Prop)) b) ((eq a) x))
% 220.31/220.61 Found (((eta_expansion a) Prop) b) as proof of (((eq (a->Prop)) b) ((eq a) x))
% 220.31/220.61 Found (((eta_expansion a) Prop) b) as proof of (((eq (a->Prop)) b) ((eq a) x))
% 220.31/220.61 Found eta_expansion000:=(eta_expansion00 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))):(((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) (fun (x0:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))))
% 220.31/220.61 Found (eta_expansion00 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 220.31/220.61 Found ((eta_expansion0 Prop) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 222.72/223.06 Found (((eta_expansion a) Prop) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 222.72/223.06 Found (((eta_expansion a) Prop) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 222.72/223.06 Found (((eta_expansion a) Prop) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 222.72/223.06 Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq (a->Prop)) b) (fun (x:a)=> (b x)))
% 222.72/223.06 Found (eta_expansion_dep00 b) as proof of (((eq (a->Prop)) b) ((eq a) x))
% 222.72/223.06 Found ((eta_expansion_dep0 (fun (x1:a)=> Prop)) b) as proof of (((eq (a->Prop)) b) ((eq a) x))
% 222.72/223.06 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) b) as proof of (((eq (a->Prop)) b) ((eq a) x))
% 222.72/223.06 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) b) as proof of (((eq (a->Prop)) b) ((eq a) x))
% 222.72/223.06 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) b) as proof of (((eq (a->Prop)) b) ((eq a) x))
% 222.72/223.06 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))):(((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) (fun (x0:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))))
% 222.72/223.06 Found (eta_expansion_dep00 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 222.72/223.06 Found ((eta_expansion_dep0 (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 222.72/223.06 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 222.72/223.06 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 222.72/223.06 Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) as proof of (((eq (a->Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) b)
% 222.72/223.06 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))->(P (fun (x0:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))))
% 222.72/223.06 Found (eta_expansion_dep000 P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 222.72/223.06 Found ((eta_expansion_dep00 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 222.72/223.06 Found (((eta_expansion_dep0 (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 222.72/223.06 Found ((((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 222.72/223.06 Found ((((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 222.72/223.06 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))->(P (fun (x0:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))))
% 224.73/225.10 Found (eta_expansion_dep000 P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 224.73/225.10 Found ((eta_expansion_dep00 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 224.73/225.10 Found (((eta_expansion_dep0 (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 224.73/225.10 Found ((((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 224.73/225.10 Found ((((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 224.73/225.10 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))->(P (fun (x0:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))))
% 224.73/225.10 Found (eta_expansion_dep000 P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 224.73/225.10 Found ((eta_expansion_dep00 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 224.73/225.10 Found (((eta_expansion_dep0 (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 224.73/225.10 Found ((((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 224.73/225.10 Found ((((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 224.73/225.10 Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))->(P (fun (x0:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))))
% 224.73/225.10 Found (eta_expansion_dep000 P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 224.73/225.10 Found ((eta_expansion_dep00 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 224.73/225.10 Found (((eta_expansion_dep0 (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 224.73/225.10 Found ((((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 224.73/225.10 Found ((((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy)))))) P) as proof of (P0 (fun (Xz:a)=> ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) Xz) Xy))))))
% 224.73/225.10 Found eq_ref000:=(eq_ref00 P):((P ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))->(P ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))))
% 224.73/225.10 Found (eq_ref00 P) as proof of (P0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 224.73/225.10 Found ((eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P) as proof of (P0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 230.39/230.73 Found (((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P) as proof of (P0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 230.39/230.73 Found (((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P) as proof of (P0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 230.39/230.73 Found eq_ref000:=(eq_ref00 P):((P ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))->(P ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))))
% 230.39/230.73 Found (eq_ref00 P) as proof of (P0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 230.39/230.73 Found ((eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P) as proof of (P0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 230.39/230.73 Found (((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P) as proof of (P0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 230.39/230.73 Found (((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P) as proof of (P0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 230.39/230.73 Found x1:(P (((eq a) x) x0))
% 230.39/230.73 Instantiate: b:=(((eq a) x) x0):Prop
% 230.39/230.73 Found x1 as proof of (P0 b)
% 230.39/230.73 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 230.39/230.73 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 230.39/230.73 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 230.39/230.73 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 230.39/230.73 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 230.39/230.73 Found x1:(P (((eq a) x) x0))
% 230.39/230.73 Instantiate: b:=(((eq a) x) x0):Prop
% 230.39/230.73 Found x1 as proof of (P0 b)
% 230.39/230.73 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 230.39/230.73 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 230.39/230.73 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 230.39/230.73 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 230.39/230.73 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b)
% 230.39/230.73 Found eq_ref000:=(eq_ref00 P):((P (((eq a) x) x0))->(P (((eq a) x) x0)))
% 230.39/230.73 Found (eq_ref00 P) as proof of (P0 (((eq a) x) x0))
% 230.39/230.73 Found ((eq_ref0 (((eq a) x) x0)) P) as proof of (P0 (((eq a) x) x0))
% 230.39/230.73 Found (((eq_ref Prop) (((eq a) x) x0)) P) as proof of (P0 (((eq a) x) x0))
% 230.39/230.73 Found (((eq_ref Prop) (((eq a) x) x0)) P) as proof of (P0 (((eq a) x) x0))
% 230.39/230.73 Found eq_ref000:=(eq_ref00 P):((P (((eq a) x) x0))->(P (((eq a) x) x0)))
% 230.39/230.73 Found (eq_ref00 P) as proof of (P0 (((eq a) x) x0))
% 230.39/230.73 Found ((eq_ref0 (((eq a) x) x0)) P) as proof of (P0 (((eq a) x) x0))
% 230.39/230.73 Found (((eq_ref Prop) (((eq a) x) x0)) P) as proof of (P0 (((eq a) x) x0))
% 230.39/230.73 Found (((eq_ref Prop) (((eq a) x) x0)) P) as proof of (P0 (((eq a) x) x0))
% 230.39/230.73 Found eq_ref000:=(eq_ref00 P):((P (((eq a) x) x0))->(P (((eq a) x) x0)))
% 230.39/230.73 Found (eq_ref00 P) as proof of (P0 (((eq a) x) x0))
% 232.07/232.47 Found ((eq_ref0 (((eq a) x) x0)) P) as proof of (P0 (((eq a) x) x0))
% 232.07/232.47 Found (((eq_ref Prop) (((eq a) x) x0)) P) as proof of (P0 (((eq a) x) x0))
% 232.07/232.47 Found (((eq_ref Prop) (((eq a) x) x0)) P) as proof of (P0 (((eq a) x) x0))
% 232.07/232.47 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 232.07/232.47 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b0)
% 232.07/232.47 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b0)
% 232.07/232.47 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b0)
% 232.07/232.47 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b0)
% 232.07/232.47 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 232.07/232.47 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x0))
% 232.07/232.47 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 232.07/232.47 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 232.07/232.47 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 232.07/232.47 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 232.07/232.47 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b0)
% 232.07/232.47 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b0)
% 232.07/232.47 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b0)
% 232.07/232.47 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b0)
% 232.07/232.47 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 232.07/232.47 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x0))
% 232.07/232.47 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 232.07/232.47 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 232.07/232.47 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 232.07/232.47 Found eq_ref000:=(eq_ref00 P):((P (((eq a) x) x0))->(P (((eq a) x) x0)))
% 232.07/232.47 Found (eq_ref00 P) as proof of (P0 (((eq a) x) x0))
% 232.07/232.47 Found ((eq_ref0 (((eq a) x) x0)) P) as proof of (P0 (((eq a) x) x0))
% 232.07/232.47 Found (((eq_ref Prop) (((eq a) x) x0)) P) as proof of (P0 (((eq a) x) x0))
% 232.07/232.47 Found (((eq_ref Prop) (((eq a) x) x0)) P) as proof of (P0 (((eq a) x) x0))
% 232.07/232.47 Found eta_expansion0000:=(eta_expansion000 P):((P ((eq a) x))->(P (fun (x0:a)=> (((eq a) x) x0))))
% 232.07/232.47 Found (eta_expansion000 P) as proof of (P0 ((eq a) x))
% 232.07/232.47 Found ((eta_expansion00 ((eq a) x)) P) as proof of (P0 ((eq a) x))
% 232.07/232.47 Found (((eta_expansion0 Prop) ((eq a) x)) P) as proof of (P0 ((eq a) x))
% 232.07/232.47 Found ((((eta_expansion a) Prop) ((eq a) x)) P) as proof of (P0 ((eq a) x))
% 232.07/232.47 Found ((((eta_expansion a) Prop) ((eq a) x)) P) as proof of (P0 ((eq a) x))
% 232.07/232.47 Found eq_ref000:=(eq_ref00 P):((P ((eq a) x))->(P ((eq a) x)))
% 232.07/232.47 Found (eq_ref00 P) as proof of (P0 ((eq a) x))
% 232.07/232.47 Found ((eq_ref0 ((eq a) x)) P) as proof of (P0 ((eq a) x))
% 232.07/232.47 Found (((eq_ref (a->Prop)) ((eq a) x)) P) as proof of (P0 ((eq a) x))
% 232.07/232.47 Found (((eq_ref (a->Prop)) ((eq a) x)) P) as proof of (P0 ((eq a) x))
% 232.07/232.47 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 232.07/232.47 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b0)
% 239.28/239.67 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b0)
% 239.28/239.67 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b0)
% 239.28/239.67 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b0)
% 239.28/239.67 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 239.28/239.67 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x0))
% 239.28/239.67 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 239.28/239.67 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 239.28/239.67 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 239.28/239.67 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 239.28/239.67 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b0)
% 239.28/239.67 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b0)
% 239.28/239.67 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b0)
% 239.28/239.67 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b0)
% 239.28/239.67 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 239.28/239.67 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x0))
% 239.28/239.67 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 239.28/239.67 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 239.28/239.67 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 239.28/239.67 Found eq_ref00:=(eq_ref0 (b x0)):(((eq Prop) (b x0)) (b x0))
% 239.28/239.67 Found (eq_ref0 (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 239.28/239.67 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 239.28/239.67 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 239.28/239.67 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 239.28/239.67 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 239.28/239.67 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq a) x) x0))
% 239.28/239.67 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq a) x) x0))
% 239.28/239.67 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq a) x) x0))
% 239.28/239.67 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq a) x) x0))
% 239.28/239.67 Found eq_ref00:=(eq_ref0 (b x0)):(((eq Prop) (b x0)) (b x0))
% 239.28/239.67 Found (eq_ref0 (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 239.28/239.67 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 239.28/239.67 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 239.28/239.67 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 239.28/239.67 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 239.28/239.67 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq a) x) x0))
% 239.28/239.67 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq a) x) x0))
% 239.28/239.67 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq a) x) x0))
% 239.28/239.67 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq a) x) x0))
% 239.28/239.67 Found x11:(P b)
% 239.28/239.67 Found (fun (x11:(P b))=> x11) as proof of (P b)
% 239.28/239.67 Found (fun (x11:(P b))=> x11) as proof of (P0 b)
% 239.28/239.67 Found eq_ref00:=(eq_ref0 (((eq a) x) x0)):(((eq Prop) (((eq a) x) x0)) (((eq a) x) x0))
% 239.28/239.67 Found (eq_ref0 (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 239.28/239.67 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 239.28/239.67 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 239.28/239.67 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 239.28/239.67 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 239.28/239.67 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 242.50/242.86 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 242.50/242.86 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 242.50/242.86 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 242.50/242.86 Found eq_ref00:=(eq_ref0 (((eq a) x) x0)):(((eq Prop) (((eq a) x) x0)) (((eq a) x) x0))
% 242.50/242.86 Found (eq_ref0 (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 242.50/242.86 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 242.50/242.86 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 242.50/242.86 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 242.50/242.86 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 242.50/242.86 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 242.50/242.86 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 242.50/242.86 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 242.50/242.86 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 242.50/242.86 Found eq_ref00:=(eq_ref0 (((eq a) x) x0)):(((eq Prop) (((eq a) x) x0)) (((eq a) x) x0))
% 242.50/242.86 Found (eq_ref0 (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 242.50/242.86 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 242.50/242.86 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 242.50/242.86 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 242.50/242.86 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 242.50/242.86 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 242.50/242.86 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 242.50/242.86 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 242.50/242.86 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 242.50/242.86 Found eq_ref00:=(eq_ref0 (((eq a) x) x0)):(((eq Prop) (((eq a) x) x0)) (((eq a) x) x0))
% 242.50/242.86 Found (eq_ref0 (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 242.50/242.86 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 242.50/242.86 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 242.50/242.86 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 242.50/242.86 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 242.50/242.86 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 242.50/242.86 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 242.50/242.86 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 242.50/242.86 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 242.50/242.86 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 242.50/242.86 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq a) x) x0))
% 242.50/242.86 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq a) x) x0))
% 242.50/242.86 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq a) x) x0))
% 242.50/242.86 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq a) x) x0))
% 242.50/242.86 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 242.50/242.86 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b0)
% 242.50/242.86 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b0)
% 242.50/242.86 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b0)
% 244.79/245.18 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b0)
% 244.79/245.18 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 244.79/245.18 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b0)
% 244.79/245.18 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b0)
% 244.79/245.18 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b0)
% 244.79/245.18 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b0)
% 244.79/245.18 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 244.79/245.18 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq a) x) x0))
% 244.79/245.18 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq a) x) x0))
% 244.79/245.18 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq a) x) x0))
% 244.79/245.18 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq a) x) x0))
% 244.79/245.18 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 244.79/245.18 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b0)
% 244.79/245.18 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b0)
% 244.79/245.18 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b0)
% 244.79/245.18 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b0)
% 244.79/245.18 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 244.79/245.18 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq a) x) x0))
% 244.79/245.18 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq a) x) x0))
% 244.79/245.18 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq a) x) x0))
% 244.79/245.18 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq a) x) x0))
% 244.79/245.18 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 244.79/245.18 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b0)
% 244.79/245.18 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b0)
% 244.79/245.18 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b0)
% 244.79/245.18 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b0)
% 244.79/245.18 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 244.79/245.18 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 244.79/245.18 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 244.79/245.18 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 244.79/245.18 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 250.17/250.50 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 250.17/250.50 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b0)
% 250.17/250.50 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b0)
% 250.17/250.50 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b0)
% 250.17/250.50 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b0)
% 250.17/250.50 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 250.17/250.50 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 250.17/250.50 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 250.17/250.50 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 250.17/250.50 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 250.17/250.50 Found eq_ref000:=(eq_ref00 P):((P (((eq a) x) x0))->(P (((eq a) x) x0)))
% 250.17/250.50 Found (eq_ref00 P) as proof of (P0 (((eq a) x) x0))
% 250.17/250.50 Found ((eq_ref0 (((eq a) x) x0)) P) as proof of (P0 (((eq a) x) x0))
% 250.17/250.50 Found (((eq_ref Prop) (((eq a) x) x0)) P) as proof of (P0 (((eq a) x) x0))
% 250.17/250.50 Found (((eq_ref Prop) (((eq a) x) x0)) P) as proof of (P0 (((eq a) x) x0))
% 250.17/250.50 Found eq_ref000:=(eq_ref00 P):((P (((eq a) x) x0))->(P (((eq a) x) x0)))
% 250.17/250.50 Found (eq_ref00 P) as proof of (P0 (((eq a) x) x0))
% 250.17/250.50 Found ((eq_ref0 (((eq a) x) x0)) P) as proof of (P0 (((eq a) x) x0))
% 250.17/250.50 Found (((eq_ref Prop) (((eq a) x) x0)) P) as proof of (P0 (((eq a) x) x0))
% 250.17/250.50 Found (((eq_ref Prop) (((eq a) x) x0)) P) as proof of (P0 (((eq a) x) x0))
% 250.17/250.50 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 250.17/250.50 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 250.17/250.50 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 250.17/250.50 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 250.17/250.50 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 250.17/250.50 Found eq_ref00:=(eq_ref0 (((eq a) x) x0)):(((eq Prop) (((eq a) x) x0)) (((eq a) x) x0))
% 250.17/250.50 Found (eq_ref0 (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 250.17/250.50 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 250.17/250.50 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 250.17/250.50 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 250.17/250.50 Found eq_ref00:=(eq_ref0 (((eq a) x) x0)):(((eq Prop) (((eq a) x) x0)) (((eq a) x) x0))
% 250.17/250.50 Found (eq_ref0 (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 250.17/250.50 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 250.17/250.50 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 250.17/250.50 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 250.17/250.50 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 250.17/250.50 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 250.17/250.50 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 250.17/250.50 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 250.17/250.50 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 250.17/250.50 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 250.17/250.50 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 250.17/250.50 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 250.17/250.50 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 251.89/252.22 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 251.89/252.22 Found eq_ref00:=(eq_ref0 (((eq a) x) x0)):(((eq Prop) (((eq a) x) x0)) (((eq a) x) x0))
% 251.89/252.22 Found (eq_ref0 (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 251.89/252.22 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 251.89/252.22 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 251.89/252.22 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 251.89/252.22 Found eq_ref00:=(eq_ref0 (((eq a) x) x0)):(((eq Prop) (((eq a) x) x0)) (((eq a) x) x0))
% 251.89/252.22 Found (eq_ref0 (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 251.89/252.22 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 251.89/252.22 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 251.89/252.22 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 251.89/252.22 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 251.89/252.22 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 251.89/252.22 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 251.89/252.22 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 251.89/252.22 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 251.89/252.22 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 251.89/252.22 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 251.89/252.22 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 251.89/252.22 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 251.89/252.22 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 251.89/252.22 Found eq_ref00:=(eq_ref0 (((eq a) x) x0)):(((eq Prop) (((eq a) x) x0)) (((eq a) x) x0))
% 251.89/252.22 Found (eq_ref0 (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 251.89/252.22 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 251.89/252.22 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 251.89/252.22 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 251.89/252.22 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 251.89/252.22 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 251.89/252.22 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 251.89/252.22 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 251.89/252.22 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 251.89/252.22 Found eq_ref00:=(eq_ref0 (((eq a) x) x0)):(((eq Prop) (((eq a) x) x0)) (((eq a) x) x0))
% 251.89/252.22 Found (eq_ref0 (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 251.89/252.22 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 251.89/252.22 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 251.89/252.22 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 251.89/252.22 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 251.89/252.22 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 251.89/252.22 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 251.89/252.22 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 251.89/252.22 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 251.89/252.22 Found eq_ref00:=(eq_ref0 (((eq a) x) x0)):(((eq Prop) (((eq a) x) x0)) (((eq a) x) x0))
% 251.89/252.22 Found (eq_ref0 (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 251.89/252.22 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 254.11/254.43 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 254.11/254.43 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 254.11/254.43 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 254.11/254.43 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 254.11/254.43 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 254.11/254.43 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 254.11/254.43 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 254.11/254.43 Found eq_ref00:=(eq_ref0 (((eq a) x) x0)):(((eq Prop) (((eq a) x) x0)) (((eq a) x) x0))
% 254.11/254.43 Found (eq_ref0 (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 254.11/254.43 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 254.11/254.43 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 254.11/254.43 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 254.11/254.43 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 254.11/254.43 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 254.11/254.43 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 254.11/254.43 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 254.11/254.43 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 254.11/254.43 Found eq_ref00:=(eq_ref0 (((eq a) x) x0)):(((eq Prop) (((eq a) x) x0)) (((eq a) x) x0))
% 254.11/254.43 Found (eq_ref0 (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 254.11/254.43 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 254.11/254.43 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 254.11/254.43 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 254.11/254.43 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 254.11/254.43 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 254.11/254.43 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 254.11/254.43 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 254.11/254.43 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 254.11/254.43 Found eq_ref00:=(eq_ref0 (((eq a) x) x0)):(((eq Prop) (((eq a) x) x0)) (((eq a) x) x0))
% 254.11/254.43 Found (eq_ref0 (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 254.11/254.43 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 254.11/254.43 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 254.11/254.43 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 254.11/254.43 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 254.11/254.43 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 254.11/254.43 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 254.11/254.43 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 254.11/254.43 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 254.11/254.43 Found eq_ref00:=(eq_ref0 (((eq a) x) x0)):(((eq Prop) (((eq a) x) x0)) (((eq a) x) x0))
% 254.11/254.43 Found (eq_ref0 (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 254.11/254.43 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 254.11/254.43 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 254.11/254.43 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 254.11/254.43 Found eq_ref00:=(eq_ref0 (((eq a) x) x0)):(((eq Prop) (((eq a) x) x0)) (((eq a) x) x0))
% 254.11/254.43 Found (eq_ref0 (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 254.11/254.43 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 256.59/256.94 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 256.59/256.94 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 256.59/256.94 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 256.59/256.94 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 256.59/256.94 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 256.59/256.94 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 256.59/256.94 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 256.59/256.94 Found eq_ref00:=(eq_ref0 (((eq a) x) x0)):(((eq Prop) (((eq a) x) x0)) (((eq a) x) x0))
% 256.59/256.94 Found (eq_ref0 (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 256.59/256.94 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 256.59/256.94 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 256.59/256.94 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 256.59/256.94 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 256.59/256.94 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 256.59/256.94 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 256.59/256.94 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 256.59/256.94 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 256.59/256.94 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 256.59/256.94 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 256.59/256.94 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 256.59/256.94 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 256.59/256.94 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 256.59/256.94 Found eq_ref00:=(eq_ref0 (((eq a) x) x0)):(((eq Prop) (((eq a) x) x0)) (((eq a) x) x0))
% 256.59/256.94 Found (eq_ref0 (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 256.59/256.94 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 256.59/256.94 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 256.59/256.94 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 256.59/256.94 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 256.59/256.94 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 256.59/256.94 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 256.59/256.94 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 256.59/256.94 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 256.59/256.94 Found eq_ref00:=(eq_ref0 (((eq a) x) x0)):(((eq Prop) (((eq a) x) x0)) (((eq a) x) x0))
% 256.59/256.94 Found (eq_ref0 (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 256.59/256.94 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 256.59/256.94 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 256.59/256.94 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 256.59/256.94 Found eq_ref00:=(eq_ref0 (((eq a) x) x0)):(((eq Prop) (((eq a) x) x0)) (((eq a) x) x0))
% 256.59/256.94 Found (eq_ref0 (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 256.59/256.94 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 256.59/256.94 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 256.59/256.94 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 256.59/256.94 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 256.59/256.94 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 256.59/256.94 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 267.61/267.97 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 267.61/267.97 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 267.61/267.97 Found x11:(P b)
% 267.61/267.97 Found (fun (x11:(P b))=> x11) as proof of (P b)
% 267.61/267.97 Found (fun (x11:(P b))=> x11) as proof of (P0 b)
% 267.61/267.97 Found x11:(P b)
% 267.61/267.97 Found (fun (x11:(P b))=> x11) as proof of (P b)
% 267.61/267.97 Found (fun (x11:(P b))=> x11) as proof of (P0 b)
% 267.61/267.97 Found x11:(P (b x0))
% 267.61/267.97 Found (fun (x11:(P (b x0)))=> x11) as proof of (P (b x0))
% 267.61/267.97 Found (fun (x11:(P (b x0)))=> x11) as proof of (P0 (b x0))
% 267.61/267.97 Found x11:(P (b x0))
% 267.61/267.97 Found (fun (x11:(P (b x0)))=> x11) as proof of (P (b x0))
% 267.61/267.97 Found (fun (x11:(P (b x0)))=> x11) as proof of (P0 (b x0))
% 267.61/267.97 Found eq_ref000:=(eq_ref00 P):((P ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))->(P ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))))
% 267.61/267.97 Found (eq_ref00 P) as proof of (P0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 267.61/267.97 Found ((eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P) as proof of (P0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 267.61/267.97 Found (((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P) as proof of (P0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 267.61/267.97 Found (((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P) as proof of (P0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 267.61/267.97 Found eq_ref000:=(eq_ref00 P):((P ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))->(P ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))))
% 267.61/267.97 Found (eq_ref00 P) as proof of (P0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 267.61/267.97 Found ((eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P) as proof of (P0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 267.61/267.97 Found (((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P) as proof of (P0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 267.61/267.97 Found (((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) P) as proof of (P0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 267.61/267.97 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 267.61/267.97 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x0))
% 267.61/267.97 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 267.61/267.97 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 267.61/267.97 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 267.61/267.97 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 267.61/267.97 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b0)
% 267.61/267.97 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b0)
% 267.61/267.97 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b0)
% 267.61/267.97 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b0)
% 267.61/267.97 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 267.61/267.97 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x0))
% 267.61/267.97 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 267.61/267.97 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 267.61/267.97 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 267.61/267.97 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 267.61/267.97 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b0)
% 269.87/270.23 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b0)
% 269.87/270.23 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b0)
% 269.87/270.23 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b0)
% 269.87/270.23 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 269.87/270.23 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b0)
% 269.87/270.23 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b0)
% 269.87/270.23 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b0)
% 269.87/270.23 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b0)
% 269.87/270.23 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 269.87/270.23 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x0))
% 269.87/270.23 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 269.87/270.23 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 269.87/270.23 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 269.87/270.23 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 269.87/270.23 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b0)
% 269.87/270.23 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b0)
% 269.87/270.23 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b0)
% 269.87/270.23 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b0)
% 269.87/270.23 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 269.87/270.23 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x0))
% 269.87/270.23 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 269.87/270.23 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 269.87/270.23 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 269.87/270.23 Found eq_ref00:=(eq_ref0 (b x0)):(((eq Prop) (b x0)) (b x0))
% 269.87/270.23 Found (eq_ref0 (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 269.87/270.23 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 269.87/270.23 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 269.87/270.23 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 269.87/270.23 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 269.87/270.23 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq a) x) x0))
% 269.87/270.23 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq a) x) x0))
% 269.87/270.23 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq a) x) x0))
% 269.87/270.23 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq a) x) x0))
% 269.87/270.23 Found eq_ref00:=(eq_ref0 (b x0)):(((eq Prop) (b x0)) (b x0))
% 269.87/270.23 Found (eq_ref0 (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 269.87/270.23 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 269.87/270.23 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 269.87/270.23 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 281.84/282.27 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 281.84/282.27 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq a) x) x0))
% 281.84/282.27 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq a) x) x0))
% 281.84/282.27 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq a) x) x0))
% 281.84/282.27 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq a) x) x0))
% 281.84/282.27 Found x11:(P b)
% 281.84/282.27 Found (fun (x11:(P b))=> x11) as proof of (P b)
% 281.84/282.27 Found (fun (x11:(P b))=> x11) as proof of (P0 b)
% 281.84/282.27 Found x11:(P b)
% 281.84/282.27 Found (fun (x11:(P b))=> x11) as proof of (P b)
% 281.84/282.27 Found (fun (x11:(P b))=> x11) as proof of (P0 b)
% 281.84/282.27 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 281.84/282.27 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b0)
% 281.84/282.27 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b0)
% 281.84/282.27 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b0)
% 281.84/282.27 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b0)
% 281.84/282.27 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 281.84/282.27 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq a) x) x0))
% 281.84/282.27 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq a) x) x0))
% 281.84/282.27 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq a) x) x0))
% 281.84/282.27 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq a) x) x0))
% 281.84/282.27 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 281.84/282.27 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq a) x) x0))
% 281.84/282.27 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq a) x) x0))
% 281.84/282.27 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq a) x) x0))
% 281.84/282.27 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq a) x) x0))
% 281.84/282.27 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 281.84/282.27 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b0)
% 281.84/282.27 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b0)
% 281.84/282.27 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b0)
% 281.84/282.27 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b0)
% 281.84/282.27 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 281.84/282.27 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b0)
% 281.84/282.27 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b0)
% 281.84/282.27 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b0)
% 281.84/282.27 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b0)
% 281.84/282.27 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 289.63/289.97 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq a) x) x0))
% 289.63/289.97 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq a) x) x0))
% 289.63/289.97 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq a) x) x0))
% 289.63/289.97 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq a) x) x0))
% 289.63/289.97 Found eq_ref00:=(eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))):(((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 289.63/289.97 Found (eq_ref0 ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b0)
% 289.63/289.97 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b0)
% 289.63/289.97 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b0)
% 289.63/289.97 Found ((eq_ref Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) as proof of (((eq Prop) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy))))) b0)
% 289.63/289.97 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 289.63/289.97 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq a) x) x0))
% 289.63/289.97 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq a) x) x0))
% 289.63/289.97 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq a) x) x0))
% 289.63/289.97 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq a) x) x0))
% 289.63/289.97 Found eq_ref000:=(eq_ref00 P):((P (((eq a) x) x0))->(P (((eq a) x) x0)))
% 289.63/289.97 Found (eq_ref00 P) as proof of (P0 (((eq a) x) x0))
% 289.63/289.97 Found ((eq_ref0 (((eq a) x) x0)) P) as proof of (P0 (((eq a) x) x0))
% 289.63/289.97 Found (((eq_ref Prop) (((eq a) x) x0)) P) as proof of (P0 (((eq a) x) x0))
% 289.63/289.97 Found (((eq_ref Prop) (((eq a) x) x0)) P) as proof of (P0 (((eq a) x) x0))
% 289.63/289.97 Found eq_ref000:=(eq_ref00 P):((P (((eq a) x) x0))->(P (((eq a) x) x0)))
% 289.63/289.97 Found (eq_ref00 P) as proof of (P0 (((eq a) x) x0))
% 289.63/289.97 Found ((eq_ref0 (((eq a) x) x0)) P) as proof of (P0 (((eq a) x) x0))
% 289.63/289.97 Found (((eq_ref Prop) (((eq a) x) x0)) P) as proof of (P0 (((eq a) x) x0))
% 289.63/289.97 Found (((eq_ref Prop) (((eq a) x) x0)) P) as proof of (P0 (((eq a) x) x0))
% 289.63/289.97 Found eq_ref00:=(eq_ref0 (((eq a) x) x0)):(((eq Prop) (((eq a) x) x0)) (((eq a) x) x0))
% 289.63/289.97 Found (eq_ref0 (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 289.63/289.97 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 289.63/289.97 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 289.63/289.97 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 289.63/289.97 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 289.63/289.97 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 289.63/289.97 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 289.63/289.97 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 289.63/289.97 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 289.63/289.97 Found eq_ref00:=(eq_ref0 (((eq a) x) x0)):(((eq Prop) (((eq a) x) x0)) (((eq a) x) x0))
% 289.63/289.97 Found (eq_ref0 (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 289.63/289.97 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 289.63/289.97 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 289.63/289.97 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 289.63/289.97 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 289.63/289.97 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 289.63/289.97 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 289.63/289.97 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 289.63/289.97 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 291.84/292.21 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 291.84/292.21 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 291.84/292.21 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 291.84/292.21 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 291.84/292.21 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 291.84/292.21 Found eq_ref00:=(eq_ref0 (((eq a) x) x0)):(((eq Prop) (((eq a) x) x0)) (((eq a) x) x0))
% 291.84/292.21 Found (eq_ref0 (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 291.84/292.21 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 291.84/292.21 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 291.84/292.21 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 291.84/292.21 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 291.84/292.21 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 291.84/292.21 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 291.84/292.21 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 291.84/292.21 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 291.84/292.21 Found eq_ref00:=(eq_ref0 (((eq a) x) x0)):(((eq Prop) (((eq a) x) x0)) (((eq a) x) x0))
% 291.84/292.21 Found (eq_ref0 (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 291.84/292.21 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 291.84/292.21 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 291.84/292.21 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 291.84/292.21 Found eq_ref00:=(eq_ref0 (((eq a) x) x0)):(((eq Prop) (((eq a) x) x0)) (((eq a) x) x0))
% 291.84/292.21 Found (eq_ref0 (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 291.84/292.21 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 291.84/292.21 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 291.84/292.21 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 291.84/292.21 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 291.84/292.21 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 291.84/292.21 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 291.84/292.21 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 291.84/292.21 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 291.84/292.21 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 291.84/292.21 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 291.84/292.21 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 291.84/292.21 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 291.84/292.21 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 291.84/292.21 Found eq_ref00:=(eq_ref0 (((eq a) x) x0)):(((eq Prop) (((eq a) x) x0)) (((eq a) x) x0))
% 291.84/292.21 Found (eq_ref0 (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 291.84/292.21 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 291.84/292.21 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 291.84/292.21 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 291.84/292.21 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 291.84/292.21 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 291.84/292.21 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 291.84/292.21 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 291.84/292.21 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 293.19/293.54 Found eq_ref00:=(eq_ref0 (((eq a) x) x0)):(((eq Prop) (((eq a) x) x0)) (((eq a) x) x0))
% 293.19/293.54 Found (eq_ref0 (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 293.19/293.54 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 293.19/293.54 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 293.19/293.54 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 293.19/293.54 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 293.19/293.54 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 293.19/293.54 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 293.19/293.54 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 293.19/293.54 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 293.19/293.54 Found eq_ref00:=(eq_ref0 (((eq a) x) x0)):(((eq Prop) (((eq a) x) x0)) (((eq a) x) x0))
% 293.19/293.54 Found (eq_ref0 (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 293.19/293.54 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 293.19/293.54 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 293.19/293.54 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 293.19/293.54 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 293.19/293.54 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 293.19/293.54 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 293.19/293.54 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 293.19/293.54 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 293.19/293.54 Found eq_ref00:=(eq_ref0 (((eq a) x) x0)):(((eq Prop) (((eq a) x) x0)) (((eq a) x) x0))
% 293.19/293.54 Found (eq_ref0 (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 293.19/293.54 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 293.19/293.54 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 293.19/293.54 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 293.19/293.54 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 293.19/293.54 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 293.19/293.54 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 293.19/293.54 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 293.19/293.54 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 293.19/293.54 Found eq_ref00:=(eq_ref0 (((eq a) x) x0)):(((eq Prop) (((eq a) x) x0)) (((eq a) x) x0))
% 293.19/293.54 Found (eq_ref0 (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 293.19/293.54 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 293.19/293.54 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 293.19/293.54 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 293.19/293.54 Found eq_ref00:=(eq_ref0 (((eq a) x) x0)):(((eq Prop) (((eq a) x) x0)) (((eq a) x) x0))
% 293.19/293.54 Found (eq_ref0 (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 293.19/293.54 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 293.19/293.54 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 293.19/293.54 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 293.19/293.54 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 293.19/293.54 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 293.19/293.54 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 293.19/293.54 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 293.19/293.54 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 294.39/294.79 Found eq_ref00:=(eq_ref0 (((eq a) x) x0)):(((eq Prop) (((eq a) x) x0)) (((eq a) x) x0))
% 294.39/294.79 Found (eq_ref0 (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 294.39/294.79 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 294.39/294.79 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 294.39/294.79 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 294.39/294.79 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 294.39/294.79 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 294.39/294.79 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 294.39/294.79 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 294.39/294.79 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 294.39/294.79 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 294.39/294.79 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 294.39/294.79 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 294.39/294.79 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 294.39/294.79 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 294.39/294.79 Found eq_ref00:=(eq_ref0 (((eq a) x) x0)):(((eq Prop) (((eq a) x) x0)) (((eq a) x) x0))
% 294.39/294.79 Found (eq_ref0 (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 294.39/294.79 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 294.39/294.79 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 294.39/294.79 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 294.39/294.79 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 294.39/294.79 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 294.39/294.79 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 294.39/294.79 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 294.39/294.79 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 294.39/294.79 Found eq_ref00:=(eq_ref0 (((eq a) x) x0)):(((eq Prop) (((eq a) x) x0)) (((eq a) x) x0))
% 294.39/294.79 Found (eq_ref0 (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 294.39/294.79 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 294.39/294.79 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 294.39/294.79 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 294.39/294.79 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 294.39/294.79 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 294.39/294.79 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 294.39/294.79 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 294.39/294.79 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 294.39/294.79 Found eq_ref00:=(eq_ref0 (((eq a) x) x0)):(((eq Prop) (((eq a) x) x0)) (((eq a) x) x0))
% 294.39/294.79 Found (eq_ref0 (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 294.39/294.79 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 294.39/294.79 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 294.39/294.79 Found ((eq_ref Prop) (((eq a) x) x0)) as proof of (((eq Prop) (((eq a) x) x0)) b)
% 294.39/294.79 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 294.39/294.79 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 294.39/294.79 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex a) (fun (Xy:a)=> ((and (((eq a) Xy) x)) (((eq a) x0) Xy)))))
% 294.39/294.79 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((e
%------------------------------------------------------------------------------