TSTP Solution File: SYO192^5 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SYO192^5 : TPTP v7.5.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.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 00:50:52 EDT 2022
% Result : Timeout 287.50s 287.84s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO192^5 : TPTP v7.5.0. Released v4.0.0.
% 0.11/0.12 % Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPUModel : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % RAMPerCPU : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % DateTime : Fri Mar 11 17:32:47 EST 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.34 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.19/0.34 Python 2.7.5
% 1.15/1.34 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox2/benchmark/', '/export/starexec/sandbox2/benchmark/']
% 1.15/1.34 FOF formula ((ex Prop) (fun (Xx:Prop)=> ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) Xx) Xy))))) of role conjecture named cCT12
% 1.15/1.34 Conjecture to prove = ((ex Prop) (fun (Xx:Prop)=> ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) Xx) Xy))))):Prop
% 1.15/1.34 We need to prove ['((ex Prop) (fun (Xx:Prop)=> ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) Xx) Xy)))))']
% 1.15/1.34 Trying to prove ((ex Prop) (fun (Xx:Prop)=> ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) Xx) Xy)))))
% 1.15/1.34 Found eta_expansion000:=(eta_expansion00 (fun (Xx:Prop)=> ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) Xx) Xy))))):(((eq (Prop->Prop)) (fun (Xx:Prop)=> ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) Xx) Xy))))) (fun (x:Prop)=> ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))))
% 1.15/1.34 Found (eta_expansion00 (fun (Xx:Prop)=> ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) Xx) Xy))))) as proof of (((eq (Prop->Prop)) (fun (Xx:Prop)=> ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) Xx) Xy))))) b)
% 1.15/1.34 Found ((eta_expansion0 Prop) (fun (Xx:Prop)=> ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) Xx) Xy))))) as proof of (((eq (Prop->Prop)) (fun (Xx:Prop)=> ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) Xx) Xy))))) b)
% 1.15/1.34 Found (((eta_expansion Prop) Prop) (fun (Xx:Prop)=> ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) Xx) Xy))))) as proof of (((eq (Prop->Prop)) (fun (Xx:Prop)=> ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) Xx) Xy))))) b)
% 1.15/1.34 Found (((eta_expansion Prop) Prop) (fun (Xx:Prop)=> ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) Xx) Xy))))) as proof of (((eq (Prop->Prop)) (fun (Xx:Prop)=> ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) Xx) Xy))))) b)
% 1.15/1.34 Found (((eta_expansion Prop) Prop) (fun (Xx:Prop)=> ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) Xx) Xy))))) as proof of (((eq (Prop->Prop)) (fun (Xx:Prop)=> ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) Xx) Xy))))) b)
% 1.15/1.34 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 1.15/1.34 Found (eq_ref0 x) as proof of (((eq Prop) x) x0)
% 1.15/1.34 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) x0)
% 1.15/1.34 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) x0)
% 1.15/1.34 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) x0)
% 1.15/1.34 Found (ex_intro010 ((eq_ref Prop) x)) as proof of ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 1.15/1.34 Found eq_ref00:=(eq_ref0 (fun (Xx:Prop)=> ((ex Prop) ((eq Prop) Xx)))):(((eq (Prop->Prop)) (fun (Xx:Prop)=> ((ex Prop) ((eq Prop) Xx)))) (fun (Xx:Prop)=> ((ex Prop) ((eq Prop) Xx))))
% 1.15/1.34 Found (eq_ref0 (fun (Xx:Prop)=> ((ex Prop) ((eq Prop) Xx)))) as proof of (((eq (Prop->Prop)) (fun (Xx:Prop)=> ((ex Prop) ((eq Prop) Xx)))) b)
% 1.15/1.34 Found ((eq_ref (Prop->Prop)) (fun (Xx:Prop)=> ((ex Prop) ((eq Prop) Xx)))) as proof of (((eq (Prop->Prop)) (fun (Xx:Prop)=> ((ex Prop) ((eq Prop) Xx)))) b)
% 1.15/1.34 Found ((eq_ref (Prop->Prop)) (fun (Xx:Prop)=> ((ex Prop) ((eq Prop) Xx)))) as proof of (((eq (Prop->Prop)) (fun (Xx:Prop)=> ((ex Prop) ((eq Prop) Xx)))) b)
% 1.15/1.34 Found ((eq_ref (Prop->Prop)) (fun (Xx:Prop)=> ((ex Prop) ((eq Prop) Xx)))) as proof of (((eq (Prop->Prop)) (fun (Xx:Prop)=> ((ex Prop) ((eq Prop) Xx)))) b)
% 1.15/1.34 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 1.15/1.34 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) x) Xy))))
% 1.15/1.34 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) x) Xy))))
% 1.15/1.34 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) x) Xy))))
% 1.15/1.34 Found (fun (x:Prop)=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) x) Xy))))
% 1.15/1.34 Found (fun (x:Prop)=> ((eq_ref Prop) (f x))) as proof of (forall (x:Prop), (((eq Prop) (f x)) ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))))
% 1.15/1.34 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 1.15/1.34 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) x) Xy))))
% 1.15/1.34 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) x) Xy))))
% 1.15/1.34 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) x) Xy))))
% 1.15/1.34 Found (fun (x:Prop)=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) x) Xy))))
% 1.82/1.99 Found (fun (x:Prop)=> ((eq_ref Prop) (f x))) as proof of (forall (x:Prop), (((eq Prop) (f x)) ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))))
% 1.82/1.99 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 1.82/1.99 Found (eq_ref0 x) as proof of (((eq Prop) x) x0)
% 1.82/1.99 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) x0)
% 1.82/1.99 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) x0)
% 1.82/1.99 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) x0)
% 1.82/1.99 Found (ex_intro010 ((eq_ref Prop) x)) as proof of ((ex Prop) ((eq Prop) x))
% 1.82/1.99 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 1.82/1.99 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) ((ex Prop) ((eq Prop) x)))
% 1.82/1.99 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((ex Prop) ((eq Prop) x)))
% 1.82/1.99 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((ex Prop) ((eq Prop) x)))
% 1.82/1.99 Found (fun (x:Prop)=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) ((ex Prop) ((eq Prop) x)))
% 1.82/1.99 Found (fun (x:Prop)=> ((eq_ref Prop) (f x))) as proof of (forall (x:Prop), (((eq Prop) (f x)) ((ex Prop) ((eq Prop) x))))
% 1.82/1.99 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 1.82/1.99 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) ((ex Prop) ((eq Prop) x)))
% 1.82/1.99 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((ex Prop) ((eq Prop) x)))
% 1.82/1.99 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((ex Prop) ((eq Prop) x)))
% 1.82/1.99 Found (fun (x:Prop)=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) ((ex Prop) ((eq Prop) x)))
% 1.82/1.99 Found (fun (x:Prop)=> ((eq_ref Prop) (f x))) as proof of (forall (x:Prop), (((eq Prop) (f x)) ((ex Prop) ((eq Prop) x))))
% 1.82/1.99 Found eq_ref00:=(eq_ref0 a):(((eq (Prop->Prop)) a) a)
% 1.82/1.99 Found (eq_ref0 a) as proof of (((eq (Prop->Prop)) a) b)
% 1.82/1.99 Found ((eq_ref (Prop->Prop)) a) as proof of (((eq (Prop->Prop)) a) b)
% 1.82/1.99 Found ((eq_ref (Prop->Prop)) a) as proof of (((eq (Prop->Prop)) a) b)
% 1.82/1.99 Found ((eq_ref (Prop->Prop)) a) as proof of (((eq (Prop->Prop)) a) b)
% 1.82/1.99 Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq (Prop->Prop)) b) (fun (x:Prop)=> (b x)))
% 1.82/1.99 Found (eta_expansion_dep00 b) as proof of (((eq (Prop->Prop)) b) (fun (Xx:Prop)=> ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) Xx) Xy)))))
% 1.82/1.99 Found ((eta_expansion_dep0 (fun (x1:Prop)=> Prop)) b) as proof of (((eq (Prop->Prop)) b) (fun (Xx:Prop)=> ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) Xx) Xy)))))
% 1.82/1.99 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) b) as proof of (((eq (Prop->Prop)) b) (fun (Xx:Prop)=> ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) Xx) Xy)))))
% 1.82/1.99 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) b) as proof of (((eq (Prop->Prop)) b) (fun (Xx:Prop)=> ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) Xx) Xy)))))
% 1.82/1.99 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) b) as proof of (((eq (Prop->Prop)) b) (fun (Xx:Prop)=> ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) Xx) Xy)))))
% 1.82/1.99 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xy:Prop)=> (((eq Prop) x) Xy))):(((eq (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) (fun (x0:Prop)=> (((eq Prop) x) x0)))
% 1.82/1.99 Found (eta_expansion_dep00 (fun (Xy:Prop)=> (((eq Prop) x) Xy))) as proof of (((eq (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) b)
% 1.82/1.99 Found ((eta_expansion_dep0 (fun (x1:Prop)=> Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) as proof of (((eq (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) b)
% 1.82/1.99 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) as proof of (((eq (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) b)
% 1.82/1.99 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) as proof of (((eq (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) b)
% 1.82/1.99 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) as proof of (((eq (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) b)
% 1.82/1.99 Found eta_expansion000:=(eta_expansion00 a):(((eq (Prop->Prop)) a) (fun (x:Prop)=> (a x)))
% 1.82/1.99 Found (eta_expansion00 a) as proof of (((eq (Prop->Prop)) a) b)
% 1.82/1.99 Found ((eta_expansion0 Prop) a) as proof of (((eq (Prop->Prop)) a) b)
% 1.82/1.99 Found (((eta_expansion Prop) Prop) a) as proof of (((eq (Prop->Prop)) a) b)
% 2.75/2.93 Found (((eta_expansion Prop) Prop) a) as proof of (((eq (Prop->Prop)) a) b)
% 2.75/2.93 Found (((eta_expansion Prop) Prop) a) as proof of (((eq (Prop->Prop)) a) b)
% 2.75/2.93 Found eq_ref00:=(eq_ref0 b):(((eq (Prop->Prop)) b) b)
% 2.75/2.93 Found (eq_ref0 b) as proof of (((eq (Prop->Prop)) b) (fun (Xx:Prop)=> ((ex Prop) ((eq Prop) Xx))))
% 2.75/2.93 Found ((eq_ref (Prop->Prop)) b) as proof of (((eq (Prop->Prop)) b) (fun (Xx:Prop)=> ((ex Prop) ((eq Prop) Xx))))
% 2.75/2.93 Found ((eq_ref (Prop->Prop)) b) as proof of (((eq (Prop->Prop)) b) (fun (Xx:Prop)=> ((ex Prop) ((eq Prop) Xx))))
% 2.75/2.93 Found ((eq_ref (Prop->Prop)) b) as proof of (((eq (Prop->Prop)) b) (fun (Xx:Prop)=> ((ex Prop) ((eq Prop) Xx))))
% 2.75/2.93 Found eq_ref00:=(eq_ref0 b):(((eq (Prop->Prop)) b) b)
% 2.75/2.93 Found (eq_ref0 b) as proof of (((eq (Prop->Prop)) b) (fun (Xx:Prop)=> ((ex Prop) ((eq Prop) Xx))))
% 2.75/2.93 Found ((eq_ref (Prop->Prop)) b) as proof of (((eq (Prop->Prop)) b) (fun (Xx:Prop)=> ((ex Prop) ((eq Prop) Xx))))
% 2.75/2.93 Found ((eq_ref (Prop->Prop)) b) as proof of (((eq (Prop->Prop)) b) (fun (Xx:Prop)=> ((ex Prop) ((eq Prop) Xx))))
% 2.75/2.93 Found ((eq_ref (Prop->Prop)) b) as proof of (((eq (Prop->Prop)) b) (fun (Xx:Prop)=> ((ex Prop) ((eq Prop) Xx))))
% 2.75/2.93 Found eta_expansion_dep000:=(eta_expansion_dep00 ((eq Prop) x)):(((eq (Prop->Prop)) ((eq Prop) x)) (fun (x0:Prop)=> (((eq Prop) x) x0)))
% 2.75/2.93 Found (eta_expansion_dep00 ((eq Prop) x)) as proof of (((eq (Prop->Prop)) ((eq Prop) x)) b)
% 2.75/2.93 Found ((eta_expansion_dep0 (fun (x1:Prop)=> Prop)) ((eq Prop) x)) as proof of (((eq (Prop->Prop)) ((eq Prop) x)) b)
% 2.75/2.93 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) ((eq Prop) x)) as proof of (((eq (Prop->Prop)) ((eq Prop) x)) b)
% 2.75/2.93 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) ((eq Prop) x)) as proof of (((eq (Prop->Prop)) ((eq Prop) x)) b)
% 2.75/2.93 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) ((eq Prop) x)) as proof of (((eq (Prop->Prop)) ((eq Prop) x)) b)
% 2.75/2.93 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 2.75/2.93 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (((eq Prop) x) x0))
% 2.75/2.93 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (((eq Prop) x) x0))
% 2.75/2.93 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (((eq Prop) x) x0))
% 2.75/2.93 Found (fun (x0:Prop)=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (((eq Prop) x) x0))
% 2.75/2.93 Found (fun (x0:Prop)=> ((eq_ref Prop) (f x0))) as proof of (forall (x0:Prop), (((eq Prop) (f x0)) (((eq Prop) x) x0)))
% 2.75/2.93 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 2.75/2.93 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (((eq Prop) x) x0))
% 2.75/2.93 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (((eq Prop) x) x0))
% 2.75/2.93 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (((eq Prop) x) x0))
% 2.75/2.93 Found (fun (x0:Prop)=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (((eq Prop) x) x0))
% 2.75/2.93 Found (fun (x0:Prop)=> ((eq_ref Prop) (f x0))) as proof of (forall (x0:Prop), (((eq Prop) (f x0)) (((eq Prop) x) x0)))
% 2.75/2.93 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 2.75/2.93 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (((eq Prop) x) x0))
% 2.75/2.93 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (((eq Prop) x) x0))
% 2.75/2.93 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (((eq Prop) x) x0))
% 2.75/2.93 Found (fun (x0:Prop)=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (((eq Prop) x) x0))
% 2.75/2.93 Found (fun (x0:Prop)=> ((eq_ref Prop) (f x0))) as proof of (forall (x0:Prop), (((eq Prop) (f x0)) (((eq Prop) x) x0)))
% 2.75/2.93 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 2.75/2.93 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (((eq Prop) x) x0))
% 2.75/2.93 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (((eq Prop) x) x0))
% 2.75/2.93 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (((eq Prop) x) x0))
% 2.75/2.93 Found (fun (x0:Prop)=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (((eq Prop) x) x0))
% 2.75/2.93 Found (fun (x0:Prop)=> ((eq_ref Prop) (f x0))) as proof of (forall (x0:Prop), (((eq Prop) (f x0)) (((eq Prop) x) x0)))
% 2.75/2.93 Found eta_expansion_dep000:=(eta_expansion_dep00 a):(((eq (Prop->Prop)) a) (fun (x:Prop)=> (a x)))
% 2.75/2.93 Found (eta_expansion_dep00 a) as proof of (((eq (Prop->Prop)) a) b)
% 2.75/2.93 Found ((eta_expansion_dep0 (fun (x1:Prop)=> Prop)) a) as proof of (((eq (Prop->Prop)) a) b)
% 3.57/3.75 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) a) as proof of (((eq (Prop->Prop)) a) b)
% 3.57/3.75 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) a) as proof of (((eq (Prop->Prop)) a) b)
% 3.57/3.75 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) a) as proof of (((eq (Prop->Prop)) a) b)
% 3.57/3.75 Found eq_ref00:=(eq_ref0 b):(((eq (Prop->Prop)) b) b)
% 3.57/3.75 Found (eq_ref0 b) as proof of (((eq (Prop->Prop)) b) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 3.57/3.75 Found ((eq_ref (Prop->Prop)) b) as proof of (((eq (Prop->Prop)) b) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 3.57/3.75 Found ((eq_ref (Prop->Prop)) b) as proof of (((eq (Prop->Prop)) b) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 3.57/3.75 Found ((eq_ref (Prop->Prop)) b) as proof of (((eq (Prop->Prop)) b) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 3.57/3.75 Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq (Prop->Prop)) b) (fun (x:Prop)=> (b x)))
% 3.57/3.75 Found (eta_expansion_dep00 b) as proof of (((eq (Prop->Prop)) b) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 3.57/3.75 Found ((eta_expansion_dep0 (fun (x1:Prop)=> Prop)) b) as proof of (((eq (Prop->Prop)) b) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 3.57/3.75 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) b) as proof of (((eq (Prop->Prop)) b) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 3.57/3.75 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) b) as proof of (((eq (Prop->Prop)) b) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 3.57/3.75 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) b) as proof of (((eq (Prop->Prop)) b) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 3.57/3.75 Found eta_expansion_dep000:=(eta_expansion_dep00 a):(((eq (Prop->Prop)) a) (fun (x:Prop)=> (a x)))
% 3.57/3.75 Found (eta_expansion_dep00 a) as proof of (((eq (Prop->Prop)) a) b)
% 3.57/3.75 Found ((eta_expansion_dep0 (fun (x1:Prop)=> Prop)) a) as proof of (((eq (Prop->Prop)) a) b)
% 3.57/3.75 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) a) as proof of (((eq (Prop->Prop)) a) b)
% 3.57/3.75 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) a) as proof of (((eq (Prop->Prop)) a) b)
% 3.57/3.75 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) a) as proof of (((eq (Prop->Prop)) a) b)
% 3.57/3.75 Found eq_ref00:=(eq_ref0 b):(((eq (Prop->Prop)) b) b)
% 3.57/3.75 Found (eq_ref0 b) as proof of (((eq (Prop->Prop)) b) ((eq Prop) x))
% 3.57/3.75 Found ((eq_ref (Prop->Prop)) b) as proof of (((eq (Prop->Prop)) b) ((eq Prop) x))
% 3.57/3.75 Found ((eq_ref (Prop->Prop)) b) as proof of (((eq (Prop->Prop)) b) ((eq Prop) x))
% 3.57/3.75 Found ((eq_ref (Prop->Prop)) b) as proof of (((eq (Prop->Prop)) b) ((eq Prop) x))
% 3.57/3.75 Found eq_ref00:=(eq_ref0 b):(((eq (Prop->Prop)) b) b)
% 3.57/3.75 Found (eq_ref0 b) as proof of (((eq (Prop->Prop)) b) ((eq Prop) x))
% 3.57/3.75 Found ((eq_ref (Prop->Prop)) b) as proof of (((eq (Prop->Prop)) b) ((eq Prop) x))
% 3.57/3.75 Found ((eq_ref (Prop->Prop)) b) as proof of (((eq (Prop->Prop)) b) ((eq Prop) x))
% 3.57/3.75 Found ((eq_ref (Prop->Prop)) b) as proof of (((eq (Prop->Prop)) b) ((eq Prop) x))
% 3.57/3.75 Found x00:(P0 x)
% 3.57/3.75 Instantiate: x0:=x:Prop
% 3.57/3.75 Found (fun (x00:(P0 x))=> x00) as proof of (P0 x0)
% 3.57/3.75 Found (fun (P0:(Prop->Prop)) (x00:(P0 x))=> x00) as proof of ((P0 x)->(P0 x0))
% 3.57/3.75 Found (fun (P0:(Prop->Prop)) (x00:(P0 x))=> x00) as proof of (b x0)
% 3.57/3.75 Found (ex_intro010 (fun (P0:(Prop->Prop)) (x00:(P0 x))=> x00)) as proof of ((ex Prop) b)
% 3.57/3.75 Found ((ex_intro01 x) (fun (P0:(Prop->Prop)) (x00:(P0 x))=> x00)) as proof of ((ex Prop) b)
% 3.57/3.75 Found (((ex_intro0 b) x) (fun (P0:(Prop->Prop)) (x00:(P0 x))=> x00)) as proof of ((ex Prop) b)
% 3.57/3.75 Found (((ex_intro0 b) x) (fun (P0:(Prop->Prop)) (x00:(P0 x))=> x00)) as proof of ((ex Prop) b)
% 3.57/3.75 Found (((ex_intro0 b) x) (fun (P0:(Prop->Prop)) (x00:(P0 x))=> x00)) as proof of (P b)
% 3.57/3.75 Found ((eq_sym0000 (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))) (((ex_intro0 b) x) (fun (P0:(Prop->Prop)) (x00:(P0 x))=> x00))) as proof of ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 3.57/3.75 Found ((eq_sym0000 (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))) (((ex_intro0 b) x) (fun (P0:(Prop->Prop)) (x00:(P0 x))=> x00))) as proof of ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 3.57/3.75 Found (((fun (x0:(((eq (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) b))=> ((eq_sym000 x0) (ex Prop))) (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))) (((ex_intro0 b) x) (fun (P0:(Prop->Prop)) (x00:(P0 x))=> x00))) as proof of ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 3.65/3.85 Found (((fun (x0:(((eq (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) (fun (x01:Prop)=> (forall (P:(Prop->Prop)), ((P x)->(P x01))))))=> (((eq_sym00 (fun (x01:Prop)=> (forall (P:(Prop->Prop)), ((P x)->(P x01))))) x0) (ex Prop))) (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))) (((ex_intro0 (fun (x01:Prop)=> (forall (P:(Prop->Prop)), ((P x)->(P x01))))) x) (fun (P0:(Prop->Prop)) (x00:(P0 x))=> x00))) as proof of ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 3.65/3.85 Found (((fun (x0:(((eq (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) (fun (x01:Prop)=> (forall (P:(Prop->Prop)), ((P x)->(P x01))))))=> ((((eq_sym0 (fun (Xy:Prop)=> (((eq Prop) x) Xy))) (fun (x01:Prop)=> (forall (P:(Prop->Prop)), ((P x)->(P x01))))) x0) (ex Prop))) (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))) (((ex_intro0 (fun (x01:Prop)=> (forall (P:(Prop->Prop)), ((P x)->(P x01))))) x) (fun (P0:(Prop->Prop)) (x00:(P0 x))=> x00))) as proof of ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 3.65/3.85 Found (((fun (x0:(((eq (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) (fun (x01:Prop)=> (forall (P:(Prop->Prop)), ((P x)->(P x01))))))=> (((((eq_sym (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) (fun (x01:Prop)=> (forall (P:(Prop->Prop)), ((P x)->(P x01))))) x0) (ex Prop))) (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))) (((ex_intro0 (fun (x01:Prop)=> (forall (P:(Prop->Prop)), ((P x)->(P x01))))) x) (fun (P0:(Prop->Prop)) (x00:(P0 x))=> x00))) as proof of ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 3.65/3.85 Found (((fun (x0:(((eq (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) (fun (x01:Prop)=> (forall (P:(Prop->Prop)), ((P x)->(P x01))))))=> (((((eq_sym (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) (fun (x01:Prop)=> (forall (P:(Prop->Prop)), ((P x)->(P x01))))) x0) (ex Prop))) (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))) (((ex_intro0 (fun (x01:Prop)=> (forall (P:(Prop->Prop)), ((P x)->(P x01))))) x) (fun (P0:(Prop->Prop)) (x00:(P0 x))=> x00))) as proof of ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 3.65/3.85 Found (ex_intro000 (((fun (x0:(((eq (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) (fun (x01:Prop)=> (forall (P:(Prop->Prop)), ((P x)->(P x01))))))=> (((((eq_sym (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) (fun (x01:Prop)=> (forall (P:(Prop->Prop)), ((P x)->(P x01))))) x0) (ex Prop))) (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))) (((ex_intro0 (fun (x01:Prop)=> (forall (P:(Prop->Prop)), ((P x)->(P x01))))) x) (fun (P0:(Prop->Prop)) (x00:(P0 x))=> x00)))) as proof of ((ex Prop) (fun (Xx:Prop)=> ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) Xx) Xy)))))
% 3.65/3.85 Found x00:(P0 x)
% 3.65/3.85 Instantiate: x0:=x:Prop
% 3.65/3.85 Found (fun (x00:(P0 x))=> x00) as proof of (P0 x0)
% 3.65/3.85 Found (fun (P0:(Prop->Prop)) (x00:(P0 x))=> x00) as proof of ((P0 x)->(P0 x0))
% 3.65/3.85 Found (fun (P0:(Prop->Prop)) (x00:(P0 x))=> x00) as proof of (b x0)
% 3.65/3.85 Found (ex_intro010 (fun (P0:(Prop->Prop)) (x00:(P0 x))=> x00)) as proof of ((ex Prop) b)
% 3.65/3.85 Found ((ex_intro01 x) (fun (P0:(Prop->Prop)) (x00:(P0 x))=> x00)) as proof of ((ex Prop) b)
% 3.65/3.85 Found (((ex_intro0 b) x) (fun (P0:(Prop->Prop)) (x00:(P0 x))=> x00)) as proof of ((ex Prop) b)
% 3.65/3.85 Found (((ex_intro0 b) x) (fun (P0:(Prop->Prop)) (x00:(P0 x))=> x00)) as proof of ((ex Prop) b)
% 3.65/3.85 Found (((ex_intro0 b) x) (fun (P0:(Prop->Prop)) (x00:(P0 x))=> x00)) as proof of (P b)
% 3.65/3.85 Found ((eq_sym0000 (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) ((eq Prop) x))) (((ex_intro0 b) x) (fun (P0:(Prop->Prop)) (x00:(P0 x))=> x00))) as proof of ((ex Prop) ((eq Prop) x))
% 3.65/3.85 Found ((eq_sym0000 (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) ((eq Prop) x))) (((ex_intro0 b) x) (fun (P0:(Prop->Prop)) (x00:(P0 x))=> x00))) as proof of ((ex Prop) ((eq Prop) x))
% 3.87/4.03 Found (((fun (x0:(((eq (Prop->Prop)) ((eq Prop) x)) b))=> ((eq_sym000 x0) (ex Prop))) (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) ((eq Prop) x))) (((ex_intro0 b) x) (fun (P0:(Prop->Prop)) (x00:(P0 x))=> x00))) as proof of ((ex Prop) ((eq Prop) x))
% 3.87/4.03 Found (((fun (x0:(((eq (Prop->Prop)) ((eq Prop) x)) (fun (x01:Prop)=> (forall (P:(Prop->Prop)), ((P x)->(P x01))))))=> (((eq_sym00 (fun (x01:Prop)=> (forall (P:(Prop->Prop)), ((P x)->(P x01))))) x0) (ex Prop))) (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) ((eq Prop) x))) (((ex_intro0 (fun (x01:Prop)=> (forall (P:(Prop->Prop)), ((P x)->(P x01))))) x) (fun (P0:(Prop->Prop)) (x00:(P0 x))=> x00))) as proof of ((ex Prop) ((eq Prop) x))
% 3.87/4.03 Found (((fun (x0:(((eq (Prop->Prop)) ((eq Prop) x)) (fun (x01:Prop)=> (forall (P:(Prop->Prop)), ((P x)->(P x01))))))=> ((((eq_sym0 ((eq Prop) x)) (fun (x01:Prop)=> (forall (P:(Prop->Prop)), ((P x)->(P x01))))) x0) (ex Prop))) (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) ((eq Prop) x))) (((ex_intro0 (fun (x01:Prop)=> (forall (P:(Prop->Prop)), ((P x)->(P x01))))) x) (fun (P0:(Prop->Prop)) (x00:(P0 x))=> x00))) as proof of ((ex Prop) ((eq Prop) x))
% 3.87/4.03 Found (((fun (x0:(((eq (Prop->Prop)) ((eq Prop) x)) (fun (x01:Prop)=> (forall (P:(Prop->Prop)), ((P x)->(P x01))))))=> (((((eq_sym (Prop->Prop)) ((eq Prop) x)) (fun (x01:Prop)=> (forall (P:(Prop->Prop)), ((P x)->(P x01))))) x0) (ex Prop))) (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) ((eq Prop) x))) (((ex_intro0 (fun (x01:Prop)=> (forall (P:(Prop->Prop)), ((P x)->(P x01))))) x) (fun (P0:(Prop->Prop)) (x00:(P0 x))=> x00))) as proof of ((ex Prop) ((eq Prop) x))
% 3.87/4.03 Found (((fun (x0:(((eq (Prop->Prop)) ((eq Prop) x)) (fun (x01:Prop)=> (forall (P:(Prop->Prop)), ((P x)->(P x01))))))=> (((((eq_sym (Prop->Prop)) ((eq Prop) x)) (fun (x01:Prop)=> (forall (P:(Prop->Prop)), ((P x)->(P x01))))) x0) (ex Prop))) (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) ((eq Prop) x))) (((ex_intro0 (fun (x01:Prop)=> (forall (P:(Prop->Prop)), ((P x)->(P x01))))) x) (fun (P0:(Prop->Prop)) (x00:(P0 x))=> x00))) as proof of ((ex Prop) ((eq Prop) x))
% 3.87/4.03 Found (ex_intro000 (((fun (x0:(((eq (Prop->Prop)) ((eq Prop) x)) (fun (x01:Prop)=> (forall (P:(Prop->Prop)), ((P x)->(P x01))))))=> (((((eq_sym (Prop->Prop)) ((eq Prop) x)) (fun (x01:Prop)=> (forall (P:(Prop->Prop)), ((P x)->(P x01))))) x0) (ex Prop))) (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) ((eq Prop) x))) (((ex_intro0 (fun (x01:Prop)=> (forall (P:(Prop->Prop)), ((P x)->(P x01))))) x) (fun (P0:(Prop->Prop)) (x00:(P0 x))=> x00)))) as proof of ((ex Prop) (fun (Xx:Prop)=> ((ex Prop) ((eq Prop) Xx))))
% 3.87/4.03 Found eq_ref00:=(eq_ref0 (fun (Xx:Prop)=> ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) Xx) Xy))))):(((eq (Prop->Prop)) (fun (Xx:Prop)=> ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) Xx) Xy))))) (fun (Xx:Prop)=> ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) Xx) Xy)))))
% 3.87/4.03 Found (eq_ref0 (fun (Xx:Prop)=> ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) Xx) Xy))))) as proof of (((eq (Prop->Prop)) (fun (Xx:Prop)=> ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) Xx) Xy))))) b0)
% 3.87/4.03 Found ((eq_ref (Prop->Prop)) (fun (Xx:Prop)=> ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) Xx) Xy))))) as proof of (((eq (Prop->Prop)) (fun (Xx:Prop)=> ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) Xx) Xy))))) b0)
% 3.87/4.03 Found ((eq_ref (Prop->Prop)) (fun (Xx:Prop)=> ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) Xx) Xy))))) as proof of (((eq (Prop->Prop)) (fun (Xx:Prop)=> ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) Xx) Xy))))) b0)
% 3.87/4.03 Found ((eq_ref (Prop->Prop)) (fun (Xx:Prop)=> ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) Xx) Xy))))) as proof of (((eq (Prop->Prop)) (fun (Xx:Prop)=> ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) Xx) Xy))))) b0)
% 3.87/4.03 Found eq_ref00:=(eq_ref0 (fun (Xx:Prop)=> ((ex Prop) ((eq Prop) Xx)))):(((eq (Prop->Prop)) (fun (Xx:Prop)=> ((ex Prop) ((eq Prop) Xx)))) (fun (Xx:Prop)=> ((ex Prop) ((eq Prop) Xx))))
% 3.87/4.03 Found (eq_ref0 (fun (Xx:Prop)=> ((ex Prop) ((eq Prop) Xx)))) as proof of (((eq (Prop->Prop)) (fun (Xx:Prop)=> ((ex Prop) ((eq Prop) Xx)))) b0)
% 3.87/4.03 Found ((eq_ref (Prop->Prop)) (fun (Xx:Prop)=> ((ex Prop) ((eq Prop) Xx)))) as proof of (((eq (Prop->Prop)) (fun (Xx:Prop)=> ((ex Prop) ((eq Prop) Xx)))) b0)
% 7.53/7.71 Found ((eq_ref (Prop->Prop)) (fun (Xx:Prop)=> ((ex Prop) ((eq Prop) Xx)))) as proof of (((eq (Prop->Prop)) (fun (Xx:Prop)=> ((ex Prop) ((eq Prop) Xx)))) b0)
% 7.53/7.71 Found ((eq_ref (Prop->Prop)) (fun (Xx:Prop)=> ((ex Prop) ((eq Prop) Xx)))) as proof of (((eq (Prop->Prop)) (fun (Xx:Prop)=> ((ex Prop) ((eq Prop) Xx)))) b0)
% 7.53/7.71 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 7.53/7.71 Found (eq_ref0 x) as proof of (((eq Prop) x) x0)
% 7.53/7.71 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) x0)
% 7.53/7.71 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) x0)
% 7.53/7.71 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) x0)
% 7.53/7.71 Found (ex_intro010 ((eq_ref Prop) x)) as proof of ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 7.53/7.71 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 7.53/7.71 Found (eq_ref0 x) as proof of (((eq Prop) x) x0)
% 7.53/7.71 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) x0)
% 7.53/7.71 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) x0)
% 7.53/7.71 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) x0)
% 7.53/7.71 Found (ex_intro010 ((eq_ref Prop) x)) as proof of ((ex Prop) ((eq Prop) x))
% 7.53/7.71 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 7.53/7.71 Found (eq_ref0 x) as proof of (((eq Prop) x) x0)
% 7.53/7.71 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) x0)
% 7.53/7.71 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) x0)
% 7.53/7.71 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) x0)
% 7.53/7.71 Found (ex_intro010 ((eq_ref Prop) x)) as proof of ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 7.53/7.71 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 7.53/7.71 Found (eq_ref0 x) as proof of (((eq Prop) x) x0)
% 7.53/7.71 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) x0)
% 7.53/7.71 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) x0)
% 7.53/7.71 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) x0)
% 7.53/7.71 Found (ex_intro010 ((eq_ref Prop) x)) as proof of ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 7.53/7.71 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 7.53/7.71 Found (eq_ref0 x) as proof of (((eq Prop) x) x0)
% 7.53/7.71 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) x0)
% 7.53/7.71 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) x0)
% 7.53/7.71 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) x0)
% 7.53/7.71 Found (ex_intro010 ((eq_ref Prop) x)) as proof of ((ex Prop) ((eq Prop) x))
% 7.53/7.71 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 7.53/7.71 Found (eq_ref0 x) as proof of (((eq Prop) x) x0)
% 7.53/7.71 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) x0)
% 7.53/7.71 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) x0)
% 7.53/7.71 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) x0)
% 7.53/7.71 Found (ex_intro010 ((eq_ref Prop) x)) as proof of ((ex Prop) ((eq Prop) x))
% 7.53/7.71 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 7.53/7.71 Found (eq_ref0 x) as proof of (((eq Prop) x) x0)
% 7.53/7.71 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) x0)
% 7.53/7.71 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) x0)
% 7.53/7.71 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) x0)
% 7.53/7.71 Found (ex_intro010 ((eq_ref Prop) x)) as proof of ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 7.53/7.71 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 7.53/7.71 Found (eq_ref0 x) as proof of (((eq Prop) x) x0)
% 7.53/7.71 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) x0)
% 7.53/7.71 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) x0)
% 7.53/7.71 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) x0)
% 7.53/7.71 Found (ex_intro010 ((eq_ref Prop) x)) as proof of ((ex Prop) ((eq Prop) x))
% 7.53/7.71 Found eq_ref00:=(eq_ref0 (fun (Xy:Prop)=> (((eq Prop) x) Xy))):(((eq (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 7.53/7.71 Found (eq_ref0 (fun (Xy:Prop)=> (((eq Prop) x) Xy))) as proof of (((eq (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) b0)
% 7.53/7.71 Found ((eq_ref (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) as proof of (((eq (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) b0)
% 7.53/7.71 Found ((eq_ref (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) as proof of (((eq (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) b0)
% 7.53/7.71 Found ((eq_ref (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) as proof of (((eq (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) b0)
% 7.53/7.71 Found eq_ref00:=(eq_ref0 ((eq Prop) x)):(((eq (Prop->Prop)) ((eq Prop) x)) ((eq Prop) x))
% 7.53/7.71 Found (eq_ref0 ((eq Prop) x)) as proof of (((eq (Prop->Prop)) ((eq Prop) x)) b0)
% 7.53/7.71 Found ((eq_ref (Prop->Prop)) ((eq Prop) x)) as proof of (((eq (Prop->Prop)) ((eq Prop) x)) b0)
% 8.11/8.28 Found ((eq_ref (Prop->Prop)) ((eq Prop) x)) as proof of (((eq (Prop->Prop)) ((eq Prop) x)) b0)
% 8.11/8.28 Found ((eq_ref (Prop->Prop)) ((eq Prop) x)) as proof of (((eq (Prop->Prop)) ((eq Prop) x)) b0)
% 8.11/8.28 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xy:Prop)=> (((eq Prop) x) Xy))):(((eq (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) (fun (x0:Prop)=> (((eq Prop) x) x0)))
% 8.11/8.28 Found (eta_expansion_dep00 (fun (Xy:Prop)=> (((eq Prop) x) Xy))) as proof of (((eq (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) b)
% 8.11/8.28 Found ((eta_expansion_dep0 (fun (x1:Prop)=> Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) as proof of (((eq (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) b)
% 8.11/8.28 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) as proof of (((eq (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) b)
% 8.11/8.28 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) as proof of (((eq (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) b)
% 8.11/8.28 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) as proof of (((eq (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) b)
% 8.11/8.28 Found eta_expansion000:=(eta_expansion00 (fun (Xy:Prop)=> (((eq Prop) x) Xy))):(((eq (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) (fun (x0:Prop)=> (((eq Prop) x) x0)))
% 8.11/8.28 Found (eta_expansion00 (fun (Xy:Prop)=> (((eq Prop) x) Xy))) as proof of (((eq (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) b)
% 8.11/8.28 Found ((eta_expansion0 Prop) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) as proof of (((eq (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) b)
% 8.11/8.28 Found (((eta_expansion Prop) Prop) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) as proof of (((eq (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) b)
% 8.11/8.28 Found (((eta_expansion Prop) Prop) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) as proof of (((eq (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) b)
% 8.11/8.28 Found (((eta_expansion Prop) Prop) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) as proof of (((eq (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) b)
% 8.11/8.28 Found eq_ref00:=(eq_ref0 (f0 x0)):(((eq Prop) (f0 x0)) (f0 x0))
% 8.11/8.28 Found (eq_ref0 (f0 x0)) as proof of (((eq Prop) (f0 x0)) (((eq Prop) x) x0))
% 8.11/8.28 Found ((eq_ref Prop) (f0 x0)) as proof of (((eq Prop) (f0 x0)) (((eq Prop) x) x0))
% 8.11/8.28 Found ((eq_ref Prop) (f0 x0)) as proof of (((eq Prop) (f0 x0)) (((eq Prop) x) x0))
% 8.11/8.28 Found (fun (x0:Prop)=> ((eq_ref Prop) (f0 x0))) as proof of (((eq Prop) (f0 x0)) (((eq Prop) x) x0))
% 8.11/8.28 Found (fun (x0:Prop)=> ((eq_ref Prop) (f0 x0))) as proof of (forall (x0:Prop), (((eq Prop) (f0 x0)) (((eq Prop) x) x0)))
% 8.11/8.28 Found eq_ref00:=(eq_ref0 (f0 x0)):(((eq Prop) (f0 x0)) (f0 x0))
% 8.11/8.28 Found (eq_ref0 (f0 x0)) as proof of (((eq Prop) (f0 x0)) (((eq Prop) x) x0))
% 8.11/8.28 Found ((eq_ref Prop) (f0 x0)) as proof of (((eq Prop) (f0 x0)) (((eq Prop) x) x0))
% 8.11/8.28 Found ((eq_ref Prop) (f0 x0)) as proof of (((eq Prop) (f0 x0)) (((eq Prop) x) x0))
% 8.11/8.28 Found (fun (x0:Prop)=> ((eq_ref Prop) (f0 x0))) as proof of (((eq Prop) (f0 x0)) (((eq Prop) x) x0))
% 8.11/8.28 Found (fun (x0:Prop)=> ((eq_ref Prop) (f0 x0))) as proof of (forall (x0:Prop), (((eq Prop) (f0 x0)) (((eq Prop) x) x0)))
% 8.11/8.28 Found eta_expansion_dep000:=(eta_expansion_dep00 ((eq Prop) x)):(((eq (Prop->Prop)) ((eq Prop) x)) (fun (x0:Prop)=> (((eq Prop) x) x0)))
% 8.11/8.28 Found (eta_expansion_dep00 ((eq Prop) x)) as proof of (((eq (Prop->Prop)) ((eq Prop) x)) b)
% 8.11/8.28 Found ((eta_expansion_dep0 (fun (x1:Prop)=> Prop)) ((eq Prop) x)) as proof of (((eq (Prop->Prop)) ((eq Prop) x)) b)
% 8.11/8.28 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) ((eq Prop) x)) as proof of (((eq (Prop->Prop)) ((eq Prop) x)) b)
% 8.11/8.28 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) ((eq Prop) x)) as proof of (((eq (Prop->Prop)) ((eq Prop) x)) b)
% 8.11/8.28 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) ((eq Prop) x)) as proof of (((eq (Prop->Prop)) ((eq Prop) x)) b)
% 8.11/8.28 Found eq_ref00:=(eq_ref0 ((eq Prop) x)):(((eq (Prop->Prop)) ((eq Prop) x)) ((eq Prop) x))
% 8.11/8.28 Found (eq_ref0 ((eq Prop) x)) as proof of (((eq (Prop->Prop)) ((eq Prop) x)) b)
% 8.11/8.28 Found ((eq_ref (Prop->Prop)) ((eq Prop) x)) as proof of (((eq (Prop->Prop)) ((eq Prop) x)) b)
% 8.86/9.04 Found ((eq_ref (Prop->Prop)) ((eq Prop) x)) as proof of (((eq (Prop->Prop)) ((eq Prop) x)) b)
% 8.86/9.04 Found ((eq_ref (Prop->Prop)) ((eq Prop) x)) as proof of (((eq (Prop->Prop)) ((eq Prop) x)) b)
% 8.86/9.04 Found eq_ref00:=(eq_ref0 (f0 x0)):(((eq Prop) (f0 x0)) (f0 x0))
% 8.86/9.04 Found (eq_ref0 (f0 x0)) as proof of (((eq Prop) (f0 x0)) (((eq Prop) x) x0))
% 8.86/9.04 Found ((eq_ref Prop) (f0 x0)) as proof of (((eq Prop) (f0 x0)) (((eq Prop) x) x0))
% 8.86/9.04 Found ((eq_ref Prop) (f0 x0)) as proof of (((eq Prop) (f0 x0)) (((eq Prop) x) x0))
% 8.86/9.04 Found (fun (x0:Prop)=> ((eq_ref Prop) (f0 x0))) as proof of (((eq Prop) (f0 x0)) (((eq Prop) x) x0))
% 8.86/9.04 Found (fun (x0:Prop)=> ((eq_ref Prop) (f0 x0))) as proof of (forall (x0:Prop), (((eq Prop) (f0 x0)) (((eq Prop) x) x0)))
% 8.86/9.04 Found eq_ref00:=(eq_ref0 (f0 x0)):(((eq Prop) (f0 x0)) (f0 x0))
% 8.86/9.04 Found (eq_ref0 (f0 x0)) as proof of (((eq Prop) (f0 x0)) (((eq Prop) x) x0))
% 8.86/9.04 Found ((eq_ref Prop) (f0 x0)) as proof of (((eq Prop) (f0 x0)) (((eq Prop) x) x0))
% 8.86/9.04 Found ((eq_ref Prop) (f0 x0)) as proof of (((eq Prop) (f0 x0)) (((eq Prop) x) x0))
% 8.86/9.04 Found (fun (x0:Prop)=> ((eq_ref Prop) (f0 x0))) as proof of (((eq Prop) (f0 x0)) (((eq Prop) x) x0))
% 8.86/9.04 Found (fun (x0:Prop)=> ((eq_ref Prop) (f0 x0))) as proof of (forall (x0:Prop), (((eq Prop) (f0 x0)) (((eq Prop) x) x0)))
% 8.86/9.04 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 8.86/9.04 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (((eq Prop) x) x0))
% 8.86/9.04 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (((eq Prop) x) x0))
% 8.86/9.04 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (((eq Prop) x) x0))
% 8.86/9.04 Found (fun (x0:Prop)=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (((eq Prop) x) x0))
% 8.86/9.04 Found (fun (x0:Prop)=> ((eq_ref Prop) (f x0))) as proof of (forall (x0:Prop), (((eq Prop) (f x0)) (((eq Prop) x) x0)))
% 8.86/9.04 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 8.86/9.04 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (((eq Prop) x) x0))
% 8.86/9.04 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (((eq Prop) x) x0))
% 8.86/9.04 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (((eq Prop) x) x0))
% 8.86/9.04 Found (fun (x0:Prop)=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (((eq Prop) x) x0))
% 8.86/9.04 Found (fun (x0:Prop)=> ((eq_ref Prop) (f x0))) as proof of (forall (x0:Prop), (((eq Prop) (f x0)) (((eq Prop) x) x0)))
% 8.86/9.04 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 8.86/9.04 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (((eq Prop) x) x0))
% 8.86/9.04 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (((eq Prop) x) x0))
% 8.86/9.04 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (((eq Prop) x) x0))
% 8.86/9.04 Found (fun (x0:Prop)=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (((eq Prop) x) x0))
% 8.86/9.04 Found (fun (x0:Prop)=> ((eq_ref Prop) (f x0))) as proof of (forall (x0:Prop), (((eq Prop) (f x0)) (((eq Prop) x) x0)))
% 8.86/9.04 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 8.86/9.04 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (((eq Prop) x) x0))
% 8.86/9.04 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (((eq Prop) x) x0))
% 8.86/9.04 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (((eq Prop) x) x0))
% 8.86/9.04 Found (fun (x0:Prop)=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (((eq Prop) x) x0))
% 8.86/9.04 Found (fun (x0:Prop)=> ((eq_ref Prop) (f x0))) as proof of (forall (x0:Prop), (((eq Prop) (f x0)) (((eq Prop) x) x0)))
% 8.86/9.04 Found eta_expansion_dep000:=(eta_expansion_dep00 a):(((eq (Prop->Prop)) a) (fun (x:Prop)=> (a x)))
% 8.86/9.04 Found (eta_expansion_dep00 a) as proof of (((eq (Prop->Prop)) a) b)
% 8.86/9.04 Found ((eta_expansion_dep0 (fun (x1:Prop)=> Prop)) a) as proof of (((eq (Prop->Prop)) a) b)
% 8.86/9.04 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) a) as proof of (((eq (Prop->Prop)) a) b)
% 8.86/9.04 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) a) as proof of (((eq (Prop->Prop)) a) b)
% 8.86/9.04 Found eta_expansion_dep000:=(eta_expansion_dep00 a):(((eq (Prop->Prop)) a) (fun (x:Prop)=> (a x)))
% 8.86/9.04 Found (eta_expansion_dep00 a) as proof of (((eq (Prop->Prop)) a) b)
% 8.86/9.04 Found ((eta_expansion_dep0 (fun (x1:Prop)=> Prop)) a) as proof of (((eq (Prop->Prop)) a) b)
% 8.86/9.04 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) a) as proof of (((eq (Prop->Prop)) a) b)
% 14.82/15.04 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) a) as proof of (((eq (Prop->Prop)) a) b)
% 14.82/15.04 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 14.82/15.04 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b)
% 14.82/15.04 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 14.82/15.04 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 14.82/15.04 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 14.82/15.04 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 14.82/15.04 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq Prop) x) x0))
% 14.82/15.04 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x) x0))
% 14.82/15.04 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x) x0))
% 14.82/15.04 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x) x0))
% 14.82/15.04 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 14.82/15.04 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b)
% 14.82/15.04 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 14.82/15.04 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 14.82/15.04 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 14.82/15.04 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 14.82/15.04 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq Prop) x) x0))
% 14.82/15.04 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x) x0))
% 14.82/15.04 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x) x0))
% 14.82/15.04 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x) x0))
% 14.82/15.04 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 14.82/15.04 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b)
% 14.82/15.04 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 14.82/15.04 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 14.82/15.04 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 14.82/15.04 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 14.82/15.04 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq Prop) x) x0))
% 14.82/15.04 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x) x0))
% 14.82/15.04 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x) x0))
% 14.82/15.04 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x) x0))
% 14.82/15.04 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 14.82/15.04 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b)
% 14.82/15.04 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 14.82/15.04 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 14.82/15.04 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 14.82/15.04 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 14.82/15.04 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq Prop) x) x0))
% 14.82/15.04 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x) x0))
% 14.82/15.04 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x) x0))
% 14.82/15.04 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x) x0))
% 14.82/15.04 Found x11:(P1 (f x0))
% 14.82/15.04 Found (fun (x11:(P1 (f x0)))=> x11) as proof of (P1 (f x0))
% 14.82/15.04 Found (fun (x11:(P1 (f x0)))=> x11) as proof of (P2 (f x0))
% 14.82/15.04 Found x11:(P1 (f x0))
% 14.82/15.04 Found (fun (x11:(P1 (f x0)))=> x11) as proof of (P1 (f x0))
% 14.82/15.04 Found (fun (x11:(P1 (f x0)))=> x11) as proof of (P2 (f x0))
% 14.82/15.04 Found x11:(P1 (f x0))
% 14.82/15.04 Found (fun (x11:(P1 (f x0)))=> x11) as proof of (P1 (f x0))
% 14.82/15.04 Found (fun (x11:(P1 (f x0)))=> x11) as proof of (P2 (f x0))
% 14.82/15.04 Found x11:(P1 (f x0))
% 14.82/15.04 Found (fun (x11:(P1 (f x0)))=> x11) as proof of (P1 (f x0))
% 14.82/15.04 Found (fun (x11:(P1 (f x0)))=> x11) as proof of (P2 (f x0))
% 14.82/15.04 Found eq_ref00:=(eq_ref0 (((eq Prop) x) x0)):(((eq Prop) (((eq Prop) x) x0)) (((eq Prop) x) x0))
% 14.82/15.04 Found (eq_ref0 (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 14.82/15.04 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 14.82/15.04 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 14.82/15.04 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 14.82/15.04 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 14.82/15.04 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x0))
% 14.82/15.04 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 14.82/15.04 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 14.82/15.04 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 14.82/15.04 Found eq_ref00:=(eq_ref0 (((eq Prop) x) x0)):(((eq Prop) (((eq Prop) x) x0)) (((eq Prop) x) x0))
% 14.82/15.04 Found (eq_ref0 (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 20.41/20.67 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 20.41/20.67 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 20.41/20.67 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 20.41/20.67 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 20.41/20.67 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x0))
% 20.41/20.67 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 20.41/20.67 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 20.41/20.67 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 20.41/20.67 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 20.41/20.67 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x0))
% 20.41/20.67 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 20.41/20.67 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 20.41/20.67 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 20.41/20.67 Found eq_ref00:=(eq_ref0 (((eq Prop) x) x0)):(((eq Prop) (((eq Prop) x) x0)) (((eq Prop) x) x0))
% 20.41/20.67 Found (eq_ref0 (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 20.41/20.67 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 20.41/20.67 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 20.41/20.67 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 20.41/20.67 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 20.41/20.67 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x0))
% 20.41/20.67 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 20.41/20.67 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 20.41/20.67 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 20.41/20.67 Found eq_ref00:=(eq_ref0 (((eq Prop) x) x0)):(((eq Prop) (((eq Prop) x) x0)) (((eq Prop) x) x0))
% 20.41/20.67 Found (eq_ref0 (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 20.41/20.67 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 20.41/20.67 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 20.41/20.67 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 20.41/20.67 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 20.41/20.67 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b)
% 20.41/20.67 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 20.41/20.67 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 20.41/20.67 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 20.41/20.67 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 20.41/20.67 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq Prop) x) x0))
% 20.41/20.67 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x) x0))
% 20.41/20.67 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x) x0))
% 20.41/20.67 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x) x0))
% 20.41/20.67 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 20.41/20.67 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b)
% 20.41/20.67 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 20.41/20.67 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 20.41/20.67 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 20.41/20.67 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 20.41/20.67 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq Prop) x) x0))
% 20.41/20.67 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x) x0))
% 20.41/20.67 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x) x0))
% 20.41/20.67 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x) x0))
% 20.41/20.67 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 20.41/20.67 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b)
% 20.41/20.67 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 20.41/20.67 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 20.41/20.67 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 20.41/20.67 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 20.41/20.67 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq Prop) x) x0))
% 20.41/20.67 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x) x0))
% 20.41/20.67 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x) x0))
% 20.41/20.67 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x) x0))
% 20.41/20.67 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 20.41/20.67 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b)
% 20.41/20.67 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 29.34/29.52 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 29.34/29.52 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 29.34/29.52 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 29.34/29.52 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq Prop) x) x0))
% 29.34/29.52 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x) x0))
% 29.34/29.52 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x) x0))
% 29.34/29.52 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x) x0))
% 29.34/29.52 Found x11:(P1 (f x0))
% 29.34/29.52 Found (fun (x11:(P1 (f x0)))=> x11) as proof of (P1 (f x0))
% 29.34/29.52 Found (fun (x11:(P1 (f x0)))=> x11) as proof of (P2 (f x0))
% 29.34/29.52 Found x11:(P1 (f x0))
% 29.34/29.52 Found (fun (x11:(P1 (f x0)))=> x11) as proof of (P1 (f x0))
% 29.34/29.52 Found (fun (x11:(P1 (f x0)))=> x11) as proof of (P2 (f x0))
% 29.34/29.52 Found x11:(P1 (f x0))
% 29.34/29.52 Found (fun (x11:(P1 (f x0)))=> x11) as proof of (P1 (f x0))
% 29.34/29.52 Found (fun (x11:(P1 (f x0)))=> x11) as proof of (P2 (f x0))
% 29.34/29.52 Found x11:(P1 (f x0))
% 29.34/29.52 Found (fun (x11:(P1 (f x0)))=> x11) as proof of (P1 (f x0))
% 29.34/29.52 Found (fun (x11:(P1 (f x0)))=> x11) as proof of (P2 (f x0))
% 29.34/29.52 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 29.34/29.52 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x0))
% 29.34/29.52 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 29.34/29.52 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 29.34/29.52 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 29.34/29.52 Found eq_ref00:=(eq_ref0 (((eq Prop) x) x0)):(((eq Prop) (((eq Prop) x) x0)) (((eq Prop) x) x0))
% 29.34/29.52 Found (eq_ref0 (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 29.34/29.52 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 29.34/29.52 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 29.34/29.52 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 29.34/29.52 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 29.34/29.52 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x0))
% 29.34/29.52 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 29.34/29.52 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 29.34/29.52 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 29.34/29.52 Found eq_ref00:=(eq_ref0 (((eq Prop) x) x0)):(((eq Prop) (((eq Prop) x) x0)) (((eq Prop) x) x0))
% 29.34/29.52 Found (eq_ref0 (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 29.34/29.52 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 29.34/29.52 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 29.34/29.52 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 29.34/29.52 Found eq_ref00:=(eq_ref0 (((eq Prop) x) x0)):(((eq Prop) (((eq Prop) x) x0)) (((eq Prop) x) x0))
% 29.34/29.52 Found (eq_ref0 (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 29.34/29.52 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 29.34/29.52 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 29.34/29.52 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 29.34/29.52 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 29.34/29.52 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x0))
% 29.34/29.52 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 29.34/29.52 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 29.34/29.52 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 29.34/29.52 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 29.34/29.52 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x0))
% 29.34/29.52 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 29.34/29.52 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 29.34/29.52 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 29.34/29.52 Found eq_ref00:=(eq_ref0 (((eq Prop) x) x0)):(((eq Prop) (((eq Prop) x) x0)) (((eq Prop) x) x0))
% 29.34/29.52 Found (eq_ref0 (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 29.34/29.52 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 29.34/29.52 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 29.34/29.52 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 29.34/29.52 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 29.34/29.52 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x0))
% 29.34/29.52 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 29.34/29.52 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 37.73/37.89 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 37.73/37.89 Found eq_ref00:=(eq_ref0 (((eq Prop) x) x0)):(((eq Prop) (((eq Prop) x) x0)) (((eq Prop) x) x0))
% 37.73/37.89 Found (eq_ref0 (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 37.73/37.89 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 37.73/37.89 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 37.73/37.89 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 37.73/37.89 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 37.73/37.89 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x0))
% 37.73/37.89 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 37.73/37.89 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 37.73/37.89 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 37.73/37.89 Found eq_ref00:=(eq_ref0 (((eq Prop) x) x0)):(((eq Prop) (((eq Prop) x) x0)) (((eq Prop) x) x0))
% 37.73/37.89 Found (eq_ref0 (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 37.73/37.89 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 37.73/37.89 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 37.73/37.89 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 37.73/37.89 Found eq_ref00:=(eq_ref0 (((eq Prop) x) x0)):(((eq Prop) (((eq Prop) x) x0)) (((eq Prop) x) x0))
% 37.73/37.89 Found (eq_ref0 (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 37.73/37.89 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 37.73/37.89 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 37.73/37.89 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 37.73/37.89 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 37.73/37.89 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x0))
% 37.73/37.89 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 37.73/37.89 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 37.73/37.89 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 37.73/37.89 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 37.73/37.89 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x0))
% 37.73/37.89 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 37.73/37.89 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 37.73/37.89 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 37.73/37.89 Found eq_ref00:=(eq_ref0 (((eq Prop) x) x0)):(((eq Prop) (((eq Prop) x) x0)) (((eq Prop) x) x0))
% 37.73/37.89 Found (eq_ref0 (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 37.73/37.89 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 37.73/37.89 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 37.73/37.89 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 37.73/37.89 Found eq_ref00:=(eq_ref0 (fun (Xy:Prop)=> (((eq Prop) x) Xy))):(((eq (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 37.73/37.89 Found (eq_ref0 (fun (Xy:Prop)=> (((eq Prop) x) Xy))) as proof of (((eq (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) b0)
% 37.73/37.89 Found ((eq_ref (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) as proof of (((eq (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) b0)
% 37.73/37.89 Found ((eq_ref (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) as proof of (((eq (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) b0)
% 37.73/37.89 Found ((eq_ref (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) as proof of (((eq (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) b0)
% 37.73/37.89 Found eq_ref00:=(eq_ref0 ((eq Prop) x)):(((eq (Prop->Prop)) ((eq Prop) x)) ((eq Prop) x))
% 37.73/37.89 Found (eq_ref0 ((eq Prop) x)) as proof of (((eq (Prop->Prop)) ((eq Prop) x)) b0)
% 37.73/37.89 Found ((eq_ref (Prop->Prop)) ((eq Prop) x)) as proof of (((eq (Prop->Prop)) ((eq Prop) x)) b0)
% 37.73/37.89 Found ((eq_ref (Prop->Prop)) ((eq Prop) x)) as proof of (((eq (Prop->Prop)) ((eq Prop) x)) b0)
% 37.73/37.89 Found ((eq_ref (Prop->Prop)) ((eq Prop) x)) as proof of (((eq (Prop->Prop)) ((eq Prop) x)) b0)
% 37.73/37.89 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 37.73/37.89 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (((eq Prop) x) x0))
% 37.73/37.89 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (((eq Prop) x) x0))
% 37.73/37.89 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (((eq Prop) x) x0))
% 38.05/38.22 Found (fun (x0:Prop)=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (((eq Prop) x) x0))
% 38.05/38.22 Found (fun (x0:Prop)=> ((eq_ref Prop) (f x0))) as proof of (forall (x0:Prop), (((eq Prop) (f x0)) (((eq Prop) x) x0)))
% 38.05/38.22 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 38.05/38.22 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (((eq Prop) x) x0))
% 38.05/38.22 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (((eq Prop) x) x0))
% 38.05/38.22 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (((eq Prop) x) x0))
% 38.05/38.22 Found (fun (x0:Prop)=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (((eq Prop) x) x0))
% 38.05/38.22 Found (fun (x0:Prop)=> ((eq_ref Prop) (f x0))) as proof of (forall (x0:Prop), (((eq Prop) (f x0)) (((eq Prop) x) x0)))
% 38.05/38.22 Found eta_expansion_dep000:=(eta_expansion_dep00 b0):(((eq (Prop->Prop)) b0) (fun (x:Prop)=> (b0 x)))
% 38.05/38.22 Found (eta_expansion_dep00 b0) as proof of (((eq (Prop->Prop)) b0) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 38.05/38.22 Found ((eta_expansion_dep0 (fun (x1:Prop)=> Prop)) b0) as proof of (((eq (Prop->Prop)) b0) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 38.05/38.22 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) b0) as proof of (((eq (Prop->Prop)) b0) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 38.05/38.22 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) b0) as proof of (((eq (Prop->Prop)) b0) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 38.05/38.22 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) b0) as proof of (((eq (Prop->Prop)) b0) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 38.05/38.22 Found eta_expansion000:=(eta_expansion00 a):(((eq (Prop->Prop)) a) (fun (x:Prop)=> (a x)))
% 38.05/38.22 Found (eta_expansion00 a) as proof of (((eq (Prop->Prop)) a) b0)
% 38.05/38.22 Found ((eta_expansion0 Prop) a) as proof of (((eq (Prop->Prop)) a) b0)
% 38.05/38.22 Found (((eta_expansion Prop) Prop) a) as proof of (((eq (Prop->Prop)) a) b0)
% 38.05/38.22 Found (((eta_expansion Prop) Prop) a) as proof of (((eq (Prop->Prop)) a) b0)
% 38.05/38.22 Found (((eta_expansion Prop) Prop) a) as proof of (((eq (Prop->Prop)) a) b0)
% 38.05/38.22 Found eq_ref00:=(eq_ref0 a):(((eq (Prop->Prop)) a) a)
% 38.05/38.22 Found (eq_ref0 a) as proof of (((eq (Prop->Prop)) a) b0)
% 38.05/38.22 Found ((eq_ref (Prop->Prop)) a) as proof of (((eq (Prop->Prop)) a) b0)
% 38.05/38.22 Found ((eq_ref (Prop->Prop)) a) as proof of (((eq (Prop->Prop)) a) b0)
% 38.05/38.22 Found ((eq_ref (Prop->Prop)) a) as proof of (((eq (Prop->Prop)) a) b0)
% 38.05/38.22 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 38.05/38.22 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (((eq Prop) x) x0))
% 38.05/38.22 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (((eq Prop) x) x0))
% 38.05/38.22 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (((eq Prop) x) x0))
% 38.05/38.22 Found (fun (x0:Prop)=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (((eq Prop) x) x0))
% 38.05/38.22 Found (fun (x0:Prop)=> ((eq_ref Prop) (f x0))) as proof of (forall (x0:Prop), (((eq Prop) (f x0)) (((eq Prop) x) x0)))
% 38.05/38.22 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 38.05/38.22 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (((eq Prop) x) x0))
% 38.05/38.22 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (((eq Prop) x) x0))
% 38.05/38.22 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (((eq Prop) x) x0))
% 38.05/38.22 Found (fun (x0:Prop)=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (((eq Prop) x) x0))
% 38.05/38.22 Found (fun (x0:Prop)=> ((eq_ref Prop) (f x0))) as proof of (forall (x0:Prop), (((eq Prop) (f x0)) (((eq Prop) x) x0)))
% 38.05/38.22 Found eta_expansion_dep000:=(eta_expansion_dep00 b0):(((eq (Prop->Prop)) b0) (fun (x:Prop)=> (b0 x)))
% 38.05/38.22 Found (eta_expansion_dep00 b0) as proof of (((eq (Prop->Prop)) b0) ((eq Prop) x))
% 38.05/38.22 Found ((eta_expansion_dep0 (fun (x1:Prop)=> Prop)) b0) as proof of (((eq (Prop->Prop)) b0) ((eq Prop) x))
% 38.05/38.22 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) b0) as proof of (((eq (Prop->Prop)) b0) ((eq Prop) x))
% 38.05/38.22 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) b0) as proof of (((eq (Prop->Prop)) b0) ((eq Prop) x))
% 38.05/38.22 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) b0) as proof of (((eq (Prop->Prop)) b0) ((eq Prop) x))
% 38.05/38.22 Found eta_expansion000:=(eta_expansion00 a):(((eq (Prop->Prop)) a) (fun (x:Prop)=> (a x)))
% 38.05/38.22 Found (eta_expansion00 a) as proof of (((eq (Prop->Prop)) a) b0)
% 39.12/39.31 Found ((eta_expansion0 Prop) a) as proof of (((eq (Prop->Prop)) a) b0)
% 39.12/39.31 Found (((eta_expansion Prop) Prop) a) as proof of (((eq (Prop->Prop)) a) b0)
% 39.12/39.31 Found (((eta_expansion Prop) Prop) a) as proof of (((eq (Prop->Prop)) a) b0)
% 39.12/39.31 Found (((eta_expansion Prop) Prop) a) as proof of (((eq (Prop->Prop)) a) b0)
% 39.12/39.31 Found eq_ref00:=(eq_ref0 a):(((eq (Prop->Prop)) a) a)
% 39.12/39.31 Found (eq_ref0 a) as proof of (((eq (Prop->Prop)) a) b0)
% 39.12/39.31 Found ((eq_ref (Prop->Prop)) a) as proof of (((eq (Prop->Prop)) a) b0)
% 39.12/39.31 Found ((eq_ref (Prop->Prop)) a) as proof of (((eq (Prop->Prop)) a) b0)
% 39.12/39.31 Found ((eq_ref (Prop->Prop)) a) as proof of (((eq (Prop->Prop)) a) b0)
% 39.12/39.31 Found eq_ref00:=(eq_ref0 b):(((eq (Prop->Prop)) b) b)
% 39.12/39.31 Found (eq_ref0 b) as proof of (((eq (Prop->Prop)) b) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 39.12/39.31 Found ((eq_ref (Prop->Prop)) b) as proof of (((eq (Prop->Prop)) b) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 39.12/39.31 Found ((eq_ref (Prop->Prop)) b) as proof of (((eq (Prop->Prop)) b) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 39.12/39.31 Found ((eq_ref (Prop->Prop)) b) as proof of (((eq (Prop->Prop)) b) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 39.12/39.31 Found eta_expansion000:=(eta_expansion00 a):(((eq (Prop->Prop)) a) (fun (x:Prop)=> (a x)))
% 39.12/39.31 Found (eta_expansion00 a) as proof of (((eq (Prop->Prop)) a) b)
% 39.12/39.31 Found ((eta_expansion0 Prop) a) as proof of (((eq (Prop->Prop)) a) b)
% 39.12/39.31 Found (((eta_expansion Prop) Prop) a) as proof of (((eq (Prop->Prop)) a) b)
% 39.12/39.31 Found (((eta_expansion Prop) Prop) a) as proof of (((eq (Prop->Prop)) a) b)
% 39.12/39.31 Found (((eta_expansion Prop) Prop) a) as proof of (((eq (Prop->Prop)) a) b)
% 39.12/39.31 Found eq_ref00:=(eq_ref0 a):(((eq (Prop->Prop)) a) a)
% 39.12/39.31 Found (eq_ref0 a) as proof of (((eq (Prop->Prop)) a) b)
% 39.12/39.31 Found ((eq_ref (Prop->Prop)) a) as proof of (((eq (Prop->Prop)) a) b)
% 39.12/39.31 Found ((eq_ref (Prop->Prop)) a) as proof of (((eq (Prop->Prop)) a) b)
% 39.12/39.31 Found ((eq_ref (Prop->Prop)) a) as proof of (((eq (Prop->Prop)) a) b)
% 39.12/39.31 Found eq_ref00:=(eq_ref0 b):(((eq (Prop->Prop)) b) b)
% 39.12/39.31 Found (eq_ref0 b) as proof of (((eq (Prop->Prop)) b) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 39.12/39.31 Found ((eq_ref (Prop->Prop)) b) as proof of (((eq (Prop->Prop)) b) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 39.12/39.31 Found ((eq_ref (Prop->Prop)) b) as proof of (((eq (Prop->Prop)) b) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 39.12/39.31 Found ((eq_ref (Prop->Prop)) b) as proof of (((eq (Prop->Prop)) b) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 39.12/39.31 Found eq_ref00:=(eq_ref0 a):(((eq (Prop->Prop)) a) a)
% 39.12/39.31 Found (eq_ref0 a) as proof of (((eq (Prop->Prop)) a) b)
% 39.12/39.31 Found ((eq_ref (Prop->Prop)) a) as proof of (((eq (Prop->Prop)) a) b)
% 39.12/39.31 Found ((eq_ref (Prop->Prop)) a) as proof of (((eq (Prop->Prop)) a) b)
% 39.12/39.31 Found ((eq_ref (Prop->Prop)) a) as proof of (((eq (Prop->Prop)) a) b)
% 39.12/39.31 Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq (Prop->Prop)) b) (fun (x:Prop)=> (b x)))
% 39.12/39.31 Found (eta_expansion_dep00 b) as proof of (((eq (Prop->Prop)) b) ((eq Prop) x))
% 39.12/39.31 Found ((eta_expansion_dep0 (fun (x1:Prop)=> Prop)) b) as proof of (((eq (Prop->Prop)) b) ((eq Prop) x))
% 39.12/39.31 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) b) as proof of (((eq (Prop->Prop)) b) ((eq Prop) x))
% 39.12/39.31 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) b) as proof of (((eq (Prop->Prop)) b) ((eq Prop) x))
% 39.12/39.31 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) b) as proof of (((eq (Prop->Prop)) b) ((eq Prop) x))
% 39.12/39.31 Found eq_ref00:=(eq_ref0 a):(((eq (Prop->Prop)) a) a)
% 39.12/39.31 Found (eq_ref0 a) as proof of (((eq (Prop->Prop)) a) b)
% 39.12/39.31 Found ((eq_ref (Prop->Prop)) a) as proof of (((eq (Prop->Prop)) a) b)
% 39.12/39.31 Found ((eq_ref (Prop->Prop)) a) as proof of (((eq (Prop->Prop)) a) b)
% 39.12/39.31 Found ((eq_ref (Prop->Prop)) a) as proof of (((eq (Prop->Prop)) a) b)
% 39.12/39.31 Found eq_ref00:=(eq_ref0 b):(((eq (Prop->Prop)) b) b)
% 39.12/39.31 Found (eq_ref0 b) as proof of (((eq (Prop->Prop)) b) ((eq Prop) x))
% 39.12/39.31 Found ((eq_ref (Prop->Prop)) b) as proof of (((eq (Prop->Prop)) b) ((eq Prop) x))
% 39.12/39.31 Found ((eq_ref (Prop->Prop)) b) as proof of (((eq (Prop->Prop)) b) ((eq Prop) x))
% 39.12/39.31 Found ((eq_ref (Prop->Prop)) b) as proof of (((eq (Prop->Prop)) b) ((eq Prop) x))
% 39.12/39.31 Found eta_expansion000:=(eta_expansion00 a):(((eq (Prop->Prop)) a) (fun (x:Prop)=> (a x)))
% 39.12/39.31 Found (eta_expansion00 a) as proof of (((eq (Prop->Prop)) a) b)
% 42.63/42.84 Found ((eta_expansion0 Prop) a) as proof of (((eq (Prop->Prop)) a) b)
% 42.63/42.84 Found (((eta_expansion Prop) Prop) a) as proof of (((eq (Prop->Prop)) a) b)
% 42.63/42.84 Found (((eta_expansion Prop) Prop) a) as proof of (((eq (Prop->Prop)) a) b)
% 42.63/42.84 Found (((eta_expansion Prop) Prop) a) as proof of (((eq (Prop->Prop)) a) b)
% 42.63/42.84 Found eq_ref00:=(eq_ref0 a):(((eq (Prop->Prop)) a) a)
% 42.63/42.84 Found (eq_ref0 a) as proof of (((eq (Prop->Prop)) a) b)
% 42.63/42.84 Found ((eq_ref (Prop->Prop)) a) as proof of (((eq (Prop->Prop)) a) b)
% 42.63/42.84 Found ((eq_ref (Prop->Prop)) a) as proof of (((eq (Prop->Prop)) a) b)
% 42.63/42.84 Found ((eq_ref (Prop->Prop)) a) as proof of (((eq (Prop->Prop)) a) b)
% 42.63/42.84 Found eta_expansion_dep000:=(eta_expansion_dep00 a):(((eq (Prop->Prop)) a) (fun (x:Prop)=> (a x)))
% 42.63/42.84 Found (eta_expansion_dep00 a) as proof of (((eq (Prop->Prop)) a) b0)
% 42.63/42.84 Found ((eta_expansion_dep0 (fun (x1:Prop)=> Prop)) a) as proof of (((eq (Prop->Prop)) a) b0)
% 42.63/42.84 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) a) as proof of (((eq (Prop->Prop)) a) b0)
% 42.63/42.84 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) a) as proof of (((eq (Prop->Prop)) a) b0)
% 42.63/42.84 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) a) as proof of (((eq (Prop->Prop)) a) b0)
% 42.63/42.84 Found eq_ref00:=(eq_ref0 b0):(((eq (Prop->Prop)) b0) b0)
% 42.63/42.84 Found (eq_ref0 b0) as proof of (((eq (Prop->Prop)) b0) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 42.63/42.84 Found ((eq_ref (Prop->Prop)) b0) as proof of (((eq (Prop->Prop)) b0) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 42.63/42.84 Found ((eq_ref (Prop->Prop)) b0) as proof of (((eq (Prop->Prop)) b0) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 42.63/42.84 Found ((eq_ref (Prop->Prop)) b0) as proof of (((eq (Prop->Prop)) b0) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 42.63/42.84 Found eta_expansion_dep000:=(eta_expansion_dep00 b0):(((eq (Prop->Prop)) b0) (fun (x:Prop)=> (b0 x)))
% 42.63/42.84 Found (eta_expansion_dep00 b0) as proof of (((eq (Prop->Prop)) b0) ((eq Prop) x))
% 42.63/42.84 Found ((eta_expansion_dep0 (fun (x1:Prop)=> Prop)) b0) as proof of (((eq (Prop->Prop)) b0) ((eq Prop) x))
% 42.63/42.84 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) b0) as proof of (((eq (Prop->Prop)) b0) ((eq Prop) x))
% 42.63/42.84 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) b0) as proof of (((eq (Prop->Prop)) b0) ((eq Prop) x))
% 42.63/42.84 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) b0) as proof of (((eq (Prop->Prop)) b0) ((eq Prop) x))
% 42.63/42.84 Found eta_expansion_dep000:=(eta_expansion_dep00 a):(((eq (Prop->Prop)) a) (fun (x:Prop)=> (a x)))
% 42.63/42.84 Found (eta_expansion_dep00 a) as proof of (((eq (Prop->Prop)) a) b0)
% 42.63/42.84 Found ((eta_expansion_dep0 (fun (x1:Prop)=> Prop)) a) as proof of (((eq (Prop->Prop)) a) b0)
% 42.63/42.84 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) a) as proof of (((eq (Prop->Prop)) a) b0)
% 42.63/42.84 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) a) as proof of (((eq (Prop->Prop)) a) b0)
% 42.63/42.84 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) a) as proof of (((eq (Prop->Prop)) a) b0)
% 42.63/42.84 Found eq_ref00:=(eq_ref0 (fun (Xx:Prop)=> ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) Xx) Xy))))):(((eq (Prop->Prop)) (fun (Xx:Prop)=> ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) Xx) Xy))))) (fun (Xx:Prop)=> ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) Xx) Xy)))))
% 42.63/42.84 Found (eq_ref0 (fun (Xx:Prop)=> ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) Xx) Xy))))) as proof of (((eq (Prop->Prop)) (fun (Xx:Prop)=> ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) Xx) Xy))))) b1)
% 42.63/42.84 Found ((eq_ref (Prop->Prop)) (fun (Xx:Prop)=> ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) Xx) Xy))))) as proof of (((eq (Prop->Prop)) (fun (Xx:Prop)=> ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) Xx) Xy))))) b1)
% 42.63/42.84 Found ((eq_ref (Prop->Prop)) (fun (Xx:Prop)=> ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) Xx) Xy))))) as proof of (((eq (Prop->Prop)) (fun (Xx:Prop)=> ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) Xx) Xy))))) b1)
% 42.63/42.84 Found ((eq_ref (Prop->Prop)) (fun (Xx:Prop)=> ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) Xx) Xy))))) as proof of (((eq (Prop->Prop)) (fun (Xx:Prop)=> ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) Xx) Xy))))) b1)
% 42.63/42.84 Found eta_expansion000:=(eta_expansion00 (fun (Xx:Prop)=> ((ex Prop) ((eq Prop) Xx)))):(((eq (Prop->Prop)) (fun (Xx:Prop)=> ((ex Prop) ((eq Prop) Xx)))) (fun (x:Prop)=> ((ex Prop) ((eq Prop) x))))
% 52.36/52.55 Found (eta_expansion00 (fun (Xx:Prop)=> ((ex Prop) ((eq Prop) Xx)))) as proof of (((eq (Prop->Prop)) (fun (Xx:Prop)=> ((ex Prop) ((eq Prop) Xx)))) b1)
% 52.36/52.55 Found ((eta_expansion0 Prop) (fun (Xx:Prop)=> ((ex Prop) ((eq Prop) Xx)))) as proof of (((eq (Prop->Prop)) (fun (Xx:Prop)=> ((ex Prop) ((eq Prop) Xx)))) b1)
% 52.36/52.55 Found (((eta_expansion Prop) Prop) (fun (Xx:Prop)=> ((ex Prop) ((eq Prop) Xx)))) as proof of (((eq (Prop->Prop)) (fun (Xx:Prop)=> ((ex Prop) ((eq Prop) Xx)))) b1)
% 52.36/52.55 Found (((eta_expansion Prop) Prop) (fun (Xx:Prop)=> ((ex Prop) ((eq Prop) Xx)))) as proof of (((eq (Prop->Prop)) (fun (Xx:Prop)=> ((ex Prop) ((eq Prop) Xx)))) b1)
% 52.36/52.55 Found (((eta_expansion Prop) Prop) (fun (Xx:Prop)=> ((ex Prop) ((eq Prop) Xx)))) as proof of (((eq (Prop->Prop)) (fun (Xx:Prop)=> ((ex Prop) ((eq Prop) Xx)))) b1)
% 52.36/52.55 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 52.36/52.55 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x0))
% 52.36/52.55 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 52.36/52.55 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 52.36/52.55 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 52.36/52.55 Found eq_ref00:=(eq_ref0 (((eq Prop) x) x0)):(((eq Prop) (((eq Prop) x) x0)) (((eq Prop) x) x0))
% 52.36/52.55 Found (eq_ref0 (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 52.36/52.55 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 52.36/52.55 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 52.36/52.55 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 52.36/52.55 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 52.36/52.55 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x0))
% 52.36/52.55 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 52.36/52.55 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 52.36/52.55 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 52.36/52.55 Found eq_ref00:=(eq_ref0 (((eq Prop) x) x0)):(((eq Prop) (((eq Prop) x) x0)) (((eq Prop) x) x0))
% 52.36/52.55 Found (eq_ref0 (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 52.36/52.55 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 52.36/52.55 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 52.36/52.55 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 52.36/52.55 Found eq_ref00:=(eq_ref0 (((eq Prop) x) x0)):(((eq Prop) (((eq Prop) x) x0)) (((eq Prop) x) x0))
% 52.36/52.55 Found (eq_ref0 (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 52.36/52.55 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 52.36/52.55 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 52.36/52.55 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 52.36/52.55 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 52.36/52.55 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x0))
% 52.36/52.55 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 52.36/52.55 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 52.36/52.55 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 52.36/52.55 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 52.36/52.55 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x0))
% 52.36/52.55 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 52.36/52.55 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 52.36/52.55 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 52.36/52.55 Found eq_ref00:=(eq_ref0 (((eq Prop) x) x0)):(((eq Prop) (((eq Prop) x) x0)) (((eq Prop) x) x0))
% 52.36/52.55 Found (eq_ref0 (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 52.36/52.55 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 52.36/52.55 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 52.36/52.55 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 52.36/52.55 Found x1:(P1 (f x0))
% 52.36/52.55 Instantiate: b:=(f x0):Prop
% 52.36/52.55 Found x1 as proof of (P2 b)
% 52.36/52.55 Found x1:(P1 (f x0))
% 52.36/52.55 Instantiate: b:=(f x0):Prop
% 52.36/52.55 Found x1 as proof of (P2 b)
% 52.36/52.55 Found eq_ref00:=(eq_ref0 (((eq Prop) x) x0)):(((eq Prop) (((eq Prop) x) x0)) (((eq Prop) x) x0))
% 52.36/52.55 Found (eq_ref0 (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 52.36/52.55 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 57.64/57.80 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 57.64/57.80 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 57.64/57.80 Found eq_ref00:=(eq_ref0 (((eq Prop) x) x0)):(((eq Prop) (((eq Prop) x) x0)) (((eq Prop) x) x0))
% 57.64/57.80 Found (eq_ref0 (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 57.64/57.80 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 57.64/57.80 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 57.64/57.80 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 57.64/57.80 Found x1:(P1 (f x0))
% 57.64/57.80 Instantiate: b:=(f x0):Prop
% 57.64/57.80 Found x1 as proof of (P2 b)
% 57.64/57.80 Found x1:(P1 (f x0))
% 57.64/57.80 Instantiate: b:=(f x0):Prop
% 57.64/57.80 Found x1 as proof of (P2 b)
% 57.64/57.80 Found eq_ref00:=(eq_ref0 (((eq Prop) x) x0)):(((eq Prop) (((eq Prop) x) x0)) (((eq Prop) x) x0))
% 57.64/57.80 Found (eq_ref0 (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 57.64/57.80 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 57.64/57.80 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 57.64/57.80 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 57.64/57.80 Found eq_ref00:=(eq_ref0 (((eq Prop) x) x0)):(((eq Prop) (((eq Prop) x) x0)) (((eq Prop) x) x0))
% 57.64/57.80 Found (eq_ref0 (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 57.64/57.80 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 57.64/57.80 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 57.64/57.80 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 57.64/57.80 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 57.64/57.80 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b)
% 57.64/57.80 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 57.64/57.80 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 57.64/57.80 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 57.64/57.80 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 57.64/57.80 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq Prop) x) x0))
% 57.64/57.80 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x) x0))
% 57.64/57.80 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x) x0))
% 57.64/57.80 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x) x0))
% 57.64/57.80 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 57.64/57.80 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b)
% 57.64/57.80 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 57.64/57.80 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 57.64/57.80 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 57.64/57.80 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 57.64/57.80 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq Prop) x) x0))
% 57.64/57.80 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x) x0))
% 57.64/57.80 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x) x0))
% 57.64/57.80 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x) x0))
% 57.64/57.80 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 57.64/57.80 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b)
% 57.64/57.80 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 57.64/57.80 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 57.64/57.80 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 57.64/57.80 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 57.64/57.80 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq Prop) x) x0))
% 57.64/57.80 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x) x0))
% 57.64/57.80 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x) x0))
% 57.64/57.80 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x) x0))
% 57.64/57.80 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 57.64/57.80 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b)
% 57.64/57.80 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 57.64/57.80 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 57.64/57.80 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 57.64/57.80 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 57.64/57.80 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq Prop) x) x0))
% 57.64/57.80 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x) x0))
% 57.64/57.80 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x) x0))
% 63.53/63.71 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x) x0))
% 63.53/63.71 Found x12:(P1 (f x0))
% 63.53/63.71 Found (fun (x12:(P1 (f x0)))=> x12) as proof of (P1 (f x0))
% 63.53/63.71 Found (fun (x12:(P1 (f x0)))=> x12) as proof of (P2 (f x0))
% 63.53/63.71 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 63.53/63.71 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b)
% 63.53/63.71 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 63.53/63.71 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 63.53/63.71 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 63.53/63.71 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 63.53/63.71 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq Prop) x) x0))
% 63.53/63.71 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x) x0))
% 63.53/63.71 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x) x0))
% 63.53/63.71 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x) x0))
% 63.53/63.71 Found x12:(P1 (f x0))
% 63.53/63.71 Found (fun (x12:(P1 (f x0)))=> x12) as proof of (P1 (f x0))
% 63.53/63.71 Found (fun (x12:(P1 (f x0)))=> x12) as proof of (P2 (f x0))
% 63.53/63.71 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 63.53/63.71 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b)
% 63.53/63.71 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 63.53/63.71 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 63.53/63.71 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 63.53/63.71 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 63.53/63.71 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq Prop) x) x0))
% 63.53/63.71 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x) x0))
% 63.53/63.71 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x) x0))
% 63.53/63.71 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x) x0))
% 63.53/63.71 Found x12:(P1 (f x0))
% 63.53/63.71 Found (fun (x12:(P1 (f x0)))=> x12) as proof of (P1 (f x0))
% 63.53/63.71 Found (fun (x12:(P1 (f x0)))=> x12) as proof of (P2 (f x0))
% 63.53/63.71 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 63.53/63.71 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b)
% 63.53/63.71 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 63.53/63.71 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 63.53/63.71 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 63.53/63.71 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 63.53/63.71 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq Prop) x) x0))
% 63.53/63.71 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x) x0))
% 63.53/63.71 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x) x0))
% 63.53/63.71 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x) x0))
% 63.53/63.71 Found x12:(P1 (f x0))
% 63.53/63.71 Found (fun (x12:(P1 (f x0)))=> x12) as proof of (P1 (f x0))
% 63.53/63.71 Found (fun (x12:(P1 (f x0)))=> x12) as proof of (P2 (f x0))
% 63.53/63.71 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 63.53/63.71 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b)
% 63.53/63.71 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 63.53/63.71 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 63.53/63.71 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 63.53/63.71 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 63.53/63.71 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq Prop) x) x0))
% 63.53/63.71 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x) x0))
% 63.53/63.71 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x) x0))
% 63.53/63.71 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x) x0))
% 63.53/63.71 Found eq_ref00:=(eq_ref0 (((eq Prop) x) x0)):(((eq Prop) (((eq Prop) x) x0)) (((eq Prop) x) x0))
% 63.53/63.71 Found (eq_ref0 (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 63.53/63.71 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 63.53/63.71 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 63.53/63.71 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 63.53/63.71 Found x1:(P2 b)
% 63.53/63.71 Instantiate: b:=((ex Prop) (fun (Xy:Prop)=> (((eq Prop) x0) Xy))):Prop
% 63.53/63.71 Found (fun (x1:(P2 b))=> x1) as proof of (P2 (f x0))
% 63.53/63.71 Found (fun (P2:(Prop->Prop)) (x1:(P2 b))=> x1) as proof of ((P2 b)->(P2 (f x0)))
% 63.53/63.71 Found (fun (P2:(Prop->Prop)) (x1:(P2 b))=> x1) as proof of (P1 b)
% 63.53/63.71 Found eq_ref00:=(eq_ref0 (((eq Prop) x) x0)):(((eq Prop) (((eq Prop) x) x0)) (((eq Prop) x) x0))
% 63.53/63.71 Found (eq_ref0 (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 63.53/63.78 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 63.53/63.78 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 63.53/63.78 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 63.53/63.78 Found x1:(P2 b)
% 63.53/63.78 Instantiate: b:=((ex Prop) (fun (Xy:Prop)=> (((eq Prop) x0) Xy))):Prop
% 63.53/63.78 Found (fun (x1:(P2 b))=> x1) as proof of (P2 (f x0))
% 63.53/63.78 Found (fun (P2:(Prop->Prop)) (x1:(P2 b))=> x1) as proof of ((P2 b)->(P2 (f x0)))
% 63.53/63.78 Found (fun (P2:(Prop->Prop)) (x1:(P2 b))=> x1) as proof of (P1 b)
% 63.53/63.78 Found x00:(P1 x)
% 63.53/63.78 Instantiate: x0:=x:Prop
% 63.53/63.78 Found (fun (x00:(P1 x))=> x00) as proof of (P1 x0)
% 63.53/63.78 Found (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00) as proof of ((P1 x)->(P1 x0))
% 63.53/63.78 Found (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00) as proof of (b0 x0)
% 63.53/63.78 Found (ex_intro010 (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00)) as proof of ((ex Prop) b0)
% 63.53/63.78 Found ((ex_intro01 x) (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00)) as proof of ((ex Prop) b0)
% 63.53/63.78 Found (((ex_intro0 b0) x) (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00)) as proof of ((ex Prop) b0)
% 63.53/63.78 Found (((ex_intro0 b0) x) (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00)) as proof of ((ex Prop) b0)
% 63.53/63.78 Found (((ex_intro0 b0) x) (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00)) as proof of (P0 b0)
% 63.53/63.78 Found ((eq_sym0100 ((eq_ref (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))) (((ex_intro0 b0) x) (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00))) as proof of ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 63.53/63.78 Found ((eq_sym0100 ((eq_ref (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))) (((ex_intro0 b0) x) (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00))) as proof of ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 63.53/63.78 Found (((fun (x0:(((eq (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) b0))=> ((eq_sym010 x0) (ex Prop))) ((eq_ref (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))) (((ex_intro0 b0) x) (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00))) as proof of ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 63.53/63.78 Found (((fun (x0:(((eq (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) (fun (Xy:Prop)=> (forall (P:(Prop->Prop)), ((P x)->(P Xy))))))=> (((eq_sym01 (fun (Xy:Prop)=> (forall (P:(Prop->Prop)), ((P x)->(P Xy))))) x0) (ex Prop))) ((eq_ref (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))) (((ex_intro0 (fun (Xy:Prop)=> (forall (P:(Prop->Prop)), ((P x)->(P Xy))))) x) (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00))) as proof of ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 63.53/63.78 Found (((fun (x0:(((eq (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) (fun (Xy:Prop)=> (forall (P:(Prop->Prop)), ((P x)->(P Xy))))))=> ((((eq_sym0 (fun (Xy:Prop)=> (((eq Prop) x) Xy))) (fun (Xy:Prop)=> (forall (P:(Prop->Prop)), ((P x)->(P Xy))))) x0) (ex Prop))) ((eq_ref (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))) (((ex_intro0 (fun (Xy:Prop)=> (forall (P:(Prop->Prop)), ((P x)->(P Xy))))) x) (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00))) as proof of ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 63.53/63.78 Found (((fun (x0:(((eq (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) (fun (Xy:Prop)=> (forall (P:(Prop->Prop)), ((P x)->(P Xy))))))=> ((((eq_sym0 (fun (Xy:Prop)=> (((eq Prop) x) Xy))) (fun (Xy:Prop)=> (forall (P:(Prop->Prop)), ((P x)->(P Xy))))) x0) (ex Prop))) ((eq_ref (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))) (((ex_intro0 (fun (Xy:Prop)=> (forall (P:(Prop->Prop)), ((P x)->(P Xy))))) x) (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00))) as proof of ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 63.53/63.78 Found (((fun (x0:(((eq (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) (fun (Xy:Prop)=> (forall (P:(Prop->Prop)), ((P x)->(P Xy))))))=> ((((eq_sym0 (fun (Xy:Prop)=> (((eq Prop) x) Xy))) (fun (Xy:Prop)=> (forall (P:(Prop->Prop)), ((P x)->(P Xy))))) x0) (ex Prop))) ((eq_ref (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))) (((ex_intro0 (fun (Xy:Prop)=> (forall (P:(Prop->Prop)), ((P x)->(P Xy))))) x) (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00))) as proof of (b x)
% 63.53/63.78 Found (ex_intro000 (((fun (x0:(((eq (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) (fun (Xy:Prop)=> (forall (P:(Prop->Prop)), ((P x)->(P Xy))))))=> ((((eq_sym0 (fun (Xy:Prop)=> (((eq Prop) x) Xy))) (fun (Xy:Prop)=> (forall (P:(Prop->Prop)), ((P x)->(P Xy))))) x0) (ex Prop))) ((eq_ref (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))) (((ex_intro0 (fun (Xy:Prop)=> (forall (P:(Prop->Prop)), ((P x)->(P Xy))))) x) (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00)))) as proof of ((ex Prop) b)
% 64.61/64.79 Found x00:(P1 x)
% 64.61/64.79 Instantiate: x0:=x:Prop
% 64.61/64.79 Found (fun (x00:(P1 x))=> x00) as proof of (P1 x0)
% 64.61/64.79 Found (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00) as proof of ((P1 x)->(P1 x0))
% 64.61/64.79 Found (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00) as proof of (b0 x0)
% 64.61/64.79 Found (ex_intro010 (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00)) as proof of ((ex Prop) b0)
% 64.61/64.79 Found ((ex_intro01 x) (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00)) as proof of ((ex Prop) b0)
% 64.61/64.79 Found (((ex_intro0 b0) x) (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00)) as proof of ((ex Prop) b0)
% 64.61/64.79 Found (((ex_intro0 b0) x) (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00)) as proof of ((ex Prop) b0)
% 64.61/64.79 Found (((ex_intro0 b0) x) (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00)) as proof of (P0 b0)
% 64.61/64.79 Found ((eq_sym0100 ((eq_ref (Prop->Prop)) ((eq Prop) x))) (((ex_intro0 b0) x) (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00))) as proof of ((ex Prop) ((eq Prop) x))
% 64.61/64.79 Found ((eq_sym0100 ((eq_ref (Prop->Prop)) ((eq Prop) x))) (((ex_intro0 b0) x) (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00))) as proof of ((ex Prop) ((eq Prop) x))
% 64.61/64.79 Found (((fun (x0:(((eq (Prop->Prop)) ((eq Prop) x)) b0))=> ((eq_sym010 x0) (ex Prop))) ((eq_ref (Prop->Prop)) ((eq Prop) x))) (((ex_intro0 b0) x) (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00))) as proof of ((ex Prop) ((eq Prop) x))
% 64.61/64.79 Found (((fun (x0:(((eq (Prop->Prop)) ((eq Prop) x)) (fun (b1:Prop)=> (forall (P:(Prop->Prop)), ((P x)->(P b1))))))=> (((eq_sym01 (fun (b1:Prop)=> (forall (P:(Prop->Prop)), ((P x)->(P b1))))) x0) (ex Prop))) ((eq_ref (Prop->Prop)) ((eq Prop) x))) (((ex_intro0 (fun (b1:Prop)=> (forall (P:(Prop->Prop)), ((P x)->(P b1))))) x) (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00))) as proof of ((ex Prop) ((eq Prop) x))
% 64.61/64.79 Found (((fun (x0:(((eq (Prop->Prop)) ((eq Prop) x)) (fun (b1:Prop)=> (forall (P:(Prop->Prop)), ((P x)->(P b1))))))=> ((((eq_sym0 ((eq Prop) x)) (fun (b1:Prop)=> (forall (P:(Prop->Prop)), ((P x)->(P b1))))) x0) (ex Prop))) ((eq_ref (Prop->Prop)) ((eq Prop) x))) (((ex_intro0 (fun (b1:Prop)=> (forall (P:(Prop->Prop)), ((P x)->(P b1))))) x) (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00))) as proof of ((ex Prop) ((eq Prop) x))
% 64.61/64.79 Found (((fun (x0:(((eq (Prop->Prop)) ((eq Prop) x)) (fun (b1:Prop)=> (forall (P:(Prop->Prop)), ((P x)->(P b1))))))=> ((((eq_sym0 ((eq Prop) x)) (fun (b1:Prop)=> (forall (P:(Prop->Prop)), ((P x)->(P b1))))) x0) (ex Prop))) ((eq_ref (Prop->Prop)) ((eq Prop) x))) (((ex_intro0 (fun (b1:Prop)=> (forall (P:(Prop->Prop)), ((P x)->(P b1))))) x) (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00))) as proof of ((ex Prop) ((eq Prop) x))
% 64.61/64.79 Found (((fun (x0:(((eq (Prop->Prop)) ((eq Prop) x)) (fun (b1:Prop)=> (forall (P:(Prop->Prop)), ((P x)->(P b1))))))=> ((((eq_sym0 ((eq Prop) x)) (fun (b1:Prop)=> (forall (P:(Prop->Prop)), ((P x)->(P b1))))) x0) (ex Prop))) ((eq_ref (Prop->Prop)) ((eq Prop) x))) (((ex_intro0 (fun (b1:Prop)=> (forall (P:(Prop->Prop)), ((P x)->(P b1))))) x) (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00))) as proof of (b x)
% 64.61/64.79 Found (ex_intro000 (((fun (x0:(((eq (Prop->Prop)) ((eq Prop) x)) (fun (b1:Prop)=> (forall (P:(Prop->Prop)), ((P x)->(P b1))))))=> ((((eq_sym0 ((eq Prop) x)) (fun (b1:Prop)=> (forall (P:(Prop->Prop)), ((P x)->(P b1))))) x0) (ex Prop))) ((eq_ref (Prop->Prop)) ((eq Prop) x))) (((ex_intro0 (fun (b1:Prop)=> (forall (P:(Prop->Prop)), ((P x)->(P b1))))) x) (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00)))) as proof of ((ex Prop) b)
% 64.61/64.79 Found eq_ref00:=(eq_ref0 (((eq Prop) x) x0)):(((eq Prop) (((eq Prop) x) x0)) (((eq Prop) x) x0))
% 64.61/64.79 Found (eq_ref0 (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 64.61/64.79 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 64.61/64.79 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 64.61/64.79 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 66.05/66.23 Found x1:(P2 b)
% 66.05/66.23 Instantiate: b:=((ex Prop) ((eq Prop) x0)):Prop
% 66.05/66.23 Found (fun (x1:(P2 b))=> x1) as proof of (P2 (f x0))
% 66.05/66.23 Found (fun (P2:(Prop->Prop)) (x1:(P2 b))=> x1) as proof of ((P2 b)->(P2 (f x0)))
% 66.05/66.23 Found (fun (P2:(Prop->Prop)) (x1:(P2 b))=> x1) as proof of (P1 b)
% 66.05/66.23 Found eq_ref00:=(eq_ref0 (((eq Prop) x) x0)):(((eq Prop) (((eq Prop) x) x0)) (((eq Prop) x) x0))
% 66.05/66.23 Found (eq_ref0 (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 66.05/66.23 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 66.05/66.23 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 66.05/66.23 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b)
% 66.05/66.23 Found x1:(P2 b)
% 66.05/66.23 Instantiate: b:=((ex Prop) ((eq Prop) x0)):Prop
% 66.05/66.23 Found (fun (x1:(P2 b))=> x1) as proof of (P2 (f x0))
% 66.05/66.23 Found (fun (P2:(Prop->Prop)) (x1:(P2 b))=> x1) as proof of ((P2 b)->(P2 (f x0)))
% 66.05/66.23 Found (fun (P2:(Prop->Prop)) (x1:(P2 b))=> x1) as proof of (P1 b)
% 66.05/66.23 Found x00:(P1 x)
% 66.05/66.23 Instantiate: x0:=x:Prop
% 66.05/66.23 Found (fun (x00:(P1 x))=> x00) as proof of (P1 x0)
% 66.05/66.23 Found (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00) as proof of ((P1 x)->(P1 x0))
% 66.05/66.23 Found (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00) as proof of (f0 x0)
% 66.05/66.23 Found (ex_intro010 (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00)) as proof of ((ex Prop) f0)
% 66.05/66.23 Found ((ex_intro01 x) (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00)) as proof of ((ex Prop) f0)
% 66.05/66.23 Found (((ex_intro0 f0) x) (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00)) as proof of ((ex Prop) f0)
% 66.05/66.23 Found (((ex_intro0 f0) x) (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00)) as proof of ((ex Prop) f0)
% 66.05/66.23 Found (((ex_intro0 f0) x) (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00)) as proof of (P0 f0)
% 66.05/66.23 Found ((functional_extensionality_dep00100 (fun (x0:Prop)=> ((eq_ref Prop) (f0 x0)))) (((ex_intro0 f0) x) (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00))) as proof of ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 66.05/66.23 Found ((functional_extensionality_dep00100 (fun (x0:Prop)=> ((eq_ref Prop) (f0 x0)))) (((ex_intro0 f0) x) (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00))) as proof of ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 66.05/66.23 Found (((fun (x0:(forall (x0:Prop), (((eq Prop) (f0 x0)) (((eq Prop) x) x0))))=> ((functional_extensionality_dep0010 x0) (ex Prop))) (fun (x0:Prop)=> ((eq_ref Prop) (f0 x0)))) (((ex_intro0 f0) x) (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00))) as proof of ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 66.05/66.23 Found (((fun (x0:(forall (x0:Prop), (((eq Prop) (f0 x0)) (((eq Prop) x) x0))))=> (((functional_extensionality_dep001 (fun (Xy:Prop)=> (((eq Prop) x) Xy))) x0) (ex Prop))) (fun (x0:Prop)=> ((eq_ref Prop) (f0 x0)))) (((ex_intro0 f0) x) (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00))) as proof of ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 66.05/66.23 Found (((fun (x0:(forall (x0:Prop), (((eq Prop) (((eq Prop) x) x0)) (((eq Prop) x) x0))))=> ((((functional_extensionality_dep00 ((eq Prop) x)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) x0) (ex Prop))) (fun (x0:Prop)=> ((eq_ref Prop) (((eq Prop) x) x0)))) (((ex_intro0 ((eq Prop) x)) x) (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00))) as proof of ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 66.05/66.23 Found (((fun (x0:(forall (x0:Prop), (((eq Prop) (((eq Prop) x) x0)) (((eq Prop) x) x0))))=> ((((functional_extensionality_dep00 ((eq Prop) x)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) x0) (ex Prop))) (fun (x0:Prop)=> ((eq_ref Prop) (((eq Prop) x) x0)))) (((ex_intro0 ((eq Prop) x)) x) (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00))) as proof of ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 66.05/66.23 Found (((fun (x0:(forall (x0:Prop), (((eq Prop) (((eq Prop) x) x0)) (((eq Prop) x) x0))))=> ((((functional_extensionality_dep00 ((eq Prop) x)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) x0) (ex Prop))) (fun (x0:Prop)=> ((eq_ref Prop) (((eq Prop) x) x0)))) (((ex_intro0 ((eq Prop) x)) x) (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00))) as proof of (f x)
% 66.05/66.23 Found (ex_intro000 (((fun (x0:(forall (x0:Prop), (((eq Prop) (((eq Prop) x) x0)) (((eq Prop) x) x0))))=> ((((functional_extensionality_dep00 ((eq Prop) x)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) x0) (ex Prop))) (fun (x0:Prop)=> ((eq_ref Prop) (((eq Prop) x) x0)))) (((ex_intro0 ((eq Prop) x)) x) (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00)))) as proof of ((ex Prop) f)
% 66.61/66.80 Found x00:(P1 x)
% 66.61/66.80 Instantiate: x0:=x:Prop
% 66.61/66.80 Found (fun (x00:(P1 x))=> x00) as proof of (P1 x0)
% 66.61/66.80 Found (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00) as proof of ((P1 x)->(P1 x0))
% 66.61/66.80 Found (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00) as proof of (f0 x0)
% 66.61/66.80 Found (ex_intro010 (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00)) as proof of ((ex Prop) f0)
% 66.61/66.80 Found ((ex_intro01 x) (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00)) as proof of ((ex Prop) f0)
% 66.61/66.80 Found (((ex_intro0 f0) x) (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00)) as proof of ((ex Prop) f0)
% 66.61/66.80 Found (((ex_intro0 f0) x) (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00)) as proof of ((ex Prop) f0)
% 66.61/66.80 Found (((ex_intro0 f0) x) (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00)) as proof of (P0 f0)
% 66.61/66.80 Found ((functional_extensionality00100 (fun (x0:Prop)=> ((eq_ref Prop) (f0 x0)))) (((ex_intro0 f0) x) (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00))) as proof of ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 66.61/66.80 Found ((functional_extensionality00100 (fun (x0:Prop)=> ((eq_ref Prop) (f0 x0)))) (((ex_intro0 f0) x) (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00))) as proof of ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 66.61/66.80 Found (((fun (x0:(forall (x0:Prop), (((eq Prop) (f0 x0)) (((eq Prop) x) x0))))=> ((functional_extensionality0010 x0) (ex Prop))) (fun (x0:Prop)=> ((eq_ref Prop) (f0 x0)))) (((ex_intro0 f0) x) (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00))) as proof of ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 66.61/66.80 Found (((fun (x0:(forall (x0:Prop), (((eq Prop) (f0 x0)) (((eq Prop) x) x0))))=> (((functional_extensionality001 (fun (Xy:Prop)=> (((eq Prop) x) Xy))) x0) (ex Prop))) (fun (x0:Prop)=> ((eq_ref Prop) (f0 x0)))) (((ex_intro0 f0) x) (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00))) as proof of ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 66.61/66.80 Found (((fun (x0:(forall (x0:Prop), (((eq Prop) (((eq Prop) x) x0)) (((eq Prop) x) x0))))=> ((((functional_extensionality00 ((eq Prop) x)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) x0) (ex Prop))) (fun (x0:Prop)=> ((eq_ref Prop) (((eq Prop) x) x0)))) (((ex_intro0 ((eq Prop) x)) x) (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00))) as proof of ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 66.61/66.80 Found (((fun (x0:(forall (x0:Prop), (((eq Prop) (((eq Prop) x) x0)) (((eq Prop) x) x0))))=> ((((functional_extensionality00 ((eq Prop) x)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) x0) (ex Prop))) (fun (x0:Prop)=> ((eq_ref Prop) (((eq Prop) x) x0)))) (((ex_intro0 ((eq Prop) x)) x) (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00))) as proof of ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 66.61/66.80 Found (((fun (x0:(forall (x0:Prop), (((eq Prop) (((eq Prop) x) x0)) (((eq Prop) x) x0))))=> ((((functional_extensionality00 ((eq Prop) x)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) x0) (ex Prop))) (fun (x0:Prop)=> ((eq_ref Prop) (((eq Prop) x) x0)))) (((ex_intro0 ((eq Prop) x)) x) (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00))) as proof of (f x)
% 66.61/66.80 Found (ex_intro000 (((fun (x0:(forall (x0:Prop), (((eq Prop) (((eq Prop) x) x0)) (((eq Prop) x) x0))))=> ((((functional_extensionality00 ((eq Prop) x)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) x0) (ex Prop))) (fun (x0:Prop)=> ((eq_ref Prop) (((eq Prop) x) x0)))) (((ex_intro0 ((eq Prop) x)) x) (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00)))) as proof of ((ex Prop) f)
% 66.61/66.80 Found x00:(P1 x)
% 66.61/66.80 Instantiate: x0:=x:Prop
% 66.61/66.80 Found (fun (x00:(P1 x))=> x00) as proof of (P1 x0)
% 66.61/66.80 Found (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00) as proof of ((P1 x)->(P1 x0))
% 66.61/66.80 Found (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00) as proof of (f0 x0)
% 66.61/66.80 Found (ex_intro010 (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00)) as proof of ((ex Prop) f0)
% 66.61/66.80 Found ((ex_intro01 x) (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00)) as proof of ((ex Prop) f0)
% 66.61/66.80 Found (((ex_intro0 f0) x) (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00)) as proof of ((ex Prop) f0)
% 66.61/66.80 Found (((ex_intro0 f0) x) (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00)) as proof of ((ex Prop) f0)
% 66.61/66.80 Found (((ex_intro0 f0) x) (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00)) as proof of (P0 f0)
% 66.73/66.94 Found ((functional_extensionality00100 (fun (x0:Prop)=> ((eq_ref Prop) (f0 x0)))) (((ex_intro0 f0) x) (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00))) as proof of ((ex Prop) ((eq Prop) x))
% 66.73/66.94 Found ((functional_extensionality00100 (fun (x0:Prop)=> ((eq_ref Prop) (f0 x0)))) (((ex_intro0 f0) x) (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00))) as proof of ((ex Prop) ((eq Prop) x))
% 66.73/66.94 Found (((fun (x0:(forall (x0:Prop), (((eq Prop) (f0 x0)) (((eq Prop) x) x0))))=> ((functional_extensionality0010 x0) (ex Prop))) (fun (x0:Prop)=> ((eq_ref Prop) (f0 x0)))) (((ex_intro0 f0) x) (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00))) as proof of ((ex Prop) ((eq Prop) x))
% 66.73/66.94 Found (((fun (x0:(forall (x0:Prop), (((eq Prop) (f0 x0)) (((eq Prop) x) x0))))=> (((functional_extensionality001 ((eq Prop) x)) x0) (ex Prop))) (fun (x0:Prop)=> ((eq_ref Prop) (f0 x0)))) (((ex_intro0 f0) x) (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00))) as proof of ((ex Prop) ((eq Prop) x))
% 66.73/66.94 Found (((fun (x0:(forall (x0:Prop), (((eq Prop) (((eq Prop) x) x0)) (((eq Prop) x) x0))))=> ((((functional_extensionality00 ((eq Prop) x)) ((eq Prop) x)) x0) (ex Prop))) (fun (x0:Prop)=> ((eq_ref Prop) (((eq Prop) x) x0)))) (((ex_intro0 ((eq Prop) x)) x) (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00))) as proof of ((ex Prop) ((eq Prop) x))
% 66.73/66.94 Found (((fun (x0:(forall (x0:Prop), (((eq Prop) (((eq Prop) x) x0)) (((eq Prop) x) x0))))=> ((((functional_extensionality00 ((eq Prop) x)) ((eq Prop) x)) x0) (ex Prop))) (fun (x0:Prop)=> ((eq_ref Prop) (((eq Prop) x) x0)))) (((ex_intro0 ((eq Prop) x)) x) (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00))) as proof of ((ex Prop) ((eq Prop) x))
% 66.73/66.94 Found (((fun (x0:(forall (x0:Prop), (((eq Prop) (((eq Prop) x) x0)) (((eq Prop) x) x0))))=> ((((functional_extensionality00 ((eq Prop) x)) ((eq Prop) x)) x0) (ex Prop))) (fun (x0:Prop)=> ((eq_ref Prop) (((eq Prop) x) x0)))) (((ex_intro0 ((eq Prop) x)) x) (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00))) as proof of (f x)
% 66.73/66.94 Found (ex_intro000 (((fun (x0:(forall (x0:Prop), (((eq Prop) (((eq Prop) x) x0)) (((eq Prop) x) x0))))=> ((((functional_extensionality00 ((eq Prop) x)) ((eq Prop) x)) x0) (ex Prop))) (fun (x0:Prop)=> ((eq_ref Prop) (((eq Prop) x) x0)))) (((ex_intro0 ((eq Prop) x)) x) (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00)))) as proof of ((ex Prop) f)
% 66.73/66.94 Found x00:(P1 x)
% 66.73/66.94 Instantiate: x0:=x:Prop
% 66.73/66.94 Found (fun (x00:(P1 x))=> x00) as proof of (P1 x0)
% 66.73/66.94 Found (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00) as proof of ((P1 x)->(P1 x0))
% 66.73/66.94 Found (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00) as proof of (f0 x0)
% 66.73/66.94 Found (ex_intro010 (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00)) as proof of ((ex Prop) f0)
% 66.73/66.94 Found ((ex_intro01 x) (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00)) as proof of ((ex Prop) f0)
% 66.73/66.94 Found (((ex_intro0 f0) x) (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00)) as proof of ((ex Prop) f0)
% 66.73/66.94 Found (((ex_intro0 f0) x) (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00)) as proof of ((ex Prop) f0)
% 66.73/66.94 Found (((ex_intro0 f0) x) (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00)) as proof of (P0 f0)
% 66.73/66.94 Found ((functional_extensionality_dep00100 (fun (x0:Prop)=> ((eq_ref Prop) (f0 x0)))) (((ex_intro0 f0) x) (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00))) as proof of ((ex Prop) ((eq Prop) x))
% 66.73/66.94 Found ((functional_extensionality_dep00100 (fun (x0:Prop)=> ((eq_ref Prop) (f0 x0)))) (((ex_intro0 f0) x) (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00))) as proof of ((ex Prop) ((eq Prop) x))
% 66.73/66.94 Found (((fun (x0:(forall (x0:Prop), (((eq Prop) (f0 x0)) (((eq Prop) x) x0))))=> ((functional_extensionality_dep0010 x0) (ex Prop))) (fun (x0:Prop)=> ((eq_ref Prop) (f0 x0)))) (((ex_intro0 f0) x) (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00))) as proof of ((ex Prop) ((eq Prop) x))
% 66.73/66.94 Found (((fun (x0:(forall (x0:Prop), (((eq Prop) (f0 x0)) (((eq Prop) x) x0))))=> (((functional_extensionality_dep001 ((eq Prop) x)) x0) (ex Prop))) (fun (x0:Prop)=> ((eq_ref Prop) (f0 x0)))) (((ex_intro0 f0) x) (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00))) as proof of ((ex Prop) ((eq Prop) x))
% 66.73/66.94 Found (((fun (x0:(forall (x0:Prop), (((eq Prop) (((eq Prop) x) x0)) (((eq Prop) x) x0))))=> ((((functional_extensionality_dep00 ((eq Prop) x)) ((eq Prop) x)) x0) (ex Prop))) (fun (x0:Prop)=> ((eq_ref Prop) (((eq Prop) x) x0)))) (((ex_intro0 ((eq Prop) x)) x) (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00))) as proof of ((ex Prop) ((eq Prop) x))
% 70.61/70.86 Found (((fun (x0:(forall (x0:Prop), (((eq Prop) (((eq Prop) x) x0)) (((eq Prop) x) x0))))=> ((((functional_extensionality_dep00 ((eq Prop) x)) ((eq Prop) x)) x0) (ex Prop))) (fun (x0:Prop)=> ((eq_ref Prop) (((eq Prop) x) x0)))) (((ex_intro0 ((eq Prop) x)) x) (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00))) as proof of ((ex Prop) ((eq Prop) x))
% 70.61/70.86 Found (((fun (x0:(forall (x0:Prop), (((eq Prop) (((eq Prop) x) x0)) (((eq Prop) x) x0))))=> ((((functional_extensionality_dep00 ((eq Prop) x)) ((eq Prop) x)) x0) (ex Prop))) (fun (x0:Prop)=> ((eq_ref Prop) (((eq Prop) x) x0)))) (((ex_intro0 ((eq Prop) x)) x) (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00))) as proof of (f x)
% 70.61/70.86 Found (ex_intro000 (((fun (x0:(forall (x0:Prop), (((eq Prop) (((eq Prop) x) x0)) (((eq Prop) x) x0))))=> ((((functional_extensionality_dep00 ((eq Prop) x)) ((eq Prop) x)) x0) (ex Prop))) (fun (x0:Prop)=> ((eq_ref Prop) (((eq Prop) x) x0)))) (((ex_intro0 ((eq Prop) x)) x) (fun (P1:(Prop->Prop)) (x00:(P1 x))=> x00)))) as proof of ((ex Prop) f)
% 70.61/70.86 Found eta_expansion_dep000:=(eta_expansion_dep00 a):(((eq (Prop->Prop)) a) (fun (x:Prop)=> (a x)))
% 70.61/70.86 Found (eta_expansion_dep00 a) as proof of (((eq (Prop->Prop)) a) b0)
% 70.61/70.86 Found ((eta_expansion_dep0 (fun (x1:Prop)=> Prop)) a) as proof of (((eq (Prop->Prop)) a) b0)
% 70.61/70.86 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) a) as proof of (((eq (Prop->Prop)) a) b0)
% 70.61/70.86 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) a) as proof of (((eq (Prop->Prop)) a) b0)
% 70.61/70.86 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) a) as proof of (((eq (Prop->Prop)) a) b0)
% 70.61/70.86 Found eq_ref00:=(eq_ref0 b0):(((eq (Prop->Prop)) b0) b0)
% 70.61/70.86 Found (eq_ref0 b0) as proof of (((eq (Prop->Prop)) b0) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 70.61/70.86 Found ((eq_ref (Prop->Prop)) b0) as proof of (((eq (Prop->Prop)) b0) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 70.61/70.86 Found ((eq_ref (Prop->Prop)) b0) as proof of (((eq (Prop->Prop)) b0) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 70.61/70.86 Found ((eq_ref (Prop->Prop)) b0) as proof of (((eq (Prop->Prop)) b0) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 70.61/70.86 Found x01:(P1 b)
% 70.61/70.86 Found (fun (x01:(P1 b))=> x01) as proof of (P1 b)
% 70.61/70.86 Found (fun (x01:(P1 b))=> x01) as proof of (P2 b)
% 70.61/70.86 Found eq_ref00:=(eq_ref0 b0):(((eq (Prop->Prop)) b0) b0)
% 70.61/70.86 Found (eq_ref0 b0) as proof of (((eq (Prop->Prop)) b0) ((eq Prop) x))
% 70.61/70.86 Found ((eq_ref (Prop->Prop)) b0) as proof of (((eq (Prop->Prop)) b0) ((eq Prop) x))
% 70.61/70.86 Found ((eq_ref (Prop->Prop)) b0) as proof of (((eq (Prop->Prop)) b0) ((eq Prop) x))
% 70.61/70.86 Found ((eq_ref (Prop->Prop)) b0) as proof of (((eq (Prop->Prop)) b0) ((eq Prop) x))
% 70.61/70.86 Found eq_ref00:=(eq_ref0 a):(((eq (Prop->Prop)) a) a)
% 70.61/70.86 Found (eq_ref0 a) as proof of (((eq (Prop->Prop)) a) b0)
% 70.61/70.86 Found ((eq_ref (Prop->Prop)) a) as proof of (((eq (Prop->Prop)) a) b0)
% 70.61/70.86 Found ((eq_ref (Prop->Prop)) a) as proof of (((eq (Prop->Prop)) a) b0)
% 70.61/70.86 Found ((eq_ref (Prop->Prop)) a) as proof of (((eq (Prop->Prop)) a) b0)
% 70.61/70.86 Found x01:(P1 b)
% 70.61/70.86 Found (fun (x01:(P1 b))=> x01) as proof of (P1 b)
% 70.61/70.86 Found (fun (x01:(P1 b))=> x01) as proof of (P2 b)
% 70.61/70.86 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 70.61/70.86 Found (eq_ref0 x) as proof of (((eq Prop) x) x0)
% 70.61/70.86 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) x0)
% 70.61/70.86 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) x0)
% 70.61/70.86 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) x0)
% 70.61/70.86 Found (ex_intro010 ((eq_ref Prop) x)) as proof of ((ex Prop) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 70.61/70.86 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 70.61/70.86 Found (eq_ref0 x) as proof of (((eq Prop) x) x0)
% 70.61/70.86 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) x0)
% 70.61/70.86 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) x0)
% 70.61/70.86 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) x0)
% 70.61/70.86 Found (ex_intro010 ((eq_ref Prop) x)) as proof of ((ex Prop) ((eq Prop) x))
% 70.61/70.86 Found x01:(P1 b)
% 70.61/70.86 Found (fun (x01:(P1 b))=> x01) as proof of (P1 b)
% 70.61/70.86 Found (fun (x01:(P1 b))=> x01) as proof of (P2 b)
% 70.61/70.86 Found x01:(P1 b)
% 70.61/70.86 Found (fun (x01:(P1 b))=> x01) as proof of (P1 b)
% 70.61/70.86 Found (fun (x01:(P1 b))=> x01) as proof of (P2 b)
% 82.02/82.28 Found x01:(P1 b)
% 82.02/82.28 Found (fun (x01:(P1 b))=> x01) as proof of (P1 b)
% 82.02/82.28 Found (fun (x01:(P1 b))=> x01) as proof of (P2 b)
% 82.02/82.28 Found x01:(P1 b)
% 82.02/82.28 Found (fun (x01:(P1 b))=> x01) as proof of (P1 b)
% 82.02/82.28 Found (fun (x01:(P1 b))=> x01) as proof of (P2 b)
% 82.02/82.28 Found eta_expansion000:=(eta_expansion00 (fun (Xy:Prop)=> (((eq Prop) x) Xy))):(((eq (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) (fun (x0:Prop)=> (((eq Prop) x) x0)))
% 82.02/82.28 Found (eta_expansion00 (fun (Xy:Prop)=> (((eq Prop) x) Xy))) as proof of (((eq (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) b0)
% 82.02/82.28 Found ((eta_expansion0 Prop) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) as proof of (((eq (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) b0)
% 82.02/82.28 Found (((eta_expansion Prop) Prop) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) as proof of (((eq (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) b0)
% 82.02/82.28 Found (((eta_expansion Prop) Prop) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) as proof of (((eq (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) b0)
% 82.02/82.28 Found (((eta_expansion Prop) Prop) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) as proof of (((eq (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) b0)
% 82.02/82.28 Found eta_expansion_dep000:=(eta_expansion_dep00 b0):(((eq (Prop->Prop)) b0) (fun (x:Prop)=> (b0 x)))
% 82.02/82.28 Found (eta_expansion_dep00 b0) as proof of (((eq (Prop->Prop)) b0) b)
% 82.02/82.28 Found ((eta_expansion_dep0 (fun (x1:Prop)=> Prop)) b0) as proof of (((eq (Prop->Prop)) b0) b)
% 82.02/82.28 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) b0) as proof of (((eq (Prop->Prop)) b0) b)
% 82.02/82.28 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) b0) as proof of (((eq (Prop->Prop)) b0) b)
% 82.02/82.28 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) b0) as proof of (((eq (Prop->Prop)) b0) b)
% 82.02/82.28 Found eq_ref00:=(eq_ref0 ((eq Prop) x)):(((eq (Prop->Prop)) ((eq Prop) x)) ((eq Prop) x))
% 82.02/82.28 Found (eq_ref0 ((eq Prop) x)) as proof of (((eq (Prop->Prop)) ((eq Prop) x)) b0)
% 82.02/82.28 Found ((eq_ref (Prop->Prop)) ((eq Prop) x)) as proof of (((eq (Prop->Prop)) ((eq Prop) x)) b0)
% 82.02/82.28 Found ((eq_ref (Prop->Prop)) ((eq Prop) x)) as proof of (((eq (Prop->Prop)) ((eq Prop) x)) b0)
% 82.02/82.28 Found ((eq_ref (Prop->Prop)) ((eq Prop) x)) as proof of (((eq (Prop->Prop)) ((eq Prop) x)) b0)
% 82.02/82.28 Found eta_expansion000:=(eta_expansion00 b0):(((eq (Prop->Prop)) b0) (fun (x:Prop)=> (b0 x)))
% 82.02/82.28 Found (eta_expansion00 b0) as proof of (((eq (Prop->Prop)) b0) b)
% 82.02/82.28 Found ((eta_expansion0 Prop) b0) as proof of (((eq (Prop->Prop)) b0) b)
% 82.02/82.28 Found (((eta_expansion Prop) Prop) b0) as proof of (((eq (Prop->Prop)) b0) b)
% 82.02/82.28 Found (((eta_expansion Prop) Prop) b0) as proof of (((eq (Prop->Prop)) b0) b)
% 82.02/82.28 Found (((eta_expansion Prop) Prop) b0) as proof of (((eq (Prop->Prop)) b0) b)
% 82.02/82.28 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (fun (Xy:Prop)=> (((eq Prop) x) Xy)))->(P1 (fun (x0:Prop)=> (((eq Prop) x) x0))))
% 82.02/82.28 Found (eta_expansion_dep000 P1) as proof of (P2 (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 82.02/82.28 Found ((eta_expansion_dep00 (fun (Xy:Prop)=> (((eq Prop) x) Xy))) P1) as proof of (P2 (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 82.02/82.28 Found (((eta_expansion_dep0 (fun (x1:Prop)=> Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) P1) as proof of (P2 (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 82.02/82.28 Found ((((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) P1) as proof of (P2 (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 82.02/82.28 Found ((((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) P1) as proof of (P2 (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 82.02/82.28 Found eq_ref000:=(eq_ref00 P1):((P1 (fun (Xy:Prop)=> (((eq Prop) x) Xy)))->(P1 (fun (Xy:Prop)=> (((eq Prop) x) Xy))))
% 82.02/82.28 Found (eq_ref00 P1) as proof of (P2 (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 82.02/82.28 Found ((eq_ref0 (fun (Xy:Prop)=> (((eq Prop) x) Xy))) P1) as proof of (P2 (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 82.02/82.28 Found (((eq_ref (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) P1) as proof of (P2 (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 82.02/82.28 Found (((eq_ref (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) P1) as proof of (P2 (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 82.02/82.28 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 ((eq Prop) x))->(P1 (fun (x0:Prop)=> (((eq Prop) x) x0))))
% 89.28/89.49 Found (eta_expansion_dep000 P1) as proof of (P2 ((eq Prop) x))
% 89.28/89.49 Found ((eta_expansion_dep00 ((eq Prop) x)) P1) as proof of (P2 ((eq Prop) x))
% 89.28/89.49 Found (((eta_expansion_dep0 (fun (x1:Prop)=> Prop)) ((eq Prop) x)) P1) as proof of (P2 ((eq Prop) x))
% 89.28/89.49 Found ((((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) ((eq Prop) x)) P1) as proof of (P2 ((eq Prop) x))
% 89.28/89.49 Found ((((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) ((eq Prop) x)) P1) as proof of (P2 ((eq Prop) x))
% 89.28/89.49 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 ((eq Prop) x))->(P1 (fun (x0:Prop)=> (((eq Prop) x) x0))))
% 89.28/89.49 Found (eta_expansion_dep000 P1) as proof of (P2 ((eq Prop) x))
% 89.28/89.49 Found ((eta_expansion_dep00 ((eq Prop) x)) P1) as proof of (P2 ((eq Prop) x))
% 89.28/89.49 Found (((eta_expansion_dep0 (fun (x1:Prop)=> Prop)) ((eq Prop) x)) P1) as proof of (P2 ((eq Prop) x))
% 89.28/89.49 Found ((((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) ((eq Prop) x)) P1) as proof of (P2 ((eq Prop) x))
% 89.28/89.49 Found ((((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) ((eq Prop) x)) P1) as proof of (P2 ((eq Prop) x))
% 89.28/89.49 Found eq_ref00:=(eq_ref0 (b x0)):(((eq Prop) (b x0)) (b x0))
% 89.28/89.49 Found (eq_ref0 (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 89.28/89.49 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 89.28/89.49 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 89.28/89.49 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 89.28/89.49 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 89.28/89.49 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 89.28/89.49 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 89.28/89.49 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 89.28/89.49 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 89.28/89.49 Found eq_ref00:=(eq_ref0 (b x0)):(((eq Prop) (b x0)) (b x0))
% 89.28/89.49 Found (eq_ref0 (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 89.28/89.49 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 89.28/89.49 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 89.28/89.49 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 89.28/89.49 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 89.28/89.49 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 89.28/89.49 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 89.28/89.49 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 89.28/89.49 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 89.28/89.49 Found eq_ref00:=(eq_ref0 (b x0)):(((eq Prop) (b x0)) (b x0))
% 89.28/89.49 Found (eq_ref0 (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 89.28/89.49 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 89.28/89.49 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 89.28/89.49 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 89.28/89.49 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 89.28/89.49 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 89.28/89.49 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 89.28/89.49 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 89.28/89.49 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 89.28/89.49 Found eq_ref00:=(eq_ref0 (b x0)):(((eq Prop) (b x0)) (b x0))
% 89.28/89.49 Found (eq_ref0 (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 89.28/89.49 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 89.28/89.49 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 89.28/89.49 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 89.28/89.49 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 89.28/89.49 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 89.28/89.49 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 89.28/89.49 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 89.28/89.49 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 89.28/89.49 Found x11:(P1 (b x0))
% 89.28/89.49 Found (fun (x11:(P1 (b x0)))=> x11) as proof of (P1 (b x0))
% 89.28/89.49 Found (fun (x11:(P1 (b x0)))=> x11) as proof of (P2 (b x0))
% 89.28/89.49 Found x11:(P1 (b x0))
% 89.28/89.49 Found (fun (x11:(P1 (b x0)))=> x11) as proof of (P1 (b x0))
% 89.28/89.49 Found (fun (x11:(P1 (b x0)))=> x11) as proof of (P2 (b x0))
% 89.28/89.49 Found x11:(P1 (b x0))
% 89.28/89.49 Found (fun (x11:(P1 (b x0)))=> x11) as proof of (P1 (b x0))
% 89.28/89.49 Found (fun (x11:(P1 (b x0)))=> x11) as proof of (P2 (b x0))
% 89.28/89.49 Found x11:(P1 (b x0))
% 101.22/101.43 Found (fun (x11:(P1 (b x0)))=> x11) as proof of (P1 (b x0))
% 101.22/101.43 Found (fun (x11:(P1 (b x0)))=> x11) as proof of (P2 (b x0))
% 101.22/101.43 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 101.22/101.43 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x0))
% 101.22/101.43 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 101.22/101.43 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 101.22/101.43 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 101.22/101.43 Found eq_ref00:=(eq_ref0 (((eq Prop) x) x0)):(((eq Prop) (((eq Prop) x) x0)) (((eq Prop) x) x0))
% 101.22/101.43 Found (eq_ref0 (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 101.22/101.43 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 101.22/101.43 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 101.22/101.43 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 101.22/101.43 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 101.22/101.43 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x0))
% 101.22/101.43 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 101.22/101.43 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 101.22/101.43 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 101.22/101.43 Found eq_ref00:=(eq_ref0 (((eq Prop) x) x0)):(((eq Prop) (((eq Prop) x) x0)) (((eq Prop) x) x0))
% 101.22/101.43 Found (eq_ref0 (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 101.22/101.43 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 101.22/101.43 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 101.22/101.43 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 101.22/101.43 Found eq_ref00:=(eq_ref0 (((eq Prop) x) x0)):(((eq Prop) (((eq Prop) x) x0)) (((eq Prop) x) x0))
% 101.22/101.43 Found (eq_ref0 (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 101.22/101.43 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 101.22/101.43 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 101.22/101.43 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 101.22/101.43 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 101.22/101.43 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x0))
% 101.22/101.43 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 101.22/101.43 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 101.22/101.43 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 101.22/101.43 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 101.22/101.43 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x0))
% 101.22/101.43 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 101.22/101.43 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 101.22/101.43 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 101.22/101.43 Found eq_ref00:=(eq_ref0 (((eq Prop) x) x0)):(((eq Prop) (((eq Prop) x) x0)) (((eq Prop) x) x0))
% 101.22/101.43 Found (eq_ref0 (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 101.22/101.43 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 101.22/101.43 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 101.22/101.43 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 101.22/101.43 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 101.22/101.43 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x0))
% 101.22/101.43 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 101.22/101.43 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 101.22/101.43 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 101.22/101.43 Found eq_ref00:=(eq_ref0 (((eq Prop) x) x0)):(((eq Prop) (((eq Prop) x) x0)) (((eq Prop) x) x0))
% 101.22/101.43 Found (eq_ref0 (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 101.22/101.43 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 101.22/101.43 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 101.22/101.43 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 101.22/101.43 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 101.22/101.43 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x0))
% 101.22/101.43 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 101.22/101.43 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 101.22/101.43 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 115.91/116.13 Found eq_ref00:=(eq_ref0 (((eq Prop) x) x0)):(((eq Prop) (((eq Prop) x) x0)) (((eq Prop) x) x0))
% 115.91/116.13 Found (eq_ref0 (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 115.91/116.13 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 115.91/116.13 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 115.91/116.13 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 115.91/116.13 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 115.91/116.13 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x0))
% 115.91/116.13 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 115.91/116.13 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 115.91/116.13 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 115.91/116.13 Found eq_ref00:=(eq_ref0 (((eq Prop) x) x0)):(((eq Prop) (((eq Prop) x) x0)) (((eq Prop) x) x0))
% 115.91/116.13 Found (eq_ref0 (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 115.91/116.13 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 115.91/116.13 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 115.91/116.13 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 115.91/116.13 Found eq_ref00:=(eq_ref0 (((eq Prop) x) x0)):(((eq Prop) (((eq Prop) x) x0)) (((eq Prop) x) x0))
% 115.91/116.13 Found (eq_ref0 (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 115.91/116.13 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 115.91/116.13 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 115.91/116.13 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 115.91/116.13 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 115.91/116.13 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x0))
% 115.91/116.13 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 115.91/116.13 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 115.91/116.13 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 115.91/116.13 Found eq_ref000:=(eq_ref00 P1):((P1 (((eq Prop) x) x0))->(P1 (((eq Prop) x) x0)))
% 115.91/116.13 Found (eq_ref00 P1) as proof of (P2 (((eq Prop) x) x0))
% 115.91/116.13 Found ((eq_ref0 (((eq Prop) x) x0)) P1) as proof of (P2 (((eq Prop) x) x0))
% 115.91/116.13 Found (((eq_ref Prop) (((eq Prop) x) x0)) P1) as proof of (P2 (((eq Prop) x) x0))
% 115.91/116.13 Found (((eq_ref Prop) (((eq Prop) x) x0)) P1) as proof of (P2 (((eq Prop) x) x0))
% 115.91/116.13 Found eq_ref000:=(eq_ref00 P1):((P1 (((eq Prop) x) x0))->(P1 (((eq Prop) x) x0)))
% 115.91/116.13 Found (eq_ref00 P1) as proof of (P2 (((eq Prop) x) x0))
% 115.91/116.13 Found ((eq_ref0 (((eq Prop) x) x0)) P1) as proof of (P2 (((eq Prop) x) x0))
% 115.91/116.13 Found (((eq_ref Prop) (((eq Prop) x) x0)) P1) as proof of (P2 (((eq Prop) x) x0))
% 115.91/116.13 Found (((eq_ref Prop) (((eq Prop) x) x0)) P1) as proof of (P2 (((eq Prop) x) x0))
% 115.91/116.13 Found eq_ref000:=(eq_ref00 P1):((P1 (((eq Prop) x) x0))->(P1 (((eq Prop) x) x0)))
% 115.91/116.13 Found (eq_ref00 P1) as proof of (P2 (((eq Prop) x) x0))
% 115.91/116.13 Found ((eq_ref0 (((eq Prop) x) x0)) P1) as proof of (P2 (((eq Prop) x) x0))
% 115.91/116.13 Found (((eq_ref Prop) (((eq Prop) x) x0)) P1) as proof of (P2 (((eq Prop) x) x0))
% 115.91/116.13 Found (((eq_ref Prop) (((eq Prop) x) x0)) P1) as proof of (P2 (((eq Prop) x) x0))
% 115.91/116.13 Found eq_ref000:=(eq_ref00 P1):((P1 (((eq Prop) x) x0))->(P1 (((eq Prop) x) x0)))
% 115.91/116.13 Found (eq_ref00 P1) as proof of (P2 (((eq Prop) x) x0))
% 115.91/116.13 Found ((eq_ref0 (((eq Prop) x) x0)) P1) as proof of (P2 (((eq Prop) x) x0))
% 115.91/116.13 Found (((eq_ref Prop) (((eq Prop) x) x0)) P1) as proof of (P2 (((eq Prop) x) x0))
% 115.91/116.13 Found (((eq_ref Prop) (((eq Prop) x) x0)) P1) as proof of (P2 (((eq Prop) x) x0))
% 115.91/116.13 Found x01:(P1 b)
% 115.91/116.13 Found (fun (x01:(P1 b))=> x01) as proof of (P1 b)
% 115.91/116.13 Found (fun (x01:(P1 b))=> x01) as proof of (P2 b)
% 115.91/116.13 Found x01:(P1 b)
% 115.91/116.13 Found (fun (x01:(P1 b))=> x01) as proof of (P1 b)
% 115.91/116.13 Found (fun (x01:(P1 b))=> x01) as proof of (P2 b)
% 115.91/116.13 Found x01:(P1 b)
% 115.91/116.13 Found (fun (x01:(P1 b))=> x01) as proof of (P1 b)
% 115.91/116.13 Found (fun (x01:(P1 b))=> x01) as proof of (P2 b)
% 115.91/116.13 Found x01:(P1 b)
% 115.91/116.13 Found (fun (x01:(P1 b))=> x01) as proof of (P1 b)
% 115.91/116.13 Found (fun (x01:(P1 b))=> x01) as proof of (P2 b)
% 115.91/116.13 Found x01:(P1 b)
% 115.91/116.13 Found (fun (x01:(P1 b))=> x01) as proof of (P1 b)
% 115.91/116.13 Found (fun (x01:(P1 b))=> x01) as proof of (P2 b)
% 115.91/116.13 Found x01:(P1 b)
% 115.91/116.13 Found (fun (x01:(P1 b))=> x01) as proof of (P1 b)
% 115.91/116.13 Found (fun (x01:(P1 b))=> x01) as proof of (P2 b)
% 123.73/123.96 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xy:Prop)=> (((eq Prop) x) Xy))):(((eq (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) (fun (x0:Prop)=> (((eq Prop) x) x0)))
% 123.73/123.96 Found (eta_expansion_dep00 (fun (Xy:Prop)=> (((eq Prop) x) Xy))) as proof of (((eq (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) b0)
% 123.73/123.96 Found ((eta_expansion_dep0 (fun (x1:Prop)=> Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) as proof of (((eq (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) b0)
% 123.73/123.96 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) as proof of (((eq (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) b0)
% 123.73/123.96 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) as proof of (((eq (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) b0)
% 123.73/123.96 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) as proof of (((eq (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) b0)
% 123.73/123.96 Found eta_expansion_dep000:=(eta_expansion_dep00 b0):(((eq (Prop->Prop)) b0) (fun (x:Prop)=> (b0 x)))
% 123.73/123.96 Found (eta_expansion_dep00 b0) as proof of (((eq (Prop->Prop)) b0) b)
% 123.73/123.96 Found ((eta_expansion_dep0 (fun (x1:Prop)=> Prop)) b0) as proof of (((eq (Prop->Prop)) b0) b)
% 123.73/123.96 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) b0) as proof of (((eq (Prop->Prop)) b0) b)
% 123.73/123.96 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) b0) as proof of (((eq (Prop->Prop)) b0) b)
% 123.73/123.96 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) b0) as proof of (((eq (Prop->Prop)) b0) b)
% 123.73/123.96 Found eq_ref00:=(eq_ref0 (fun (Xy:Prop)=> (((eq Prop) x) Xy))):(((eq (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 123.73/123.96 Found (eq_ref0 (fun (Xy:Prop)=> (((eq Prop) x) Xy))) as proof of (((eq (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) b0)
% 123.73/123.96 Found ((eq_ref (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) as proof of (((eq (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) b0)
% 123.73/123.96 Found ((eq_ref (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) as proof of (((eq (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) b0)
% 123.73/123.96 Found ((eq_ref (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) as proof of (((eq (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) b0)
% 123.73/123.96 Found eq_ref00:=(eq_ref0 b0):(((eq (Prop->Prop)) b0) b0)
% 123.73/123.96 Found (eq_ref0 b0) as proof of (((eq (Prop->Prop)) b0) b)
% 123.73/123.96 Found ((eq_ref (Prop->Prop)) b0) as proof of (((eq (Prop->Prop)) b0) b)
% 123.73/123.96 Found ((eq_ref (Prop->Prop)) b0) as proof of (((eq (Prop->Prop)) b0) b)
% 123.73/123.96 Found ((eq_ref (Prop->Prop)) b0) as proof of (((eq (Prop->Prop)) b0) b)
% 123.73/123.96 Found eta_expansion_dep000:=(eta_expansion_dep00 ((eq Prop) x)):(((eq (Prop->Prop)) ((eq Prop) x)) (fun (x0:Prop)=> (((eq Prop) x) x0)))
% 123.73/123.96 Found (eta_expansion_dep00 ((eq Prop) x)) as proof of (((eq (Prop->Prop)) ((eq Prop) x)) b0)
% 123.73/123.96 Found ((eta_expansion_dep0 (fun (x1:Prop)=> Prop)) ((eq Prop) x)) as proof of (((eq (Prop->Prop)) ((eq Prop) x)) b0)
% 123.73/123.96 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) ((eq Prop) x)) as proof of (((eq (Prop->Prop)) ((eq Prop) x)) b0)
% 123.73/123.96 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) ((eq Prop) x)) as proof of (((eq (Prop->Prop)) ((eq Prop) x)) b0)
% 123.73/123.96 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) ((eq Prop) x)) as proof of (((eq (Prop->Prop)) ((eq Prop) x)) b0)
% 123.73/123.96 Found eta_expansion_dep000:=(eta_expansion_dep00 b0):(((eq (Prop->Prop)) b0) (fun (x:Prop)=> (b0 x)))
% 123.73/123.96 Found (eta_expansion_dep00 b0) as proof of (((eq (Prop->Prop)) b0) b)
% 123.73/123.96 Found ((eta_expansion_dep0 (fun (x1:Prop)=> Prop)) b0) as proof of (((eq (Prop->Prop)) b0) b)
% 123.73/123.96 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) b0) as proof of (((eq (Prop->Prop)) b0) b)
% 123.73/123.96 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) b0) as proof of (((eq (Prop->Prop)) b0) b)
% 123.73/123.96 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) b0) as proof of (((eq (Prop->Prop)) b0) b)
% 123.73/123.96 Found eta_expansion_dep000:=(eta_expansion_dep00 ((eq Prop) x)):(((eq (Prop->Prop)) ((eq Prop) x)) (fun (x0:Prop)=> (((eq Prop) x) x0)))
% 123.73/123.96 Found (eta_expansion_dep00 ((eq Prop) x)) as proof of (((eq (Prop->Prop)) ((eq Prop) x)) b0)
% 136.59/136.81 Found ((eta_expansion_dep0 (fun (x1:Prop)=> Prop)) ((eq Prop) x)) as proof of (((eq (Prop->Prop)) ((eq Prop) x)) b0)
% 136.59/136.81 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) ((eq Prop) x)) as proof of (((eq (Prop->Prop)) ((eq Prop) x)) b0)
% 136.59/136.81 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) ((eq Prop) x)) as proof of (((eq (Prop->Prop)) ((eq Prop) x)) b0)
% 136.59/136.81 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) ((eq Prop) x)) as proof of (((eq (Prop->Prop)) ((eq Prop) x)) b0)
% 136.59/136.81 Found eta_expansion_dep000:=(eta_expansion_dep00 b0):(((eq (Prop->Prop)) b0) (fun (x:Prop)=> (b0 x)))
% 136.59/136.81 Found (eta_expansion_dep00 b0) as proof of (((eq (Prop->Prop)) b0) b)
% 136.59/136.81 Found ((eta_expansion_dep0 (fun (x1:Prop)=> Prop)) b0) as proof of (((eq (Prop->Prop)) b0) b)
% 136.59/136.81 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) b0) as proof of (((eq (Prop->Prop)) b0) b)
% 136.59/136.81 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) b0) as proof of (((eq (Prop->Prop)) b0) b)
% 136.59/136.81 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) b0) as proof of (((eq (Prop->Prop)) b0) b)
% 136.59/136.81 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 136.59/136.81 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 136.59/136.81 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 136.59/136.81 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 136.59/136.81 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 136.59/136.81 Found eq_ref00:=(eq_ref0 (b x0)):(((eq Prop) (b x0)) (b x0))
% 136.59/136.81 Found (eq_ref0 (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 136.59/136.81 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 136.59/136.81 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 136.59/136.81 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 136.59/136.81 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 136.59/136.81 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 136.59/136.81 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 136.59/136.81 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 136.59/136.81 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 136.59/136.81 Found eq_ref00:=(eq_ref0 (b x0)):(((eq Prop) (b x0)) (b x0))
% 136.59/136.81 Found (eq_ref0 (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 136.59/136.81 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 136.59/136.81 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 136.59/136.81 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 136.59/136.81 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 136.59/136.81 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 136.59/136.81 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 136.59/136.81 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 136.59/136.81 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 136.59/136.81 Found eq_ref00:=(eq_ref0 (b x0)):(((eq Prop) (b x0)) (b x0))
% 136.59/136.81 Found (eq_ref0 (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 136.59/136.81 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 136.59/136.81 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 136.59/136.81 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 136.59/136.81 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 136.59/136.81 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 136.59/136.81 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 136.59/136.81 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 136.59/136.81 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 136.59/136.81 Found eq_ref00:=(eq_ref0 (b x0)):(((eq Prop) (b x0)) (b x0))
% 136.59/136.81 Found (eq_ref0 (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 136.59/136.81 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 136.59/136.81 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 136.59/136.81 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 136.59/136.81 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (fun (Xy:Prop)=> (((eq Prop) x) Xy)))->(P1 (fun (x0:Prop)=> (((eq Prop) x) x0))))
% 136.59/136.81 Found (eta_expansion_dep000 P1) as proof of (P2 (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 136.59/136.81 Found ((eta_expansion_dep00 (fun (Xy:Prop)=> (((eq Prop) x) Xy))) P1) as proof of (P2 (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 136.59/136.81 Found (((eta_expansion_dep0 (fun (x1:Prop)=> Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) P1) as proof of (P2 (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 139.88/140.17 Found ((((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) P1) as proof of (P2 (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 139.88/140.17 Found ((((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) P1) as proof of (P2 (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 139.88/140.17 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (fun (Xy:Prop)=> (((eq Prop) x) Xy)))->(P1 (fun (x0:Prop)=> (((eq Prop) x) x0))))
% 139.88/140.17 Found (eta_expansion_dep000 P1) as proof of (P2 (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 139.88/140.17 Found ((eta_expansion_dep00 (fun (Xy:Prop)=> (((eq Prop) x) Xy))) P1) as proof of (P2 (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 139.88/140.17 Found (((eta_expansion_dep0 (fun (x1:Prop)=> Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) P1) as proof of (P2 (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 139.88/140.17 Found ((((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) P1) as proof of (P2 (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 139.88/140.17 Found ((((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) P1) as proof of (P2 (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 139.88/140.17 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (fun (Xy:Prop)=> (((eq Prop) x) Xy)))->(P1 (fun (x0:Prop)=> (((eq Prop) x) x0))))
% 139.88/140.17 Found (eta_expansion_dep000 P1) as proof of (P2 (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 139.88/140.17 Found ((eta_expansion_dep00 (fun (Xy:Prop)=> (((eq Prop) x) Xy))) P1) as proof of (P2 (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 139.88/140.17 Found (((eta_expansion_dep0 (fun (x1:Prop)=> Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) P1) as proof of (P2 (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 139.88/140.17 Found ((((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) P1) as proof of (P2 (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 139.88/140.17 Found ((((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) P1) as proof of (P2 (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 139.88/140.17 Found eq_ref000:=(eq_ref00 P1):((P1 (fun (Xy:Prop)=> (((eq Prop) x) Xy)))->(P1 (fun (Xy:Prop)=> (((eq Prop) x) Xy))))
% 139.88/140.17 Found (eq_ref00 P1) as proof of (P2 (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 139.88/140.17 Found ((eq_ref0 (fun (Xy:Prop)=> (((eq Prop) x) Xy))) P1) as proof of (P2 (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 139.88/140.17 Found (((eq_ref (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) P1) as proof of (P2 (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 139.88/140.17 Found (((eq_ref (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) P1) as proof of (P2 (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 139.88/140.17 Found eq_ref00:=(eq_ref0 (b x0)):(((eq Prop) (b x0)) (b x0))
% 139.88/140.17 Found (eq_ref0 (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 139.88/140.17 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 139.88/140.17 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 139.88/140.17 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 139.88/140.17 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 139.88/140.17 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 139.88/140.17 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 139.88/140.17 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 139.88/140.17 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 139.88/140.17 Found eq_ref00:=(eq_ref0 (b x0)):(((eq Prop) (b x0)) (b x0))
% 139.88/140.17 Found (eq_ref0 (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 139.88/140.17 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 139.88/140.17 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 139.88/140.17 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 139.88/140.17 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 139.88/140.17 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 139.88/140.17 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 139.88/140.17 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 139.88/140.17 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 139.88/140.17 Found eq_ref00:=(eq_ref0 (b x0)):(((eq Prop) (b x0)) (b x0))
% 139.88/140.17 Found (eq_ref0 (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 139.88/140.17 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 139.88/140.17 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 142.11/142.40 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 142.11/142.40 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 142.11/142.40 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 142.11/142.40 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 142.11/142.40 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 142.11/142.40 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 142.11/142.40 Found eq_ref00:=(eq_ref0 (b x0)):(((eq Prop) (b x0)) (b x0))
% 142.11/142.40 Found (eq_ref0 (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 142.11/142.40 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 142.11/142.40 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 142.11/142.40 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 142.11/142.40 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 142.11/142.40 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 142.11/142.40 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 142.11/142.40 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 142.11/142.40 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 142.11/142.40 Found eq_ref000:=(eq_ref00 P1):((P1 ((eq Prop) x))->(P1 ((eq Prop) x)))
% 142.11/142.40 Found (eq_ref00 P1) as proof of (P2 ((eq Prop) x))
% 142.11/142.40 Found ((eq_ref0 ((eq Prop) x)) P1) as proof of (P2 ((eq Prop) x))
% 142.11/142.40 Found (((eq_ref (Prop->Prop)) ((eq Prop) x)) P1) as proof of (P2 ((eq Prop) x))
% 142.11/142.40 Found (((eq_ref (Prop->Prop)) ((eq Prop) x)) P1) as proof of (P2 ((eq Prop) x))
% 142.11/142.40 Found eq_ref000:=(eq_ref00 P1):((P1 ((eq Prop) x))->(P1 ((eq Prop) x)))
% 142.11/142.40 Found (eq_ref00 P1) as proof of (P2 ((eq Prop) x))
% 142.11/142.40 Found ((eq_ref0 ((eq Prop) x)) P1) as proof of (P2 ((eq Prop) x))
% 142.11/142.40 Found (((eq_ref (Prop->Prop)) ((eq Prop) x)) P1) as proof of (P2 ((eq Prop) x))
% 142.11/142.40 Found (((eq_ref (Prop->Prop)) ((eq Prop) x)) P1) as proof of (P2 ((eq Prop) x))
% 142.11/142.40 Found eq_ref000:=(eq_ref00 P1):((P1 ((eq Prop) x))->(P1 ((eq Prop) x)))
% 142.11/142.40 Found (eq_ref00 P1) as proof of (P2 ((eq Prop) x))
% 142.11/142.40 Found ((eq_ref0 ((eq Prop) x)) P1) as proof of (P2 ((eq Prop) x))
% 142.11/142.40 Found (((eq_ref (Prop->Prop)) ((eq Prop) x)) P1) as proof of (P2 ((eq Prop) x))
% 142.11/142.40 Found (((eq_ref (Prop->Prop)) ((eq Prop) x)) P1) as proof of (P2 ((eq Prop) x))
% 142.11/142.40 Found eq_ref000:=(eq_ref00 P1):((P1 ((eq Prop) x))->(P1 ((eq Prop) x)))
% 142.11/142.40 Found (eq_ref00 P1) as proof of (P2 ((eq Prop) x))
% 142.11/142.40 Found ((eq_ref0 ((eq Prop) x)) P1) as proof of (P2 ((eq Prop) x))
% 142.11/142.40 Found (((eq_ref (Prop->Prop)) ((eq Prop) x)) P1) as proof of (P2 ((eq Prop) x))
% 142.11/142.40 Found (((eq_ref (Prop->Prop)) ((eq Prop) x)) P1) as proof of (P2 ((eq Prop) x))
% 142.11/142.40 Found eq_ref00:=(eq_ref0 (b x0)):(((eq Prop) (b x0)) (b x0))
% 142.11/142.40 Found (eq_ref0 (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 142.11/142.40 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 142.11/142.40 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 142.11/142.40 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 142.11/142.40 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 142.11/142.40 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 142.11/142.40 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 142.11/142.40 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 142.11/142.40 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 142.11/142.40 Found eq_ref00:=(eq_ref0 (b x0)):(((eq Prop) (b x0)) (b x0))
% 142.11/142.40 Found (eq_ref0 (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 142.11/142.40 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 142.11/142.40 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 142.11/142.40 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 142.11/142.40 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 142.11/142.40 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 142.11/142.40 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 142.11/142.40 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 142.11/142.40 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 142.11/142.40 Found eq_ref00:=(eq_ref0 (b x0)):(((eq Prop) (b x0)) (b x0))
% 142.11/142.40 Found (eq_ref0 (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 142.11/142.40 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 142.11/142.40 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 142.11/142.40 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 183.08/183.38 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 183.08/183.38 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 183.08/183.38 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 183.08/183.38 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 183.08/183.38 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 183.08/183.38 Found eq_ref00:=(eq_ref0 (b x0)):(((eq Prop) (b x0)) (b x0))
% 183.08/183.38 Found (eq_ref0 (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 183.08/183.38 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 183.08/183.38 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 183.08/183.38 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 183.08/183.38 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 183.08/183.38 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 183.08/183.38 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 183.08/183.38 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 183.08/183.38 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 183.08/183.38 Found x11:(P1 (b x0))
% 183.08/183.38 Found (fun (x11:(P1 (b x0)))=> x11) as proof of (P1 (b x0))
% 183.08/183.38 Found (fun (x11:(P1 (b x0)))=> x11) as proof of (P2 (b x0))
% 183.08/183.38 Found x11:(P1 (b x0))
% 183.08/183.38 Found (fun (x11:(P1 (b x0)))=> x11) as proof of (P1 (b x0))
% 183.08/183.38 Found (fun (x11:(P1 (b x0)))=> x11) as proof of (P2 (b x0))
% 183.08/183.38 Found x11:(P1 (b x0))
% 183.08/183.38 Found (fun (x11:(P1 (b x0)))=> x11) as proof of (P1 (b x0))
% 183.08/183.38 Found (fun (x11:(P1 (b x0)))=> x11) as proof of (P2 (b x0))
% 183.08/183.38 Found x11:(P1 (b x0))
% 183.08/183.38 Found (fun (x11:(P1 (b x0)))=> x11) as proof of (P1 (b x0))
% 183.08/183.38 Found (fun (x11:(P1 (b x0)))=> x11) as proof of (P2 (b x0))
% 183.08/183.38 Found x11:(P1 (b x0))
% 183.08/183.38 Found (fun (x11:(P1 (b x0)))=> x11) as proof of (P1 (b x0))
% 183.08/183.38 Found (fun (x11:(P1 (b x0)))=> x11) as proof of (P2 (b x0))
% 183.08/183.38 Found x11:(P1 (b x0))
% 183.08/183.38 Found (fun (x11:(P1 (b x0)))=> x11) as proof of (P1 (b x0))
% 183.08/183.38 Found (fun (x11:(P1 (b x0)))=> x11) as proof of (P2 (b x0))
% 183.08/183.38 Found x11:(P1 (b x0))
% 183.08/183.38 Found (fun (x11:(P1 (b x0)))=> x11) as proof of (P1 (b x0))
% 183.08/183.38 Found (fun (x11:(P1 (b x0)))=> x11) as proof of (P2 (b x0))
% 183.08/183.38 Found x11:(P1 (b x0))
% 183.08/183.38 Found (fun (x11:(P1 (b x0)))=> x11) as proof of (P1 (b x0))
% 183.08/183.38 Found (fun (x11:(P1 (b x0)))=> x11) as proof of (P2 (b x0))
% 183.08/183.38 Found eta_expansion000:=(eta_expansion00 b0):(((eq (Prop->Prop)) b0) (fun (x:Prop)=> (b0 x)))
% 183.08/183.38 Found (eta_expansion00 b0) as proof of (((eq (Prop->Prop)) b0) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 183.08/183.38 Found ((eta_expansion0 Prop) b0) as proof of (((eq (Prop->Prop)) b0) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 183.08/183.38 Found (((eta_expansion Prop) Prop) b0) as proof of (((eq (Prop->Prop)) b0) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 183.08/183.38 Found (((eta_expansion Prop) Prop) b0) as proof of (((eq (Prop->Prop)) b0) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 183.08/183.38 Found (((eta_expansion Prop) Prop) b0) as proof of (((eq (Prop->Prop)) b0) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 183.08/183.38 Found eq_ref00:=(eq_ref0 a0):(((eq (Prop->Prop)) a0) a0)
% 183.08/183.38 Found (eq_ref0 a0) as proof of (((eq (Prop->Prop)) a0) b0)
% 183.08/183.38 Found ((eq_ref (Prop->Prop)) a0) as proof of (((eq (Prop->Prop)) a0) b0)
% 183.08/183.38 Found ((eq_ref (Prop->Prop)) a0) as proof of (((eq (Prop->Prop)) a0) b0)
% 183.08/183.38 Found ((eq_ref (Prop->Prop)) a0) as proof of (((eq (Prop->Prop)) a0) b0)
% 183.08/183.38 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 183.08/183.38 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x0))
% 183.08/183.38 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 183.08/183.38 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 183.08/183.38 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 183.08/183.38 Found eq_ref00:=(eq_ref0 (((eq Prop) x) x0)):(((eq Prop) (((eq Prop) x) x0)) (((eq Prop) x) x0))
% 183.08/183.38 Found (eq_ref0 (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 183.08/183.38 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 183.08/183.38 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 183.08/183.38 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 183.08/183.38 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 183.08/183.38 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x0))
% 183.08/183.38 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 183.08/183.38 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 183.08/183.38 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 185.74/186.05 Found eq_ref00:=(eq_ref0 (((eq Prop) x) x0)):(((eq Prop) (((eq Prop) x) x0)) (((eq Prop) x) x0))
% 185.74/186.05 Found (eq_ref0 (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 185.74/186.05 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 185.74/186.05 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 185.74/186.05 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 185.74/186.05 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 185.74/186.05 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x0))
% 185.74/186.05 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 185.74/186.05 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 185.74/186.05 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 185.74/186.05 Found eq_ref00:=(eq_ref0 (((eq Prop) x) x0)):(((eq Prop) (((eq Prop) x) x0)) (((eq Prop) x) x0))
% 185.74/186.05 Found (eq_ref0 (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 185.74/186.05 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 185.74/186.05 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 185.74/186.05 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 185.74/186.05 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 185.74/186.05 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x0))
% 185.74/186.05 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 185.74/186.05 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 185.74/186.05 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 185.74/186.05 Found eq_ref00:=(eq_ref0 (((eq Prop) x) x0)):(((eq Prop) (((eq Prop) x) x0)) (((eq Prop) x) x0))
% 185.74/186.05 Found (eq_ref0 (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 185.74/186.05 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 185.74/186.05 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 185.74/186.05 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 185.74/186.05 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 185.74/186.05 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x0))
% 185.74/186.05 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 185.74/186.05 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 185.74/186.05 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 185.74/186.05 Found eq_ref00:=(eq_ref0 (((eq Prop) x) x0)):(((eq Prop) (((eq Prop) x) x0)) (((eq Prop) x) x0))
% 185.74/186.05 Found (eq_ref0 (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 185.74/186.05 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 185.74/186.05 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 185.74/186.05 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 185.74/186.05 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 185.74/186.05 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x0))
% 185.74/186.05 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 185.74/186.05 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 185.74/186.05 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 185.74/186.05 Found eq_ref00:=(eq_ref0 (((eq Prop) x) x0)):(((eq Prop) (((eq Prop) x) x0)) (((eq Prop) x) x0))
% 185.74/186.05 Found (eq_ref0 (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 185.74/186.05 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 185.74/186.05 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 185.74/186.05 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 185.74/186.05 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 185.74/186.05 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x0))
% 185.74/186.05 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 185.74/186.05 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 185.74/186.05 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 185.74/186.05 Found eq_ref00:=(eq_ref0 (((eq Prop) x) x0)):(((eq Prop) (((eq Prop) x) x0)) (((eq Prop) x) x0))
% 185.74/186.05 Found (eq_ref0 (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 185.74/186.05 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 185.74/186.05 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 185.74/186.05 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 187.34/187.67 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 187.34/187.67 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x0))
% 187.34/187.67 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 187.34/187.67 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 187.34/187.67 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 187.34/187.67 Found eq_ref00:=(eq_ref0 (((eq Prop) x) x0)):(((eq Prop) (((eq Prop) x) x0)) (((eq Prop) x) x0))
% 187.34/187.67 Found (eq_ref0 (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 187.34/187.67 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 187.34/187.67 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 187.34/187.67 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 187.34/187.67 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 187.34/187.67 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x0))
% 187.34/187.67 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 187.34/187.67 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 187.34/187.67 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 187.34/187.67 Found eq_ref00:=(eq_ref0 (((eq Prop) x) x0)):(((eq Prop) (((eq Prop) x) x0)) (((eq Prop) x) x0))
% 187.34/187.67 Found (eq_ref0 (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 187.34/187.67 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 187.34/187.67 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 187.34/187.67 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 187.34/187.67 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 187.34/187.67 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x0))
% 187.34/187.67 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 187.34/187.67 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 187.34/187.67 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 187.34/187.67 Found eq_ref00:=(eq_ref0 (((eq Prop) x) x0)):(((eq Prop) (((eq Prop) x) x0)) (((eq Prop) x) x0))
% 187.34/187.67 Found (eq_ref0 (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 187.34/187.67 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 187.34/187.67 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 187.34/187.67 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 187.34/187.67 Found eq_ref00:=(eq_ref0 (((eq Prop) x) x0)):(((eq Prop) (((eq Prop) x) x0)) (((eq Prop) x) x0))
% 187.34/187.67 Found (eq_ref0 (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 187.34/187.67 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 187.34/187.67 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 187.34/187.67 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 187.34/187.67 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 187.34/187.67 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x0))
% 187.34/187.67 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 187.34/187.67 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 187.34/187.67 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 187.34/187.67 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 187.34/187.67 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x0))
% 187.34/187.67 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 187.34/187.67 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 187.34/187.67 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 187.34/187.67 Found eq_ref00:=(eq_ref0 (((eq Prop) x) x0)):(((eq Prop) (((eq Prop) x) x0)) (((eq Prop) x) x0))
% 187.34/187.67 Found (eq_ref0 (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 187.34/187.67 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 187.34/187.67 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 187.34/187.67 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 187.34/187.67 Found eq_ref00:=(eq_ref0 b0):(((eq (Prop->Prop)) b0) b0)
% 187.34/187.67 Found (eq_ref0 b0) as proof of (((eq (Prop->Prop)) b0) ((eq Prop) x))
% 187.34/187.67 Found ((eq_ref (Prop->Prop)) b0) as proof of (((eq (Prop->Prop)) b0) ((eq Prop) x))
% 187.34/187.67 Found ((eq_ref (Prop->Prop)) b0) as proof of (((eq (Prop->Prop)) b0) ((eq Prop) x))
% 187.34/187.67 Found ((eq_ref (Prop->Prop)) b0) as proof of (((eq (Prop->Prop)) b0) ((eq Prop) x))
% 187.34/187.67 Found eq_ref00:=(eq_ref0 a0):(((eq (Prop->Prop)) a0) a0)
% 191.48/191.73 Found (eq_ref0 a0) as proof of (((eq (Prop->Prop)) a0) b0)
% 191.48/191.73 Found ((eq_ref (Prop->Prop)) a0) as proof of (((eq (Prop->Prop)) a0) b0)
% 191.48/191.73 Found ((eq_ref (Prop->Prop)) a0) as proof of (((eq (Prop->Prop)) a0) b0)
% 191.48/191.73 Found ((eq_ref (Prop->Prop)) a0) as proof of (((eq (Prop->Prop)) a0) b0)
% 191.48/191.73 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 191.48/191.73 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x0))
% 191.48/191.73 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 191.48/191.73 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 191.48/191.73 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 191.48/191.73 Found eq_ref00:=(eq_ref0 (((eq Prop) x) x0)):(((eq Prop) (((eq Prop) x) x0)) (((eq Prop) x) x0))
% 191.48/191.73 Found (eq_ref0 (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 191.48/191.73 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 191.48/191.73 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 191.48/191.73 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 191.48/191.73 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 191.48/191.73 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x0))
% 191.48/191.73 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 191.48/191.73 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 191.48/191.73 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 191.48/191.73 Found eq_ref00:=(eq_ref0 (((eq Prop) x) x0)):(((eq Prop) (((eq Prop) x) x0)) (((eq Prop) x) x0))
% 191.48/191.73 Found (eq_ref0 (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 191.48/191.73 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 191.48/191.73 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 191.48/191.73 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 191.48/191.73 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 191.48/191.73 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x0))
% 191.48/191.73 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 191.48/191.73 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 191.48/191.73 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 191.48/191.73 Found eq_ref00:=(eq_ref0 (((eq Prop) x) x0)):(((eq Prop) (((eq Prop) x) x0)) (((eq Prop) x) x0))
% 191.48/191.73 Found (eq_ref0 (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 191.48/191.73 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 191.48/191.73 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 191.48/191.73 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 191.48/191.73 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 191.48/191.73 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x0))
% 191.48/191.73 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 191.48/191.73 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 191.48/191.73 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 191.48/191.73 Found eq_ref00:=(eq_ref0 (((eq Prop) x) x0)):(((eq Prop) (((eq Prop) x) x0)) (((eq Prop) x) x0))
% 191.48/191.73 Found (eq_ref0 (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 191.48/191.73 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 191.48/191.73 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 191.48/191.73 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 191.48/191.73 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 191.48/191.73 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x0))
% 191.48/191.73 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 191.48/191.73 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 191.48/191.73 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 191.48/191.73 Found eq_ref00:=(eq_ref0 (((eq Prop) x) x0)):(((eq Prop) (((eq Prop) x) x0)) (((eq Prop) x) x0))
% 191.48/191.73 Found (eq_ref0 (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 191.48/191.73 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 191.48/191.73 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 191.48/191.73 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 191.48/191.73 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 191.48/191.73 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x0))
% 193.07/193.34 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 193.07/193.34 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 193.07/193.34 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 193.07/193.34 Found eq_ref00:=(eq_ref0 (((eq Prop) x) x0)):(((eq Prop) (((eq Prop) x) x0)) (((eq Prop) x) x0))
% 193.07/193.34 Found (eq_ref0 (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 193.07/193.34 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 193.07/193.34 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 193.07/193.34 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 193.07/193.34 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 193.07/193.34 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x0))
% 193.07/193.34 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 193.07/193.34 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 193.07/193.34 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 193.07/193.34 Found eq_ref00:=(eq_ref0 (((eq Prop) x) x0)):(((eq Prop) (((eq Prop) x) x0)) (((eq Prop) x) x0))
% 193.07/193.34 Found (eq_ref0 (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 193.07/193.34 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 193.07/193.34 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 193.07/193.34 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 193.07/193.34 Found eq_ref00:=(eq_ref0 (((eq Prop) x) x0)):(((eq Prop) (((eq Prop) x) x0)) (((eq Prop) x) x0))
% 193.07/193.34 Found (eq_ref0 (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 193.07/193.34 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 193.07/193.34 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 193.07/193.34 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 193.07/193.34 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 193.07/193.34 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x0))
% 193.07/193.34 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 193.07/193.34 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 193.07/193.34 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 193.07/193.34 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 193.07/193.34 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x0))
% 193.07/193.34 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 193.07/193.34 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 193.07/193.34 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 193.07/193.34 Found eq_ref00:=(eq_ref0 (((eq Prop) x) x0)):(((eq Prop) (((eq Prop) x) x0)) (((eq Prop) x) x0))
% 193.07/193.34 Found (eq_ref0 (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 193.07/193.34 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 193.07/193.34 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 193.07/193.34 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 193.07/193.34 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 193.07/193.34 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x0))
% 193.07/193.34 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 193.07/193.34 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 193.07/193.34 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 193.07/193.34 Found eq_ref00:=(eq_ref0 (((eq Prop) x) x0)):(((eq Prop) (((eq Prop) x) x0)) (((eq Prop) x) x0))
% 193.07/193.34 Found (eq_ref0 (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 193.07/193.34 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 193.07/193.34 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 193.07/193.34 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 193.07/193.34 Found eq_ref00:=(eq_ref0 (((eq Prop) x) x0)):(((eq Prop) (((eq Prop) x) x0)) (((eq Prop) x) x0))
% 193.07/193.34 Found (eq_ref0 (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 193.07/193.34 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 193.07/193.34 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 193.07/193.34 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 193.07/193.34 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 193.07/193.34 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x0))
% 201.86/202.12 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 201.86/202.12 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 201.86/202.12 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 201.86/202.12 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 201.86/202.12 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x0))
% 201.86/202.12 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 201.86/202.12 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 201.86/202.12 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 201.86/202.12 Found eq_ref00:=(eq_ref0 (((eq Prop) x) x0)):(((eq Prop) (((eq Prop) x) x0)) (((eq Prop) x) x0))
% 201.86/202.12 Found (eq_ref0 (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 201.86/202.12 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 201.86/202.12 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 201.86/202.12 Found ((eq_ref Prop) (((eq Prop) x) x0)) as proof of (((eq Prop) (((eq Prop) x) x0)) b0)
% 201.86/202.12 Found eq_ref000:=(eq_ref00 P1):((P1 (((eq Prop) x) x0))->(P1 (((eq Prop) x) x0)))
% 201.86/202.12 Found (eq_ref00 P1) as proof of (P2 (((eq Prop) x) x0))
% 201.86/202.12 Found ((eq_ref0 (((eq Prop) x) x0)) P1) as proof of (P2 (((eq Prop) x) x0))
% 201.86/202.12 Found (((eq_ref Prop) (((eq Prop) x) x0)) P1) as proof of (P2 (((eq Prop) x) x0))
% 201.86/202.12 Found (((eq_ref Prop) (((eq Prop) x) x0)) P1) as proof of (P2 (((eq Prop) x) x0))
% 201.86/202.12 Found eq_ref000:=(eq_ref00 P1):((P1 (((eq Prop) x) x0))->(P1 (((eq Prop) x) x0)))
% 201.86/202.12 Found (eq_ref00 P1) as proof of (P2 (((eq Prop) x) x0))
% 201.86/202.12 Found ((eq_ref0 (((eq Prop) x) x0)) P1) as proof of (P2 (((eq Prop) x) x0))
% 201.86/202.12 Found (((eq_ref Prop) (((eq Prop) x) x0)) P1) as proof of (P2 (((eq Prop) x) x0))
% 201.86/202.12 Found (((eq_ref Prop) (((eq Prop) x) x0)) P1) as proof of (P2 (((eq Prop) x) x0))
% 201.86/202.12 Found eq_ref000:=(eq_ref00 P1):((P1 (((eq Prop) x) x0))->(P1 (((eq Prop) x) x0)))
% 201.86/202.12 Found (eq_ref00 P1) as proof of (P2 (((eq Prop) x) x0))
% 201.86/202.12 Found ((eq_ref0 (((eq Prop) x) x0)) P1) as proof of (P2 (((eq Prop) x) x0))
% 201.86/202.12 Found (((eq_ref Prop) (((eq Prop) x) x0)) P1) as proof of (P2 (((eq Prop) x) x0))
% 201.86/202.12 Found (((eq_ref Prop) (((eq Prop) x) x0)) P1) as proof of (P2 (((eq Prop) x) x0))
% 201.86/202.12 Found eq_ref000:=(eq_ref00 P1):((P1 (((eq Prop) x) x0))->(P1 (((eq Prop) x) x0)))
% 201.86/202.12 Found (eq_ref00 P1) as proof of (P2 (((eq Prop) x) x0))
% 201.86/202.12 Found ((eq_ref0 (((eq Prop) x) x0)) P1) as proof of (P2 (((eq Prop) x) x0))
% 201.86/202.12 Found (((eq_ref Prop) (((eq Prop) x) x0)) P1) as proof of (P2 (((eq Prop) x) x0))
% 201.86/202.12 Found (((eq_ref Prop) (((eq Prop) x) x0)) P1) as proof of (P2 (((eq Prop) x) x0))
% 201.86/202.12 Found eq_ref000:=(eq_ref00 P1):((P1 (((eq Prop) x) x0))->(P1 (((eq Prop) x) x0)))
% 201.86/202.12 Found (eq_ref00 P1) as proof of (P2 (((eq Prop) x) x0))
% 201.86/202.12 Found ((eq_ref0 (((eq Prop) x) x0)) P1) as proof of (P2 (((eq Prop) x) x0))
% 201.86/202.12 Found (((eq_ref Prop) (((eq Prop) x) x0)) P1) as proof of (P2 (((eq Prop) x) x0))
% 201.86/202.12 Found (((eq_ref Prop) (((eq Prop) x) x0)) P1) as proof of (P2 (((eq Prop) x) x0))
% 201.86/202.12 Found eq_ref000:=(eq_ref00 P1):((P1 (((eq Prop) x) x0))->(P1 (((eq Prop) x) x0)))
% 201.86/202.12 Found (eq_ref00 P1) as proof of (P2 (((eq Prop) x) x0))
% 201.86/202.12 Found ((eq_ref0 (((eq Prop) x) x0)) P1) as proof of (P2 (((eq Prop) x) x0))
% 201.86/202.12 Found (((eq_ref Prop) (((eq Prop) x) x0)) P1) as proof of (P2 (((eq Prop) x) x0))
% 201.86/202.12 Found (((eq_ref Prop) (((eq Prop) x) x0)) P1) as proof of (P2 (((eq Prop) x) x0))
% 201.86/202.12 Found eq_ref000:=(eq_ref00 P1):((P1 (((eq Prop) x) x0))->(P1 (((eq Prop) x) x0)))
% 201.86/202.12 Found (eq_ref00 P1) as proof of (P2 (((eq Prop) x) x0))
% 201.86/202.12 Found ((eq_ref0 (((eq Prop) x) x0)) P1) as proof of (P2 (((eq Prop) x) x0))
% 201.86/202.12 Found (((eq_ref Prop) (((eq Prop) x) x0)) P1) as proof of (P2 (((eq Prop) x) x0))
% 201.86/202.12 Found (((eq_ref Prop) (((eq Prop) x) x0)) P1) as proof of (P2 (((eq Prop) x) x0))
% 201.86/202.12 Found eq_ref000:=(eq_ref00 P1):((P1 (((eq Prop) x) x0))->(P1 (((eq Prop) x) x0)))
% 201.86/202.12 Found (eq_ref00 P1) as proof of (P2 (((eq Prop) x) x0))
% 201.86/202.12 Found ((eq_ref0 (((eq Prop) x) x0)) P1) as proof of (P2 (((eq Prop) x) x0))
% 201.86/202.12 Found (((eq_ref Prop) (((eq Prop) x) x0)) P1) as proof of (P2 (((eq Prop) x) x0))
% 201.86/202.12 Found (((eq_ref Prop) (((eq Prop) x) x0)) P1) as proof of (P2 (((eq Prop) x) x0))
% 201.86/202.12 Found eq_ref000:=(eq_ref00 P1):((P1 (((eq Prop) x) x0))->(P1 (((eq Prop) x) x0)))
% 201.86/202.12 Found (eq_ref00 P1) as proof of (P2 (((eq Prop) x) x0))
% 244.53/244.89 Found ((eq_ref0 (((eq Prop) x) x0)) P1) as proof of (P2 (((eq Prop) x) x0))
% 244.53/244.89 Found (((eq_ref Prop) (((eq Prop) x) x0)) P1) as proof of (P2 (((eq Prop) x) x0))
% 244.53/244.89 Found (((eq_ref Prop) (((eq Prop) x) x0)) P1) as proof of (P2 (((eq Prop) x) x0))
% 244.53/244.89 Found eq_ref000:=(eq_ref00 P1):((P1 (((eq Prop) x) x0))->(P1 (((eq Prop) x) x0)))
% 244.53/244.89 Found (eq_ref00 P1) as proof of (P2 (((eq Prop) x) x0))
% 244.53/244.89 Found ((eq_ref0 (((eq Prop) x) x0)) P1) as proof of (P2 (((eq Prop) x) x0))
% 244.53/244.89 Found (((eq_ref Prop) (((eq Prop) x) x0)) P1) as proof of (P2 (((eq Prop) x) x0))
% 244.53/244.89 Found (((eq_ref Prop) (((eq Prop) x) x0)) P1) as proof of (P2 (((eq Prop) x) x0))
% 244.53/244.89 Found eq_ref000:=(eq_ref00 P1):((P1 (((eq Prop) x) x0))->(P1 (((eq Prop) x) x0)))
% 244.53/244.89 Found (eq_ref00 P1) as proof of (P2 (((eq Prop) x) x0))
% 244.53/244.89 Found ((eq_ref0 (((eq Prop) x) x0)) P1) as proof of (P2 (((eq Prop) x) x0))
% 244.53/244.89 Found (((eq_ref Prop) (((eq Prop) x) x0)) P1) as proof of (P2 (((eq Prop) x) x0))
% 244.53/244.89 Found (((eq_ref Prop) (((eq Prop) x) x0)) P1) as proof of (P2 (((eq Prop) x) x0))
% 244.53/244.89 Found eq_ref000:=(eq_ref00 P1):((P1 (((eq Prop) x) x0))->(P1 (((eq Prop) x) x0)))
% 244.53/244.89 Found (eq_ref00 P1) as proof of (P2 (((eq Prop) x) x0))
% 244.53/244.89 Found ((eq_ref0 (((eq Prop) x) x0)) P1) as proof of (P2 (((eq Prop) x) x0))
% 244.53/244.89 Found (((eq_ref Prop) (((eq Prop) x) x0)) P1) as proof of (P2 (((eq Prop) x) x0))
% 244.53/244.89 Found (((eq_ref Prop) (((eq Prop) x) x0)) P1) as proof of (P2 (((eq Prop) x) x0))
% 244.53/244.89 Found eq_ref00:=(eq_ref0 (fun (Xy:Prop)=> (((eq Prop) x) Xy))):(((eq (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 244.53/244.89 Found (eq_ref0 (fun (Xy:Prop)=> (((eq Prop) x) Xy))) as proof of (((eq (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) b0)
% 244.53/244.89 Found ((eq_ref (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) as proof of (((eq (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) b0)
% 244.53/244.89 Found ((eq_ref (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) as proof of (((eq (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) b0)
% 244.53/244.89 Found ((eq_ref (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) as proof of (((eq (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) b0)
% 244.53/244.89 Found eta_expansion_dep000:=(eta_expansion_dep00 b0):(((eq (Prop->Prop)) b0) (fun (x:Prop)=> (b0 x)))
% 244.53/244.89 Found (eta_expansion_dep00 b0) as proof of (((eq (Prop->Prop)) b0) b)
% 244.53/244.89 Found ((eta_expansion_dep0 (fun (x1:Prop)=> Prop)) b0) as proof of (((eq (Prop->Prop)) b0) b)
% 244.53/244.89 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) b0) as proof of (((eq (Prop->Prop)) b0) b)
% 244.53/244.89 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) b0) as proof of (((eq (Prop->Prop)) b0) b)
% 244.53/244.89 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) b0) as proof of (((eq (Prop->Prop)) b0) b)
% 244.53/244.89 Found eq_ref00:=(eq_ref0 ((eq Prop) x)):(((eq (Prop->Prop)) ((eq Prop) x)) ((eq Prop) x))
% 244.53/244.89 Found (eq_ref0 ((eq Prop) x)) as proof of (((eq (Prop->Prop)) ((eq Prop) x)) b0)
% 244.53/244.89 Found ((eq_ref (Prop->Prop)) ((eq Prop) x)) as proof of (((eq (Prop->Prop)) ((eq Prop) x)) b0)
% 244.53/244.89 Found ((eq_ref (Prop->Prop)) ((eq Prop) x)) as proof of (((eq (Prop->Prop)) ((eq Prop) x)) b0)
% 244.53/244.89 Found ((eq_ref (Prop->Prop)) ((eq Prop) x)) as proof of (((eq (Prop->Prop)) ((eq Prop) x)) b0)
% 244.53/244.89 Found eta_expansion_dep000:=(eta_expansion_dep00 b0):(((eq (Prop->Prop)) b0) (fun (x:Prop)=> (b0 x)))
% 244.53/244.89 Found (eta_expansion_dep00 b0) as proof of (((eq (Prop->Prop)) b0) b)
% 244.53/244.89 Found ((eta_expansion_dep0 (fun (x1:Prop)=> Prop)) b0) as proof of (((eq (Prop->Prop)) b0) b)
% 244.53/244.89 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) b0) as proof of (((eq (Prop->Prop)) b0) b)
% 244.53/244.89 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) b0) as proof of (((eq (Prop->Prop)) b0) b)
% 244.53/244.89 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) b0) as proof of (((eq (Prop->Prop)) b0) b)
% 244.53/244.89 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 244.53/244.89 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 244.53/244.89 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 244.53/244.89 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 244.53/244.89 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 244.53/244.89 Found eq_ref00:=(eq_ref0 (b x0)):(((eq Prop) (b x0)) (b x0))
% 244.53/244.89 Found (eq_ref0 (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 245.80/246.12 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 245.80/246.12 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 245.80/246.12 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 245.80/246.12 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 245.80/246.12 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 245.80/246.12 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 245.80/246.12 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 245.80/246.12 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 245.80/246.12 Found eq_ref00:=(eq_ref0 (b x0)):(((eq Prop) (b x0)) (b x0))
% 245.80/246.12 Found (eq_ref0 (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 245.80/246.12 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 245.80/246.12 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 245.80/246.12 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 245.80/246.12 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 245.80/246.12 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 245.80/246.12 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 245.80/246.12 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 245.80/246.12 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 245.80/246.12 Found eq_ref00:=(eq_ref0 (b x0)):(((eq Prop) (b x0)) (b x0))
% 245.80/246.12 Found (eq_ref0 (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 245.80/246.12 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 245.80/246.12 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 245.80/246.12 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 245.80/246.12 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 245.80/246.12 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 245.80/246.12 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 245.80/246.12 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 245.80/246.12 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 245.80/246.12 Found eq_ref00:=(eq_ref0 (b x0)):(((eq Prop) (b x0)) (b x0))
% 245.80/246.12 Found (eq_ref0 (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 245.80/246.12 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 245.80/246.12 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 245.80/246.12 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 245.80/246.12 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 245.80/246.12 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 245.80/246.12 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 245.80/246.12 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 245.80/246.12 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 245.80/246.12 Found eq_ref00:=(eq_ref0 (b x0)):(((eq Prop) (b x0)) (b x0))
% 245.80/246.12 Found (eq_ref0 (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 245.80/246.12 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 245.80/246.12 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 245.80/246.12 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 245.80/246.12 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 245.80/246.12 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 245.80/246.12 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 245.80/246.12 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 245.80/246.12 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 245.80/246.12 Found eq_ref00:=(eq_ref0 (b x0)):(((eq Prop) (b x0)) (b x0))
% 245.80/246.12 Found (eq_ref0 (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 245.80/246.12 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 245.80/246.12 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 245.80/246.12 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 245.80/246.12 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 245.80/246.12 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 245.80/246.12 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 245.80/246.12 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 245.80/246.12 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 245.80/246.12 Found eq_ref00:=(eq_ref0 (b x0)):(((eq Prop) (b x0)) (b x0))
% 245.80/246.12 Found (eq_ref0 (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 245.80/246.12 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 245.80/246.12 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 245.80/246.12 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 252.10/252.48 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 252.10/252.48 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 252.10/252.48 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 252.10/252.48 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 252.10/252.48 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 252.10/252.48 Found eq_ref00:=(eq_ref0 (b x0)):(((eq Prop) (b x0)) (b x0))
% 252.10/252.48 Found (eq_ref0 (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 252.10/252.48 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 252.10/252.48 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 252.10/252.48 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 252.10/252.48 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 252.10/252.48 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 252.10/252.48 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 252.10/252.48 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 252.10/252.48 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 252.10/252.48 Found eq_ref00:=(eq_ref0 (b x0)):(((eq Prop) (b x0)) (b x0))
% 252.10/252.48 Found (eq_ref0 (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 252.10/252.48 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 252.10/252.48 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 252.10/252.48 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 252.10/252.48 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 252.10/252.48 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 252.10/252.48 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 252.10/252.48 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 252.10/252.48 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 252.10/252.48 Found eq_ref00:=(eq_ref0 (b x0)):(((eq Prop) (b x0)) (b x0))
% 252.10/252.48 Found (eq_ref0 (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 252.10/252.48 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 252.10/252.48 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 252.10/252.48 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 252.10/252.48 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 252.10/252.48 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 252.10/252.48 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 252.10/252.48 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 252.10/252.48 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 252.10/252.48 Found eq_ref00:=(eq_ref0 (b x0)):(((eq Prop) (b x0)) (b x0))
% 252.10/252.48 Found (eq_ref0 (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 252.10/252.48 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 252.10/252.48 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 252.10/252.48 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 252.10/252.48 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 252.10/252.48 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 252.10/252.48 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 252.10/252.48 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 252.10/252.48 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 252.10/252.48 Found eq_ref00:=(eq_ref0 (b x0)):(((eq Prop) (b x0)) (b x0))
% 252.10/252.48 Found (eq_ref0 (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 252.10/252.49 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 252.10/252.49 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 252.10/252.49 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 252.10/252.49 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 252.10/252.49 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 252.10/252.49 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 252.10/252.49 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 252.10/252.49 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 252.10/252.49 Found eq_ref00:=(eq_ref0 (b x0)):(((eq Prop) (b x0)) (b x0))
% 252.10/252.49 Found (eq_ref0 (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 252.10/252.49 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 252.10/252.49 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 252.10/252.49 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 252.10/252.49 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 252.10/252.49 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 252.10/252.49 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 262.20/262.52 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 262.20/262.52 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 262.20/262.52 Found eq_ref00:=(eq_ref0 (b x0)):(((eq Prop) (b x0)) (b x0))
% 262.20/262.52 Found (eq_ref0 (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 262.20/262.52 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 262.20/262.52 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 262.20/262.52 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 262.20/262.52 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 262.20/262.52 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 262.20/262.52 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 262.20/262.52 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 262.20/262.52 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 262.20/262.52 Found eq_ref00:=(eq_ref0 (b x0)):(((eq Prop) (b x0)) (b x0))
% 262.20/262.52 Found (eq_ref0 (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 262.20/262.52 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 262.20/262.52 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 262.20/262.52 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 262.20/262.52 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 262.20/262.52 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 262.20/262.52 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 262.20/262.52 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 262.20/262.52 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 262.20/262.52 Found eq_ref00:=(eq_ref0 (b x0)):(((eq Prop) (b x0)) (b x0))
% 262.20/262.52 Found (eq_ref0 (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 262.20/262.52 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 262.20/262.52 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 262.20/262.52 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 262.20/262.52 Found eq_ref00:=(eq_ref0 b1):(((eq (Prop->Prop)) b1) b1)
% 262.20/262.52 Found (eq_ref0 b1) as proof of (((eq (Prop->Prop)) b1) b0)
% 262.20/262.52 Found ((eq_ref (Prop->Prop)) b1) as proof of (((eq (Prop->Prop)) b1) b0)
% 262.20/262.52 Found ((eq_ref (Prop->Prop)) b1) as proof of (((eq (Prop->Prop)) b1) b0)
% 262.20/262.52 Found ((eq_ref (Prop->Prop)) b1) as proof of (((eq (Prop->Prop)) b1) b0)
% 262.20/262.52 Found eta_expansion_dep000:=(eta_expansion_dep00 a):(((eq (Prop->Prop)) a) (fun (x:Prop)=> (a x)))
% 262.20/262.52 Found (eta_expansion_dep00 a) as proof of (((eq (Prop->Prop)) a) b1)
% 262.20/262.52 Found ((eta_expansion_dep0 (fun (x1:Prop)=> Prop)) a) as proof of (((eq (Prop->Prop)) a) b1)
% 262.20/262.52 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) a) as proof of (((eq (Prop->Prop)) a) b1)
% 262.20/262.52 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) a) as proof of (((eq (Prop->Prop)) a) b1)
% 262.20/262.52 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) a) as proof of (((eq (Prop->Prop)) a) b1)
% 262.20/262.52 Found eq_ref000:=(eq_ref00 P1):((P1 (fun (Xy:Prop)=> (((eq Prop) x) Xy)))->(P1 (fun (Xy:Prop)=> (((eq Prop) x) Xy))))
% 262.20/262.52 Found (eq_ref00 P1) as proof of (P2 (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 262.20/262.52 Found ((eq_ref0 (fun (Xy:Prop)=> (((eq Prop) x) Xy))) P1) as proof of (P2 (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 262.20/262.52 Found (((eq_ref (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) P1) as proof of (P2 (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 262.20/262.52 Found (((eq_ref (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) P1) as proof of (P2 (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 262.20/262.52 Found eq_ref000:=(eq_ref00 P1):((P1 (fun (Xy:Prop)=> (((eq Prop) x) Xy)))->(P1 (fun (Xy:Prop)=> (((eq Prop) x) Xy))))
% 262.20/262.52 Found (eq_ref00 P1) as proof of (P2 (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 262.20/262.52 Found ((eq_ref0 (fun (Xy:Prop)=> (((eq Prop) x) Xy))) P1) as proof of (P2 (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 262.20/262.52 Found (((eq_ref (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) P1) as proof of (P2 (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 262.20/262.52 Found (((eq_ref (Prop->Prop)) (fun (Xy:Prop)=> (((eq Prop) x) Xy))) P1) as proof of (P2 (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 262.20/262.52 Found eq_ref00:=(eq_ref0 (b x0)):(((eq Prop) (b x0)) (b x0))
% 262.20/262.52 Found (eq_ref0 (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 262.20/262.52 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 262.20/262.52 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 262.20/262.52 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 287.50/287.84 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 287.50/287.84 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 287.50/287.84 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 287.50/287.84 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 287.50/287.84 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 287.50/287.84 Found eq_ref00:=(eq_ref0 (b x0)):(((eq Prop) (b x0)) (b x0))
% 287.50/287.84 Found (eq_ref0 (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 287.50/287.84 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 287.50/287.84 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 287.50/287.84 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 287.50/287.84 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 287.50/287.84 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 287.50/287.84 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 287.50/287.84 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 287.50/287.84 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 287.50/287.84 Found eq_ref000:=(eq_ref00 P1):((P1 ((eq Prop) x))->(P1 ((eq Prop) x)))
% 287.50/287.84 Found (eq_ref00 P1) as proof of (P2 ((eq Prop) x))
% 287.50/287.84 Found ((eq_ref0 ((eq Prop) x)) P1) as proof of (P2 ((eq Prop) x))
% 287.50/287.84 Found (((eq_ref (Prop->Prop)) ((eq Prop) x)) P1) as proof of (P2 ((eq Prop) x))
% 287.50/287.84 Found (((eq_ref (Prop->Prop)) ((eq Prop) x)) P1) as proof of (P2 ((eq Prop) x))
% 287.50/287.84 Found eq_ref000:=(eq_ref00 P1):((P1 ((eq Prop) x))->(P1 ((eq Prop) x)))
% 287.50/287.84 Found (eq_ref00 P1) as proof of (P2 ((eq Prop) x))
% 287.50/287.84 Found ((eq_ref0 ((eq Prop) x)) P1) as proof of (P2 ((eq Prop) x))
% 287.50/287.84 Found (((eq_ref (Prop->Prop)) ((eq Prop) x)) P1) as proof of (P2 ((eq Prop) x))
% 287.50/287.84 Found (((eq_ref (Prop->Prop)) ((eq Prop) x)) P1) as proof of (P2 ((eq Prop) x))
% 287.50/287.84 Found eq_ref00:=(eq_ref0 (b x0)):(((eq Prop) (b x0)) (b x0))
% 287.50/287.84 Found (eq_ref0 (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 287.50/287.84 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 287.50/287.84 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 287.50/287.84 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 287.50/287.84 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 287.50/287.84 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 287.50/287.84 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 287.50/287.84 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 287.50/287.84 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 287.50/287.84 Found eq_ref00:=(eq_ref0 (b x0)):(((eq Prop) (b x0)) (b x0))
% 287.50/287.84 Found (eq_ref0 (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 287.50/287.84 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 287.50/287.84 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 287.50/287.84 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 287.50/287.84 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 287.50/287.84 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 287.50/287.84 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 287.50/287.84 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 287.50/287.84 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x) x0))
% 287.50/287.84 Found x11:(P1 (b x0))
% 287.50/287.84 Found (fun (x11:(P1 (b x0)))=> x11) as proof of (P1 (b x0))
% 287.50/287.84 Found (fun (x11:(P1 (b x0)))=> x11) as proof of (P2 (b x0))
% 287.50/287.84 Found x11:(P1 (b x0))
% 287.50/287.84 Found (fun (x11:(P1 (b x0)))=> x11) as proof of (P1 (b x0))
% 287.50/287.84 Found (fun (x11:(P1 (b x0)))=> x11) as proof of (P2 (b x0))
% 287.50/287.84 Found x11:(P1 (b x0))
% 287.50/287.84 Found (fun (x11:(P1 (b x0)))=> x11) as proof of (P1 (b x0))
% 287.50/287.84 Found (fun (x11:(P1 (b x0)))=> x11) as proof of (P2 (b x0))
% 287.50/287.84 Found x11:(P1 (b x0))
% 287.50/287.84 Found (fun (x11:(P1 (b x0)))=> x11) as proof of (P1 (b x0))
% 287.50/287.84 Found (fun (x11:(P1 (b x0)))=> x11) as proof of (P2 (b x0))
% 287.50/287.84 Found eta_expansion_dep000:=(eta_expansion_dep00 b1):(((eq (Prop->Prop)) b1) (fun (x:Prop)=> (b1 x)))
% 287.50/287.84 Found (eta_expansion_dep00 b1) as proof of (((eq (Prop->Prop)) b1) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 287.50/287.84 Found ((eta_expansion_dep0 (fun (x1:Prop)=> Prop)) b1) as proof of (((eq (Prop->Prop)) b1) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 287.50/287.84 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) b1) as proof of (((eq (Prop->Prop)) b1) (fun (Xy:Prop)=> (((eq Prop) x) Xy)))
% 287.50/287.84 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Pr
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