TSTP Solution File: SYO363^5 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SYO363^5 : TPTP v7.5.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Tue Mar 29 00:51:15 EDT 2022
% Result : Timeout 291.98s 292.32s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO363^5 : TPTP v7.5.0. Released v4.0.0.
% 0.12/0.12 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n010.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 : Sat Mar 12 07:03:37 EST 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.33 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.18/0.34 Python 2.7.5
% 6.83/7.05 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 6.83/7.05 FOF formula (<kernel.Constant object at 0x1218ef0>, <kernel.Type object at 0x1218488>) of role type named a_type
% 6.83/7.05 Using role type
% 6.83/7.05 Declaring a:Type
% 6.83/7.05 FOF formula (<kernel.Constant object at 0x121db48>, <kernel.DependentProduct object at 0x1218518>) of role type named j
% 6.83/7.05 Using role type
% 6.83/7.05 Declaring j:(a->a)
% 6.83/7.05 FOF formula (<kernel.Constant object at 0x12185a8>, <kernel.DependentProduct object at 0x1218d40>) of role type named g
% 6.83/7.05 Using role type
% 6.83/7.05 Declaring g:((a->a)->(a->a))
% 6.83/7.05 FOF formula (<kernel.Constant object at 0x1218878>, <kernel.DependentProduct object at 0x1218098>) of role type named h
% 6.83/7.05 Using role type
% 6.83/7.05 Declaring h:(a->a)
% 6.83/7.05 FOF formula (<kernel.Constant object at 0x1218ef0>, <kernel.DependentProduct object at 0x12187a0>) of role type named f
% 6.83/7.05 Using role type
% 6.83/7.05 Declaring f:((a->a)->(a->a))
% 6.83/7.05 FOF formula (((and (forall (X:(a->a)) (Y:a), (((eq a) ((f X) Y)) ((g X) Y)))) (forall (Z:a), (((eq a) (h Z)) (j Z))))->(forall (Xq:((a->a)->Prop)), ((Xq (f h))->(Xq (g j))))) of role conjecture named cEDEC2_pme
% 6.83/7.05 Conjecture to prove = (((and (forall (X:(a->a)) (Y:a), (((eq a) ((f X) Y)) ((g X) Y)))) (forall (Z:a), (((eq a) (h Z)) (j Z))))->(forall (Xq:((a->a)->Prop)), ((Xq (f h))->(Xq (g j))))):Prop
% 6.83/7.05 Parameter a_DUMMY:a.
% 6.83/7.05 We need to prove ['(((and (forall (X:(a->a)) (Y:a), (((eq a) ((f X) Y)) ((g X) Y)))) (forall (Z:a), (((eq a) (h Z)) (j Z))))->(forall (Xq:((a->a)->Prop)), ((Xq (f h))->(Xq (g j)))))']
% 6.83/7.05 Parameter a:Type.
% 6.83/7.05 Parameter j:(a->a).
% 6.83/7.05 Parameter g:((a->a)->(a->a)).
% 6.83/7.05 Parameter h:(a->a).
% 6.83/7.05 Parameter f:((a->a)->(a->a)).
% 6.83/7.05 Trying to prove (((and (forall (X:(a->a)) (Y:a), (((eq a) ((f X) Y)) ((g X) Y)))) (forall (Z:a), (((eq a) (h Z)) (j Z))))->(forall (Xq:((a->a)->Prop)), ((Xq (f h))->(Xq (g j)))))
% 6.83/7.05 Found eq_ref000:=(eq_ref00 Xq):((Xq (f h))->(Xq (f h)))
% 6.83/7.05 Found (eq_ref00 Xq) as proof of (P (f h))
% 6.83/7.05 Found ((eq_ref0 (f h)) Xq) as proof of (P (f h))
% 6.83/7.05 Found (((eq_ref (a->a)) (f h)) Xq) as proof of (P (f h))
% 6.83/7.05 Found (((eq_ref (a->a)) (f h)) Xq) as proof of (P (f h))
% 6.83/7.05 Found eq_ref000:=(eq_ref00 Xq):((Xq (f h))->(Xq (f h)))
% 6.83/7.05 Found (eq_ref00 Xq) as proof of (P (f h))
% 6.83/7.05 Found ((eq_ref0 (f h)) Xq) as proof of (P (f h))
% 6.83/7.05 Found (((eq_ref (a->a)) (f h)) Xq) as proof of (P (f h))
% 6.83/7.05 Found (((eq_ref (a->a)) (f h)) Xq) as proof of (P (f h))
% 6.83/7.05 Found eq_ref000:=(eq_ref00 Xq):((Xq (f h))->(Xq (f h)))
% 6.83/7.05 Found (eq_ref00 Xq) as proof of (P (f h))
% 6.83/7.05 Found ((eq_ref0 (f h)) Xq) as proof of (P (f h))
% 6.83/7.05 Found (((eq_ref (a->a)) (f h)) Xq) as proof of (P (f h))
% 6.83/7.05 Found (((eq_ref (a->a)) (f h)) Xq) as proof of (P (f h))
% 6.83/7.05 Found eq_ref00:=(eq_ref0 b):(((eq (a->a)) b) b)
% 6.83/7.05 Found (eq_ref0 b) as proof of (((eq (a->a)) b) (g j))
% 6.83/7.05 Found ((eq_ref (a->a)) b) as proof of (((eq (a->a)) b) (g j))
% 6.83/7.05 Found ((eq_ref (a->a)) b) as proof of (((eq (a->a)) b) (g j))
% 6.83/7.05 Found ((eq_ref (a->a)) b) as proof of (((eq (a->a)) b) (g j))
% 6.83/7.05 Found eta_expansion000:=(eta_expansion00 (f h)):(((eq (a->a)) (f h)) (fun (x:a)=> ((f h) x)))
% 6.83/7.05 Found (eta_expansion00 (f h)) as proof of (((eq (a->a)) (f h)) b)
% 6.83/7.05 Found ((eta_expansion0 a) (f h)) as proof of (((eq (a->a)) (f h)) b)
% 6.83/7.05 Found (((eta_expansion a) a) (f h)) as proof of (((eq (a->a)) (f h)) b)
% 6.83/7.05 Found (((eta_expansion a) a) (f h)) as proof of (((eq (a->a)) (f h)) b)
% 6.83/7.05 Found (((eta_expansion a) a) (f h)) as proof of (((eq (a->a)) (f h)) b)
% 6.83/7.05 Found eq_ref000:=(eq_ref00 P):((P (f h))->(P (f h)))
% 6.83/7.05 Found (eq_ref00 P) as proof of (P0 (f h))
% 6.83/7.05 Found ((eq_ref0 (f h)) P) as proof of (P0 (f h))
% 6.83/7.05 Found (((eq_ref (a->a)) (f h)) P) as proof of (P0 (f h))
% 6.83/7.05 Found (((eq_ref (a->a)) (f h)) P) as proof of (P0 (f h))
% 6.83/7.05 Found eq_ref000:=(eq_ref00 P):((P (f h))->(P (f h)))
% 6.83/7.05 Found (eq_ref00 P) as proof of (P0 (f h))
% 6.83/7.05 Found ((eq_ref0 (f h)) P) as proof of (P0 (f h))
% 6.83/7.05 Found (((eq_ref (a->a)) (f h)) P) as proof of (P0 (f h))
% 6.83/7.05 Found (((eq_ref (a->a)) (f h)) P) as proof of (P0 (f h))
% 6.83/7.05 Found eq_ref000:=(eq_ref00 P):((P (f h))->(P (f h)))
% 6.83/7.05 Found (eq_ref00 P) as proof of (P0 (f h))
% 6.83/7.05 Found ((eq_ref0 (f h)) P) as proof of (P0 (f h))
% 6.83/7.05 Found (((eq_ref (a->a)) (f h)) P) as proof of (P0 (f h))
% 6.83/7.05 Found (((eq_ref (a->a)) (f h)) P) as proof of (P0 (f h))
% 21.62/21.79 Found eq_ref000:=(eq_ref00 P):((P (g j))->(P (g j)))
% 21.62/21.79 Found (eq_ref00 P) as proof of (P0 (g j))
% 21.62/21.79 Found ((eq_ref0 (g j)) P) as proof of (P0 (g j))
% 21.62/21.79 Found (((eq_ref (a->a)) (g j)) P) as proof of (P0 (g j))
% 21.62/21.79 Found (((eq_ref (a->a)) (g j)) P) as proof of (P0 (g j))
% 21.62/21.79 Found eq_ref000:=(eq_ref00 P):((P (g j))->(P (g j)))
% 21.62/21.79 Found (eq_ref00 P) as proof of (P0 (g j))
% 21.62/21.79 Found ((eq_ref0 (g j)) P) as proof of (P0 (g j))
% 21.62/21.79 Found (((eq_ref (a->a)) (g j)) P) as proof of (P0 (g j))
% 21.62/21.79 Found (((eq_ref (a->a)) (g j)) P) as proof of (P0 (g j))
% 21.62/21.79 Found eq_ref000:=(eq_ref00 P):((P ((f h) x0))->(P ((f h) x0)))
% 21.62/21.79 Found (eq_ref00 P) as proof of (P0 ((f h) x0))
% 21.62/21.79 Found ((eq_ref0 ((f h) x0)) P) as proof of (P0 ((f h) x0))
% 21.62/21.79 Found (((eq_ref a) ((f h) x0)) P) as proof of (P0 ((f h) x0))
% 21.62/21.79 Found (((eq_ref a) ((f h) x0)) P) as proof of (P0 ((f h) x0))
% 21.62/21.79 Found eq_ref000:=(eq_ref00 P):((P ((f h) x0))->(P ((f h) x0)))
% 21.62/21.79 Found (eq_ref00 P) as proof of (P0 ((f h) x0))
% 21.62/21.79 Found ((eq_ref0 ((f h) x0)) P) as proof of (P0 ((f h) x0))
% 21.62/21.79 Found (((eq_ref a) ((f h) x0)) P) as proof of (P0 ((f h) x0))
% 21.62/21.79 Found (((eq_ref a) ((f h) x0)) P) as proof of (P0 ((f h) x0))
% 21.62/21.79 Found eq_ref00:=(eq_ref0 b):(((eq (a->a)) b) b)
% 21.62/21.79 Found (eq_ref0 b) as proof of (((eq (a->a)) b) (g j))
% 21.62/21.79 Found ((eq_ref (a->a)) b) as proof of (((eq (a->a)) b) (g j))
% 21.62/21.79 Found ((eq_ref (a->a)) b) as proof of (((eq (a->a)) b) (g j))
% 21.62/21.79 Found ((eq_ref (a->a)) b) as proof of (((eq (a->a)) b) (g j))
% 21.62/21.79 Found eq_ref00:=(eq_ref0 (f h)):(((eq (a->a)) (f h)) (f h))
% 21.62/21.79 Found (eq_ref0 (f h)) as proof of (((eq (a->a)) (f h)) b)
% 21.62/21.79 Found ((eq_ref (a->a)) (f h)) as proof of (((eq (a->a)) (f h)) b)
% 21.62/21.79 Found ((eq_ref (a->a)) (f h)) as proof of (((eq (a->a)) (f h)) b)
% 21.62/21.79 Found ((eq_ref (a->a)) (f h)) as proof of (((eq (a->a)) (f h)) b)
% 21.62/21.79 Found eq_ref000:=(eq_ref00 P):((P (f h))->(P (f h)))
% 21.62/21.79 Found (eq_ref00 P) as proof of (P0 (f h))
% 21.62/21.79 Found ((eq_ref0 (f h)) P) as proof of (P0 (f h))
% 21.62/21.79 Found (((eq_ref (a->a)) (f h)) P) as proof of (P0 (f h))
% 21.62/21.79 Found (((eq_ref (a->a)) (f h)) P) as proof of (P0 (f h))
% 21.62/21.79 Found eq_ref000:=(eq_ref00 P):((P (f h))->(P (f h)))
% 21.62/21.79 Found (eq_ref00 P) as proof of (P0 (f h))
% 21.62/21.79 Found ((eq_ref0 (f h)) P) as proof of (P0 (f h))
% 21.62/21.79 Found (((eq_ref (a->a)) (f h)) P) as proof of (P0 (f h))
% 21.62/21.79 Found (((eq_ref (a->a)) (f h)) P) as proof of (P0 (f h))
% 21.62/21.79 Found eq_ref000:=(eq_ref00 P):((P (f h))->(P (f h)))
% 21.62/21.79 Found (eq_ref00 P) as proof of (P0 (f h))
% 21.62/21.79 Found ((eq_ref0 (f h)) P) as proof of (P0 (f h))
% 21.62/21.79 Found (((eq_ref (a->a)) (f h)) P) as proof of (P0 (f h))
% 21.62/21.79 Found (((eq_ref (a->a)) (f h)) P) as proof of (P0 (f h))
% 21.62/21.79 Found eq_ref00:=(eq_ref0 b):(((eq (a->a)) b) b)
% 21.62/21.79 Found (eq_ref0 b) as proof of (((eq (a->a)) b) (f h))
% 21.62/21.79 Found ((eq_ref (a->a)) b) as proof of (((eq (a->a)) b) (f h))
% 21.62/21.79 Found ((eq_ref (a->a)) b) as proof of (((eq (a->a)) b) (f h))
% 21.62/21.79 Found ((eq_ref (a->a)) b) as proof of (((eq (a->a)) b) (f h))
% 21.62/21.79 Found eta_expansion_dep000:=(eta_expansion_dep00 (g j)):(((eq (a->a)) (g j)) (fun (x:a)=> ((g j) x)))
% 21.62/21.79 Found (eta_expansion_dep00 (g j)) as proof of (((eq (a->a)) (g j)) b)
% 21.62/21.79 Found ((eta_expansion_dep0 (fun (x1:a)=> a)) (g j)) as proof of (((eq (a->a)) (g j)) b)
% 21.62/21.79 Found (((eta_expansion_dep a) (fun (x1:a)=> a)) (g j)) as proof of (((eq (a->a)) (g j)) b)
% 21.62/21.79 Found (((eta_expansion_dep a) (fun (x1:a)=> a)) (g j)) as proof of (((eq (a->a)) (g j)) b)
% 21.62/21.79 Found (((eta_expansion_dep a) (fun (x1:a)=> a)) (g j)) as proof of (((eq (a->a)) (g j)) b)
% 21.62/21.79 Found eq_ref00:=(eq_ref0 ((f h) x0)):(((eq a) ((f h) x0)) ((f h) x0))
% 21.62/21.79 Found (eq_ref0 ((f h) x0)) as proof of (((eq a) ((f h) x0)) b)
% 21.62/21.79 Found ((eq_ref a) ((f h) x0)) as proof of (((eq a) ((f h) x0)) b)
% 21.62/21.79 Found ((eq_ref a) ((f h) x0)) as proof of (((eq a) ((f h) x0)) b)
% 21.62/21.79 Found ((eq_ref a) ((f h) x0)) as proof of (((eq a) ((f h) x0)) b)
% 21.62/21.79 Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% 21.62/21.79 Found (eq_ref0 b) as proof of (((eq a) b) ((g j) x0))
% 21.62/21.79 Found ((eq_ref a) b) as proof of (((eq a) b) ((g j) x0))
% 21.62/21.79 Found ((eq_ref a) b) as proof of (((eq a) b) ((g j) x0))
% 21.62/21.79 Found ((eq_ref a) b) as proof of (((eq a) b) ((g j) x0))
% 21.62/21.79 Found eq_ref00:=(eq_ref0 ((f h) x0)):(((eq a) ((f h) x0)) ((f h) x0))
% 21.62/21.79 Found (eq_ref0 ((f h) x0)) as proof of (((eq a) ((f h) x0)) b)
% 21.62/21.79 Found ((eq_ref a) ((f h) x0)) as proof of (((eq a) ((f h) x0)) b)
% 38.72/38.91 Found ((eq_ref a) ((f h) x0)) as proof of (((eq a) ((f h) x0)) b)
% 38.72/38.91 Found ((eq_ref a) ((f h) x0)) as proof of (((eq a) ((f h) x0)) b)
% 38.72/38.91 Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% 38.72/38.91 Found (eq_ref0 b) as proof of (((eq a) b) ((g j) x0))
% 38.72/38.91 Found ((eq_ref a) b) as proof of (((eq a) b) ((g j) x0))
% 38.72/38.91 Found ((eq_ref a) b) as proof of (((eq a) b) ((g j) x0))
% 38.72/38.91 Found ((eq_ref a) b) as proof of (((eq a) b) ((g j) x0))
% 38.72/38.91 Found eq_ref000:=(eq_ref00 P):((P (g j))->(P (g j)))
% 38.72/38.91 Found (eq_ref00 P) as proof of (P0 (g j))
% 38.72/38.91 Found ((eq_ref0 (g j)) P) as proof of (P0 (g j))
% 38.72/38.91 Found (((eq_ref (a->a)) (g j)) P) as proof of (P0 (g j))
% 38.72/38.91 Found (((eq_ref (a->a)) (g j)) P) as proof of (P0 (g j))
% 38.72/38.91 Found eq_ref000:=(eq_ref00 P):((P (g j))->(P (g j)))
% 38.72/38.91 Found (eq_ref00 P) as proof of (P0 (g j))
% 38.72/38.91 Found ((eq_ref0 (g j)) P) as proof of (P0 (g j))
% 38.72/38.91 Found (((eq_ref (a->a)) (g j)) P) as proof of (P0 (g j))
% 38.72/38.91 Found (((eq_ref (a->a)) (g j)) P) as proof of (P0 (g j))
% 38.72/38.91 Found eq_ref000:=(eq_ref00 P):((P ((f h) x0))->(P ((f h) x0)))
% 38.72/38.91 Found (eq_ref00 P) as proof of (P0 ((f h) x0))
% 38.72/38.91 Found ((eq_ref0 ((f h) x0)) P) as proof of (P0 ((f h) x0))
% 38.72/38.91 Found (((eq_ref a) ((f h) x0)) P) as proof of (P0 ((f h) x0))
% 38.72/38.91 Found (((eq_ref a) ((f h) x0)) P) as proof of (P0 ((f h) x0))
% 38.72/38.91 Found eq_ref000:=(eq_ref00 P):((P ((f h) x0))->(P ((f h) x0)))
% 38.72/38.91 Found (eq_ref00 P) as proof of (P0 ((f h) x0))
% 38.72/38.91 Found ((eq_ref0 ((f h) x0)) P) as proof of (P0 ((f h) x0))
% 38.72/38.91 Found (((eq_ref a) ((f h) x0)) P) as proof of (P0 ((f h) x0))
% 38.72/38.91 Found (((eq_ref a) ((f h) x0)) P) as proof of (P0 ((f h) x0))
% 38.72/38.91 Found eq_ref00:=(eq_ref0 b):(((eq (a->a)) b) b)
% 38.72/38.91 Found (eq_ref0 b) as proof of (((eq (a->a)) b) (g j))
% 38.72/38.91 Found ((eq_ref (a->a)) b) as proof of (((eq (a->a)) b) (g j))
% 38.72/38.91 Found ((eq_ref (a->a)) b) as proof of (((eq (a->a)) b) (g j))
% 38.72/38.91 Found ((eq_ref (a->a)) b) as proof of (((eq (a->a)) b) (g j))
% 38.72/38.91 Found eta_expansion_dep000:=(eta_expansion_dep00 (f h)):(((eq (a->a)) (f h)) (fun (x:a)=> ((f h) x)))
% 38.72/38.91 Found (eta_expansion_dep00 (f h)) as proof of (((eq (a->a)) (f h)) b)
% 38.72/38.91 Found ((eta_expansion_dep0 (fun (x3:a)=> a)) (f h)) as proof of (((eq (a->a)) (f h)) b)
% 38.75/38.91 Found (((eta_expansion_dep a) (fun (x3:a)=> a)) (f h)) as proof of (((eq (a->a)) (f h)) b)
% 38.75/38.91 Found (((eta_expansion_dep a) (fun (x3:a)=> a)) (f h)) as proof of (((eq (a->a)) (f h)) b)
% 38.75/38.91 Found (((eta_expansion_dep a) (fun (x3:a)=> a)) (f h)) as proof of (((eq (a->a)) (f h)) b)
% 38.75/38.91 Found eq_ref00:=(eq_ref0 b):(((eq (a->a)) b) b)
% 38.75/38.91 Found (eq_ref0 b) as proof of (((eq (a->a)) b) (f h))
% 38.75/38.91 Found ((eq_ref (a->a)) b) as proof of (((eq (a->a)) b) (f h))
% 38.75/38.91 Found ((eq_ref (a->a)) b) as proof of (((eq (a->a)) b) (f h))
% 38.75/38.91 Found ((eq_ref (a->a)) b) as proof of (((eq (a->a)) b) (f h))
% 38.75/38.91 Found eta_expansion_dep000:=(eta_expansion_dep00 (g j)):(((eq (a->a)) (g j)) (fun (x:a)=> ((g j) x)))
% 38.75/38.91 Found (eta_expansion_dep00 (g j)) as proof of (((eq (a->a)) (g j)) b)
% 38.75/38.91 Found ((eta_expansion_dep0 (fun (x1:a)=> a)) (g j)) as proof of (((eq (a->a)) (g j)) b)
% 38.75/38.91 Found (((eta_expansion_dep a) (fun (x1:a)=> a)) (g j)) as proof of (((eq (a->a)) (g j)) b)
% 38.75/38.91 Found (((eta_expansion_dep a) (fun (x1:a)=> a)) (g j)) as proof of (((eq (a->a)) (g j)) b)
% 38.75/38.91 Found (((eta_expansion_dep a) (fun (x1:a)=> a)) (g j)) as proof of (((eq (a->a)) (g j)) b)
% 38.75/38.91 Found eq_ref000:=(eq_ref00 P):((P (g j))->(P (g j)))
% 38.75/38.91 Found (eq_ref00 P) as proof of (P0 (g j))
% 38.75/38.91 Found ((eq_ref0 (g j)) P) as proof of (P0 (g j))
% 38.75/38.91 Found (((eq_ref (a->a)) (g j)) P) as proof of (P0 (g j))
% 38.75/38.91 Found (((eq_ref (a->a)) (g j)) P) as proof of (P0 (g j))
% 38.75/38.91 Found eq_ref000:=(eq_ref00 P):((P (g j))->(P (g j)))
% 38.75/38.91 Found (eq_ref00 P) as proof of (P0 (g j))
% 38.75/38.91 Found ((eq_ref0 (g j)) P) as proof of (P0 (g j))
% 38.75/38.91 Found (((eq_ref (a->a)) (g j)) P) as proof of (P0 (g j))
% 38.75/38.91 Found (((eq_ref (a->a)) (g j)) P) as proof of (P0 (g j))
% 38.75/38.91 Found eq_ref000:=(eq_ref00 P):((P ((g j) x0))->(P ((g j) x0)))
% 38.75/38.91 Found (eq_ref00 P) as proof of (P0 ((g j) x0))
% 38.75/38.91 Found ((eq_ref0 ((g j) x0)) P) as proof of (P0 ((g j) x0))
% 38.75/38.91 Found (((eq_ref a) ((g j) x0)) P) as proof of (P0 ((g j) x0))
% 38.75/38.91 Found (((eq_ref a) ((g j) x0)) P) as proof of (P0 ((g j) x0))
% 38.75/38.91 Found eq_ref000:=(eq_ref00 P):((P ((g j) x0))->(P ((g j) x0)))
% 38.75/38.91 Found (eq_ref00 P) as proof of (P0 ((g j) x0))
% 38.75/38.91 Found ((eq_ref0 ((g j) x0)) P) as proof of (P0 ((g j) x0))
% 58.61/58.78 Found (((eq_ref a) ((g j) x0)) P) as proof of (P0 ((g j) x0))
% 58.61/58.78 Found (((eq_ref a) ((g j) x0)) P) as proof of (P0 ((g j) x0))
% 58.61/58.78 Found eq_ref00:=(eq_ref0 ((f h) x0)):(((eq a) ((f h) x0)) ((f h) x0))
% 58.61/58.78 Found (eq_ref0 ((f h) x0)) as proof of (((eq a) ((f h) x0)) b)
% 58.61/58.78 Found ((eq_ref a) ((f h) x0)) as proof of (((eq a) ((f h) x0)) b)
% 58.61/58.78 Found ((eq_ref a) ((f h) x0)) as proof of (((eq a) ((f h) x0)) b)
% 58.61/58.78 Found ((eq_ref a) ((f h) x0)) as proof of (((eq a) ((f h) x0)) b)
% 58.61/58.78 Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% 58.61/58.78 Found (eq_ref0 b) as proof of (((eq a) b) ((g j) x0))
% 58.61/58.78 Found ((eq_ref a) b) as proof of (((eq a) b) ((g j) x0))
% 58.61/58.78 Found ((eq_ref a) b) as proof of (((eq a) b) ((g j) x0))
% 58.61/58.78 Found ((eq_ref a) b) as proof of (((eq a) b) ((g j) x0))
% 58.61/58.78 Found eq_ref00:=(eq_ref0 ((f h) x0)):(((eq a) ((f h) x0)) ((f h) x0))
% 58.61/58.78 Found (eq_ref0 ((f h) x0)) as proof of (((eq a) ((f h) x0)) b)
% 58.61/58.78 Found ((eq_ref a) ((f h) x0)) as proof of (((eq a) ((f h) x0)) b)
% 58.61/58.78 Found ((eq_ref a) ((f h) x0)) as proof of (((eq a) ((f h) x0)) b)
% 58.61/58.78 Found ((eq_ref a) ((f h) x0)) as proof of (((eq a) ((f h) x0)) b)
% 58.61/58.78 Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% 58.61/58.78 Found (eq_ref0 b) as proof of (((eq a) b) ((g j) x0))
% 58.61/58.78 Found ((eq_ref a) b) as proof of (((eq a) b) ((g j) x0))
% 58.61/58.78 Found ((eq_ref a) b) as proof of (((eq a) b) ((g j) x0))
% 58.61/58.78 Found ((eq_ref a) b) as proof of (((eq a) b) ((g j) x0))
% 58.61/58.78 Found eq_ref000:=(eq_ref00 P):((P ((f h) x0))->(P ((f h) x0)))
% 58.61/58.78 Found (eq_ref00 P) as proof of (P0 ((f h) x0))
% 58.61/58.78 Found ((eq_ref0 ((f h) x0)) P) as proof of (P0 ((f h) x0))
% 58.61/58.78 Found (((eq_ref a) ((f h) x0)) P) as proof of (P0 ((f h) x0))
% 58.61/58.78 Found (((eq_ref a) ((f h) x0)) P) as proof of (P0 ((f h) x0))
% 58.61/58.78 Found eq_ref000:=(eq_ref00 P):((P ((f h) x0))->(P ((f h) x0)))
% 58.61/58.78 Found (eq_ref00 P) as proof of (P0 ((f h) x0))
% 58.61/58.78 Found ((eq_ref0 ((f h) x0)) P) as proof of (P0 ((f h) x0))
% 58.61/58.78 Found (((eq_ref a) ((f h) x0)) P) as proof of (P0 ((f h) x0))
% 58.61/58.78 Found (((eq_ref a) ((f h) x0)) P) as proof of (P0 ((f h) x0))
% 58.61/58.78 Found eq_ref00:=(eq_ref0 b):(((eq (a->a)) b) b)
% 58.61/58.78 Found (eq_ref0 b) as proof of (((eq (a->a)) b) (f h))
% 58.61/58.78 Found ((eq_ref (a->a)) b) as proof of (((eq (a->a)) b) (f h))
% 58.61/58.78 Found ((eq_ref (a->a)) b) as proof of (((eq (a->a)) b) (f h))
% 58.61/58.78 Found ((eq_ref (a->a)) b) as proof of (((eq (a->a)) b) (f h))
% 58.61/58.78 Found eq_ref00:=(eq_ref0 (g j)):(((eq (a->a)) (g j)) (g j))
% 58.61/58.78 Found (eq_ref0 (g j)) as proof of (((eq (a->a)) (g j)) b)
% 58.61/58.78 Found ((eq_ref (a->a)) (g j)) as proof of (((eq (a->a)) (g j)) b)
% 58.61/58.78 Found ((eq_ref (a->a)) (g j)) as proof of (((eq (a->a)) (g j)) b)
% 58.61/58.78 Found ((eq_ref (a->a)) (g j)) as proof of (((eq (a->a)) (g j)) b)
% 58.61/58.78 Found eq_ref000:=(eq_ref00 P):((P (g j))->(P (g j)))
% 58.61/58.78 Found (eq_ref00 P) as proof of (P0 (g j))
% 58.61/58.78 Found ((eq_ref0 (g j)) P) as proof of (P0 (g j))
% 58.61/58.78 Found (((eq_ref (a->a)) (g j)) P) as proof of (P0 (g j))
% 58.61/58.78 Found (((eq_ref (a->a)) (g j)) P) as proof of (P0 (g j))
% 58.61/58.78 Found eq_ref000:=(eq_ref00 P):((P (g j))->(P (g j)))
% 58.61/58.78 Found (eq_ref00 P) as proof of (P0 (g j))
% 58.61/58.78 Found ((eq_ref0 (g j)) P) as proof of (P0 (g j))
% 58.61/58.78 Found (((eq_ref (a->a)) (g j)) P) as proof of (P0 (g j))
% 58.61/58.78 Found (((eq_ref (a->a)) (g j)) P) as proof of (P0 (g j))
% 58.61/58.78 Found eq_ref000:=(eq_ref00 P):((P ((f h) x2))->(P ((f h) x2)))
% 58.61/58.78 Found (eq_ref00 P) as proof of (P0 ((f h) x2))
% 58.61/58.78 Found ((eq_ref0 ((f h) x2)) P) as proof of (P0 ((f h) x2))
% 58.61/58.78 Found (((eq_ref a) ((f h) x2)) P) as proof of (P0 ((f h) x2))
% 58.61/58.78 Found (((eq_ref a) ((f h) x2)) P) as proof of (P0 ((f h) x2))
% 58.61/58.78 Found eq_ref000:=(eq_ref00 P):((P ((f h) x2))->(P ((f h) x2)))
% 58.61/58.78 Found (eq_ref00 P) as proof of (P0 ((f h) x2))
% 58.61/58.78 Found ((eq_ref0 ((f h) x2)) P) as proof of (P0 ((f h) x2))
% 58.61/58.78 Found (((eq_ref a) ((f h) x2)) P) as proof of (P0 ((f h) x2))
% 58.61/58.78 Found (((eq_ref a) ((f h) x2)) P) as proof of (P0 ((f h) x2))
% 58.61/58.78 Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% 58.61/58.78 Found (eq_ref0 b) as proof of (((eq a) b) ((f h) x0))
% 58.61/58.78 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 58.61/58.78 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 58.61/58.78 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 58.61/58.78 Found eq_ref00:=(eq_ref0 ((g j) x0)):(((eq a) ((g j) x0)) ((g j) x0))
% 58.61/58.78 Found (eq_ref0 ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 58.61/58.78 Found ((eq_ref a) ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 65.80/66.04 Found ((eq_ref a) ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 65.80/66.04 Found ((eq_ref a) ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 65.80/66.04 Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% 65.80/66.04 Found (eq_ref0 b) as proof of (((eq a) b) ((f h) x0))
% 65.80/66.04 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 65.80/66.04 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 65.80/66.04 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 65.80/66.04 Found eq_ref00:=(eq_ref0 ((g j) x0)):(((eq a) ((g j) x0)) ((g j) x0))
% 65.80/66.04 Found (eq_ref0 ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 65.80/66.04 Found ((eq_ref a) ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 65.80/66.04 Found ((eq_ref a) ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 65.80/66.04 Found ((eq_ref a) ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 65.80/66.04 Found eq_ref00:=(eq_ref0 ((g j) x0)):(((eq a) ((g j) x0)) ((g j) x0))
% 65.80/66.04 Found (eq_ref0 ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 65.80/66.04 Found ((eq_ref a) ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 65.80/66.04 Found ((eq_ref a) ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 65.80/66.04 Found ((eq_ref a) ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 65.80/66.04 Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% 65.80/66.04 Found (eq_ref0 b) as proof of (((eq a) b) ((f h) x0))
% 65.80/66.04 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 65.80/66.04 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 65.80/66.04 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 65.80/66.04 Found eq_ref00:=(eq_ref0 ((g j) x0)):(((eq a) ((g j) x0)) ((g j) x0))
% 65.80/66.04 Found (eq_ref0 ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 65.80/66.04 Found ((eq_ref a) ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 65.80/66.04 Found ((eq_ref a) ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 65.80/66.04 Found ((eq_ref a) ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 65.80/66.04 Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% 65.80/66.04 Found (eq_ref0 b) as proof of (((eq a) b) ((f h) x0))
% 65.80/66.04 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 65.80/66.04 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 65.80/66.04 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 65.80/66.04 Found eq_ref000:=(eq_ref00 P):((P (g j))->(P (g j)))
% 65.80/66.04 Found (eq_ref00 P) as proof of (P0 (g j))
% 65.80/66.04 Found ((eq_ref0 (g j)) P) as proof of (P0 (g j))
% 65.80/66.04 Found (((eq_ref (a->a)) (g j)) P) as proof of (P0 (g j))
% 65.80/66.04 Found (((eq_ref (a->a)) (g j)) P) as proof of (P0 (g j))
% 65.80/66.04 Found eq_ref000:=(eq_ref00 P):((P (g j))->(P (g j)))
% 65.80/66.04 Found (eq_ref00 P) as proof of (P0 (g j))
% 65.80/66.04 Found ((eq_ref0 (g j)) P) as proof of (P0 (g j))
% 65.80/66.04 Found (((eq_ref (a->a)) (g j)) P) as proof of (P0 (g j))
% 65.80/66.04 Found (((eq_ref (a->a)) (g j)) P) as proof of (P0 (g j))
% 65.80/66.04 Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% 65.80/66.04 Found (eq_ref0 b) as proof of (((eq a) b) ((g j) x0))
% 65.80/66.04 Found ((eq_ref a) b) as proof of (((eq a) b) ((g j) x0))
% 65.80/66.04 Found ((eq_ref a) b) as proof of (((eq a) b) ((g j) x0))
% 65.80/66.04 Found ((eq_ref a) b) as proof of (((eq a) b) ((g j) x0))
% 65.80/66.04 Found x100:=(x10 x0):(((eq a) ((f h) x0)) ((g h) x0))
% 65.80/66.04 Found (x10 x0) as proof of (((eq a) ((f h) x0)) b)
% 65.80/66.04 Found ((x1 h) x0) as proof of (((eq a) ((f h) x0)) b)
% 65.80/66.04 Found ((x1 h) x0) as proof of (((eq a) ((f h) x0)) b)
% 65.80/66.04 Found ((x1 h) x0) as proof of (((eq a) ((f h) x0)) b)
% 65.80/66.04 Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% 65.80/66.04 Found (eq_ref0 b) as proof of (((eq a) b) ((g j) x0))
% 65.80/66.04 Found ((eq_ref a) b) as proof of (((eq a) b) ((g j) x0))
% 65.80/66.04 Found ((eq_ref a) b) as proof of (((eq a) b) ((g j) x0))
% 65.80/66.04 Found ((eq_ref a) b) as proof of (((eq a) b) ((g j) x0))
% 65.80/66.04 Found x100:=(x10 x0):(((eq a) ((f h) x0)) ((g h) x0))
% 65.80/66.04 Found (x10 x0) as proof of (((eq a) ((f h) x0)) b)
% 65.80/66.04 Found ((x1 h) x0) as proof of (((eq a) ((f h) x0)) b)
% 65.80/66.04 Found ((x1 h) x0) as proof of (((eq a) ((f h) x0)) b)
% 65.80/66.04 Found ((x1 h) x0) as proof of (((eq a) ((f h) x0)) b)
% 65.80/66.04 Found eq_ref00:=(eq_ref0 b):(((eq (a->a)) b) b)
% 65.80/66.04 Found (eq_ref0 b) as proof of (((eq (a->a)) b) (f h))
% 65.80/66.04 Found ((eq_ref (a->a)) b) as proof of (((eq (a->a)) b) (f h))
% 65.80/66.04 Found ((eq_ref (a->a)) b) as proof of (((eq (a->a)) b) (f h))
% 65.80/66.04 Found ((eq_ref (a->a)) b) as proof of (((eq (a->a)) b) (f h))
% 65.80/66.04 Found eq_ref00:=(eq_ref0 (g j)):(((eq (a->a)) (g j)) (g j))
% 65.80/66.04 Found (eq_ref0 (g j)) as proof of (((eq (a->a)) (g j)) b)
% 65.80/66.04 Found ((eq_ref (a->a)) (g j)) as proof of (((eq (a->a)) (g j)) b)
% 65.80/66.04 Found ((eq_ref (a->a)) (g j)) as proof of (((eq (a->a)) (g j)) b)
% 65.80/66.04 Found ((eq_ref (a->a)) (g j)) as proof of (((eq (a->a)) (g j)) b)
% 80.25/80.44 Found eq_ref000:=(eq_ref00 P):((P ((g j) x0))->(P ((g j) x0)))
% 80.25/80.44 Found (eq_ref00 P) as proof of (P0 ((g j) x0))
% 80.25/80.44 Found ((eq_ref0 ((g j) x0)) P) as proof of (P0 ((g j) x0))
% 80.25/80.44 Found (((eq_ref a) ((g j) x0)) P) as proof of (P0 ((g j) x0))
% 80.25/80.44 Found (((eq_ref a) ((g j) x0)) P) as proof of (P0 ((g j) x0))
% 80.25/80.44 Found eq_ref000:=(eq_ref00 P):((P ((g j) x0))->(P ((g j) x0)))
% 80.25/80.44 Found (eq_ref00 P) as proof of (P0 ((g j) x0))
% 80.25/80.44 Found ((eq_ref0 ((g j) x0)) P) as proof of (P0 ((g j) x0))
% 80.25/80.44 Found (((eq_ref a) ((g j) x0)) P) as proof of (P0 ((g j) x0))
% 80.25/80.44 Found (((eq_ref a) ((g j) x0)) P) as proof of (P0 ((g j) x0))
% 80.25/80.44 Found eq_ref000:=(eq_ref00 P):((P ((f h) x0))->(P ((f h) x0)))
% 80.25/80.44 Found (eq_ref00 P) as proof of (P0 (f h))
% 80.25/80.44 Found ((eq_ref0 ((f h) x0)) P) as proof of (P0 (f h))
% 80.25/80.44 Found (((eq_ref a) ((f h) x0)) P) as proof of (P0 (f h))
% 80.25/80.44 Found (((eq_ref a) ((f h) x0)) P) as proof of (P0 (f h))
% 80.25/80.44 Found eq_ref000:=(eq_ref00 P):((P ((f h) x0))->(P ((f h) x0)))
% 80.25/80.44 Found (eq_ref00 P) as proof of (P0 (f h))
% 80.25/80.44 Found ((eq_ref0 ((f h) x0)) P) as proof of (P0 (f h))
% 80.25/80.44 Found (((eq_ref a) ((f h) x0)) P) as proof of (P0 (f h))
% 80.25/80.44 Found (((eq_ref a) ((f h) x0)) P) as proof of (P0 (f h))
% 80.25/80.44 Found eq_ref000:=(eq_ref00 P):((P ((f h) x0))->(P ((f h) x0)))
% 80.25/80.44 Found (eq_ref00 P) as proof of (P0 (f h))
% 80.25/80.44 Found ((eq_ref0 ((f h) x0)) P) as proof of (P0 (f h))
% 80.25/80.44 Found (((eq_ref a) ((f h) x0)) P) as proof of (P0 (f h))
% 80.25/80.44 Found (((eq_ref a) ((f h) x0)) P) as proof of (P0 (f h))
% 80.25/80.44 Found eq_ref000:=(eq_ref00 P):((P ((f h) x0))->(P ((f h) x0)))
% 80.25/80.44 Found (eq_ref00 P) as proof of (P0 (f h))
% 80.25/80.44 Found ((eq_ref0 ((f h) x0)) P) as proof of (P0 (f h))
% 80.25/80.44 Found (((eq_ref a) ((f h) x0)) P) as proof of (P0 (f h))
% 80.25/80.44 Found (((eq_ref a) ((f h) x0)) P) as proof of (P0 (f h))
% 80.25/80.44 Found eq_ref000:=(eq_ref00 P):((P ((f h) x0))->(P ((f h) x0)))
% 80.25/80.44 Found (eq_ref00 P) as proof of (P0 ((f h) x0))
% 80.25/80.44 Found ((eq_ref0 ((f h) x0)) P) as proof of (P0 ((f h) x0))
% 80.25/80.44 Found (((eq_ref a) ((f h) x0)) P) as proof of (P0 ((f h) x0))
% 80.25/80.44 Found (((eq_ref a) ((f h) x0)) P) as proof of (P0 ((f h) x0))
% 80.25/80.44 Found eq_ref000:=(eq_ref00 P):((P ((f h) x0))->(P ((f h) x0)))
% 80.25/80.44 Found (eq_ref00 P) as proof of (P0 ((f h) x0))
% 80.25/80.44 Found ((eq_ref0 ((f h) x0)) P) as proof of (P0 ((f h) x0))
% 80.25/80.44 Found (((eq_ref a) ((f h) x0)) P) as proof of (P0 ((f h) x0))
% 80.25/80.44 Found (((eq_ref a) ((f h) x0)) P) as proof of (P0 ((f h) x0))
% 80.25/80.44 Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% 80.25/80.44 Found (eq_ref0 b) as proof of (((eq a) b) ((g j) x2))
% 80.25/80.44 Found ((eq_ref a) b) as proof of (((eq a) b) ((g j) x2))
% 80.25/80.44 Found ((eq_ref a) b) as proof of (((eq a) b) ((g j) x2))
% 80.25/80.44 Found ((eq_ref a) b) as proof of (((eq a) b) ((g j) x2))
% 80.25/80.44 Found eq_ref00:=(eq_ref0 ((f h) x2)):(((eq a) ((f h) x2)) ((f h) x2))
% 80.25/80.44 Found (eq_ref0 ((f h) x2)) as proof of (((eq a) ((f h) x2)) b)
% 80.25/80.44 Found ((eq_ref a) ((f h) x2)) as proof of (((eq a) ((f h) x2)) b)
% 80.25/80.44 Found ((eq_ref a) ((f h) x2)) as proof of (((eq a) ((f h) x2)) b)
% 80.25/80.44 Found ((eq_ref a) ((f h) x2)) as proof of (((eq a) ((f h) x2)) b)
% 80.25/80.44 Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% 80.25/80.44 Found (eq_ref0 b) as proof of (((eq a) b) ((g j) x2))
% 80.25/80.44 Found ((eq_ref a) b) as proof of (((eq a) b) ((g j) x2))
% 80.25/80.44 Found ((eq_ref a) b) as proof of (((eq a) b) ((g j) x2))
% 80.25/80.44 Found ((eq_ref a) b) as proof of (((eq a) b) ((g j) x2))
% 80.25/80.44 Found eq_ref00:=(eq_ref0 ((f h) x2)):(((eq a) ((f h) x2)) ((f h) x2))
% 80.25/80.44 Found (eq_ref0 ((f h) x2)) as proof of (((eq a) ((f h) x2)) b)
% 80.25/80.44 Found ((eq_ref a) ((f h) x2)) as proof of (((eq a) ((f h) x2)) b)
% 80.25/80.44 Found ((eq_ref a) ((f h) x2)) as proof of (((eq a) ((f h) x2)) b)
% 80.25/80.44 Found ((eq_ref a) ((f h) x2)) as proof of (((eq a) ((f h) x2)) b)
% 80.25/80.44 Found eq_ref00:=(eq_ref0 b):(((eq (a->a)) b) b)
% 80.25/80.44 Found (eq_ref0 b) as proof of (((eq (a->a)) b) (f h))
% 80.25/80.44 Found ((eq_ref (a->a)) b) as proof of (((eq (a->a)) b) (f h))
% 80.25/80.44 Found ((eq_ref (a->a)) b) as proof of (((eq (a->a)) b) (f h))
% 80.25/80.44 Found ((eq_ref (a->a)) b) as proof of (((eq (a->a)) b) (f h))
% 80.25/80.44 Found eq_ref00:=(eq_ref0 (g j)):(((eq (a->a)) (g j)) (g j))
% 80.25/80.44 Found (eq_ref0 (g j)) as proof of (((eq (a->a)) (g j)) b)
% 80.25/80.44 Found ((eq_ref (a->a)) (g j)) as proof of (((eq (a->a)) (g j)) b)
% 80.25/80.44 Found ((eq_ref (a->a)) (g j)) as proof of (((eq (a->a)) (g j)) b)
% 80.25/80.44 Found ((eq_ref (a->a)) (g j)) as proof of (((eq (a->a)) (g j)) b)
% 97.29/97.49 Found x0:(Xq (f h))
% 97.29/97.49 Instantiate: b:=(f h):(a->a)
% 97.29/97.49 Found x0 as proof of (P b)
% 97.29/97.49 Found eq_ref00:=(eq_ref0 (g j)):(((eq (a->a)) (g j)) (g j))
% 97.29/97.49 Found (eq_ref0 (g j)) as proof of (((eq (a->a)) (g j)) b)
% 97.29/97.49 Found ((eq_ref (a->a)) (g j)) as proof of (((eq (a->a)) (g j)) b)
% 97.29/97.49 Found ((eq_ref (a->a)) (g j)) as proof of (((eq (a->a)) (g j)) b)
% 97.29/97.49 Found ((eq_ref (a->a)) (g j)) as proof of (((eq (a->a)) (g j)) b)
% 97.29/97.49 Found eq_ref000:=(eq_ref00 P):((P ((f h) x2))->(P ((f h) x2)))
% 97.29/97.49 Found (eq_ref00 P) as proof of (P0 (f h))
% 97.29/97.49 Found ((eq_ref0 ((f h) x2)) P) as proof of (P0 (f h))
% 97.29/97.49 Found (((eq_ref a) ((f h) x2)) P) as proof of (P0 (f h))
% 97.29/97.49 Found (((eq_ref a) ((f h) x2)) P) as proof of (P0 (f h))
% 97.29/97.49 Found eq_ref000:=(eq_ref00 P):((P ((f h) x2))->(P ((f h) x2)))
% 97.29/97.49 Found (eq_ref00 P) as proof of (P0 (f h))
% 97.29/97.49 Found ((eq_ref0 ((f h) x2)) P) as proof of (P0 (f h))
% 97.29/97.49 Found (((eq_ref a) ((f h) x2)) P) as proof of (P0 (f h))
% 97.29/97.49 Found (((eq_ref a) ((f h) x2)) P) as proof of (P0 (f h))
% 97.29/97.49 Found eq_ref000:=(eq_ref00 P):((P ((f h) x0))->(P ((f h) x0)))
% 97.29/97.49 Found (eq_ref00 P) as proof of (P0 ((f h) x0))
% 97.29/97.49 Found ((eq_ref0 ((f h) x0)) P) as proof of (P0 ((f h) x0))
% 97.29/97.49 Found (((eq_ref a) ((f h) x0)) P) as proof of (P0 ((f h) x0))
% 97.29/97.49 Found (((eq_ref a) ((f h) x0)) P) as proof of (P0 ((f h) x0))
% 97.29/97.49 Found eq_ref000:=(eq_ref00 P):((P ((f h) x0))->(P ((f h) x0)))
% 97.29/97.49 Found (eq_ref00 P) as proof of (P0 ((f h) x0))
% 97.29/97.49 Found ((eq_ref0 ((f h) x0)) P) as proof of (P0 ((f h) x0))
% 97.29/97.49 Found (((eq_ref a) ((f h) x0)) P) as proof of (P0 ((f h) x0))
% 97.29/97.49 Found (((eq_ref a) ((f h) x0)) P) as proof of (P0 ((f h) x0))
% 97.29/97.49 Found eq_ref000:=(eq_ref00 P):((P ((f h) x0))->(P ((f h) x0)))
% 97.29/97.49 Found (eq_ref00 P) as proof of (P0 ((f h) x0))
% 97.29/97.49 Found ((eq_ref0 ((f h) x0)) P) as proof of (P0 ((f h) x0))
% 97.29/97.49 Found (((eq_ref a) ((f h) x0)) P) as proof of (P0 ((f h) x0))
% 97.29/97.49 Found (((eq_ref a) ((f h) x0)) P) as proof of (P0 ((f h) x0))
% 97.29/97.49 Found eq_ref000:=(eq_ref00 P):((P ((f h) x0))->(P ((f h) x0)))
% 97.29/97.49 Found (eq_ref00 P) as proof of (P0 ((f h) x0))
% 97.29/97.49 Found ((eq_ref0 ((f h) x0)) P) as proof of (P0 ((f h) x0))
% 97.29/97.49 Found (((eq_ref a) ((f h) x0)) P) as proof of (P0 ((f h) x0))
% 97.29/97.49 Found (((eq_ref a) ((f h) x0)) P) as proof of (P0 ((f h) x0))
% 97.29/97.49 Found eq_ref000:=(eq_ref00 P):((P ((f h) x0))->(P ((f h) x0)))
% 97.29/97.49 Found (eq_ref00 P) as proof of (P0 ((f h) x0))
% 97.29/97.49 Found ((eq_ref0 ((f h) x0)) P) as proof of (P0 ((f h) x0))
% 97.29/97.49 Found (((eq_ref a) ((f h) x0)) P) as proof of (P0 ((f h) x0))
% 97.29/97.49 Found (((eq_ref a) ((f h) x0)) P) as proof of (P0 ((f h) x0))
% 97.29/97.49 Found eq_ref000:=(eq_ref00 P):((P ((f h) x0))->(P ((f h) x0)))
% 97.29/97.49 Found (eq_ref00 P) as proof of (P0 ((f h) x0))
% 97.29/97.49 Found ((eq_ref0 ((f h) x0)) P) as proof of (P0 ((f h) x0))
% 97.29/97.49 Found (((eq_ref a) ((f h) x0)) P) as proof of (P0 ((f h) x0))
% 97.29/97.49 Found (((eq_ref a) ((f h) x0)) P) as proof of (P0 ((f h) x0))
% 97.29/97.49 Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% 97.29/97.49 Found (eq_ref0 b) as proof of (((eq a) b) ((f h) x0))
% 97.29/97.49 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 97.29/97.49 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 97.29/97.49 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 97.29/97.49 Found eq_ref00:=(eq_ref0 ((g j) x0)):(((eq a) ((g j) x0)) ((g j) x0))
% 97.29/97.49 Found (eq_ref0 ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 97.29/97.49 Found ((eq_ref a) ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 97.29/97.49 Found ((eq_ref a) ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 97.29/97.49 Found ((eq_ref a) ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 97.29/97.49 Found eq_ref00:=(eq_ref0 ((g j) x0)):(((eq a) ((g j) x0)) ((g j) x0))
% 97.29/97.49 Found (eq_ref0 ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 97.29/97.49 Found ((eq_ref a) ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 97.29/97.49 Found ((eq_ref a) ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 97.29/97.49 Found ((eq_ref a) ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 97.29/97.49 Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% 97.29/97.49 Found (eq_ref0 b) as proof of (((eq a) b) ((f h) x0))
% 97.29/97.49 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 97.29/97.49 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 97.29/97.49 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 97.29/97.49 Found eq_ref00:=(eq_ref0 ((g j) x0)):(((eq a) ((g j) x0)) ((g j) x0))
% 97.29/97.49 Found (eq_ref0 ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 97.29/97.49 Found ((eq_ref a) ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 114.90/115.10 Found ((eq_ref a) ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 114.90/115.10 Found ((eq_ref a) ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 114.90/115.10 Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% 114.90/115.10 Found (eq_ref0 b) as proof of (((eq a) b) ((f h) x0))
% 114.90/115.10 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 114.90/115.10 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 114.90/115.10 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 114.90/115.10 Found eq_ref00:=(eq_ref0 ((g j) x0)):(((eq a) ((g j) x0)) ((g j) x0))
% 114.90/115.10 Found (eq_ref0 ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 114.90/115.10 Found ((eq_ref a) ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 114.90/115.10 Found ((eq_ref a) ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 114.90/115.10 Found ((eq_ref a) ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 114.90/115.10 Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% 114.90/115.10 Found (eq_ref0 b) as proof of (((eq a) b) ((f h) x0))
% 114.90/115.10 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 114.90/115.10 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 114.90/115.10 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 114.90/115.10 Found eq_ref00:=(eq_ref0 ((f h) x0)):(((eq a) ((f h) x0)) ((f h) x0))
% 114.90/115.10 Found (eq_ref0 ((f h) x0)) as proof of (((eq a) ((f h) x0)) b)
% 114.90/115.10 Found ((eq_ref a) ((f h) x0)) as proof of (((eq a) ((f h) x0)) b)
% 114.90/115.10 Found ((eq_ref a) ((f h) x0)) as proof of (((eq a) ((f h) x0)) b)
% 114.90/115.10 Found ((eq_ref a) ((f h) x0)) as proof of (((eq a) ((f h) x0)) b)
% 114.90/115.10 Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% 114.90/115.10 Found (eq_ref0 b) as proof of (((eq a) b) ((g j) x0))
% 114.90/115.10 Found ((eq_ref a) b) as proof of (((eq a) b) ((g j) x0))
% 114.90/115.10 Found ((eq_ref a) b) as proof of (((eq a) b) ((g j) x0))
% 114.90/115.10 Found ((eq_ref a) b) as proof of (((eq a) b) ((g j) x0))
% 114.90/115.10 Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% 114.90/115.10 Found (eq_ref0 b) as proof of (((eq a) b) ((g j) x0))
% 114.90/115.10 Found ((eq_ref a) b) as proof of (((eq a) b) ((g j) x0))
% 114.90/115.10 Found ((eq_ref a) b) as proof of (((eq a) b) ((g j) x0))
% 114.90/115.10 Found ((eq_ref a) b) as proof of (((eq a) b) ((g j) x0))
% 114.90/115.10 Found x100:=(x10 x0):(((eq a) ((f h) x0)) ((g h) x0))
% 114.90/115.10 Found (x10 x0) as proof of (((eq a) ((f h) x0)) b)
% 114.90/115.10 Found ((x1 h) x0) as proof of (((eq a) ((f h) x0)) b)
% 114.90/115.10 Found ((x1 h) x0) as proof of (((eq a) ((f h) x0)) b)
% 114.90/115.10 Found ((x1 h) x0) as proof of (((eq a) ((f h) x0)) b)
% 114.90/115.10 Found eq_ref000:=(eq_ref00 P):((P ((g j) x2))->(P ((g j) x2)))
% 114.90/115.10 Found (eq_ref00 P) as proof of (P0 ((g j) x2))
% 114.90/115.10 Found ((eq_ref0 ((g j) x2)) P) as proof of (P0 ((g j) x2))
% 114.90/115.10 Found (((eq_ref a) ((g j) x2)) P) as proof of (P0 ((g j) x2))
% 114.90/115.10 Found (((eq_ref a) ((g j) x2)) P) as proof of (P0 ((g j) x2))
% 114.90/115.10 Found eq_ref000:=(eq_ref00 P):((P ((g j) x2))->(P ((g j) x2)))
% 114.90/115.10 Found (eq_ref00 P) as proof of (P0 ((g j) x2))
% 114.90/115.10 Found ((eq_ref0 ((g j) x2)) P) as proof of (P0 ((g j) x2))
% 114.90/115.10 Found (((eq_ref a) ((g j) x2)) P) as proof of (P0 ((g j) x2))
% 114.90/115.10 Found (((eq_ref a) ((g j) x2)) P) as proof of (P0 ((g j) x2))
% 114.90/115.10 Found eq_ref000:=(eq_ref00 P):((P ((f h) x0))->(P ((f h) x0)))
% 114.90/115.10 Found (eq_ref00 P) as proof of (P0 (f h))
% 114.90/115.10 Found ((eq_ref0 ((f h) x0)) P) as proof of (P0 (f h))
% 114.90/115.10 Found (((eq_ref a) ((f h) x0)) P) as proof of (P0 (f h))
% 114.90/115.10 Found (((eq_ref a) ((f h) x0)) P) as proof of (P0 (f h))
% 114.90/115.10 Found eq_ref000:=(eq_ref00 P):((P ((f h) x0))->(P ((f h) x0)))
% 114.90/115.10 Found (eq_ref00 P) as proof of (P0 (f h))
% 114.90/115.10 Found ((eq_ref0 ((f h) x0)) P) as proof of (P0 (f h))
% 114.90/115.10 Found (((eq_ref a) ((f h) x0)) P) as proof of (P0 (f h))
% 114.90/115.10 Found (((eq_ref a) ((f h) x0)) P) as proof of (P0 (f h))
% 114.90/115.10 Found eq_ref000:=(eq_ref00 P):((P ((f h) x0))->(P ((f h) x0)))
% 114.90/115.10 Found (eq_ref00 P) as proof of (P0 (f h))
% 114.90/115.10 Found ((eq_ref0 ((f h) x0)) P) as proof of (P0 (f h))
% 114.90/115.10 Found (((eq_ref a) ((f h) x0)) P) as proof of (P0 (f h))
% 114.90/115.10 Found (((eq_ref a) ((f h) x0)) P) as proof of (P0 (f h))
% 114.90/115.10 Found eq_ref000:=(eq_ref00 P):((P ((f h) x0))->(P ((f h) x0)))
% 114.90/115.10 Found (eq_ref00 P) as proof of (P0 (f h))
% 114.90/115.10 Found ((eq_ref0 ((f h) x0)) P) as proof of (P0 (f h))
% 114.90/115.10 Found (((eq_ref a) ((f h) x0)) P) as proof of (P0 (f h))
% 114.90/115.10 Found (((eq_ref a) ((f h) x0)) P) as proof of (P0 (f h))
% 114.90/115.10 Found eq_ref000:=(eq_ref00 P):((P ((f h) x2))->(P ((f h) x2)))
% 114.90/115.10 Found (eq_ref00 P) as proof of (P0 ((f h) x2))
% 114.90/115.10 Found ((eq_ref0 ((f h) x2)) P) as proof of (P0 ((f h) x2))
% 114.90/115.10 Found (((eq_ref a) ((f h) x2)) P) as proof of (P0 ((f h) x2))
% 114.90/115.10 Found (((eq_ref a) ((f h) x2)) P) as proof of (P0 ((f h) x2))
% 132.74/132.94 Found eq_ref000:=(eq_ref00 P):((P ((f h) x2))->(P ((f h) x2)))
% 132.74/132.94 Found (eq_ref00 P) as proof of (P0 ((f h) x2))
% 132.74/132.94 Found ((eq_ref0 ((f h) x2)) P) as proof of (P0 ((f h) x2))
% 132.74/132.94 Found (((eq_ref a) ((f h) x2)) P) as proof of (P0 ((f h) x2))
% 132.74/132.94 Found (((eq_ref a) ((f h) x2)) P) as proof of (P0 ((f h) x2))
% 132.74/132.94 Found eq_ref000:=(eq_ref00 P):((P ((f h) x2))->(P ((f h) x2)))
% 132.74/132.94 Found (eq_ref00 P) as proof of (P0 ((f h) x2))
% 132.74/132.94 Found ((eq_ref0 ((f h) x2)) P) as proof of (P0 ((f h) x2))
% 132.74/132.94 Found (((eq_ref a) ((f h) x2)) P) as proof of (P0 ((f h) x2))
% 132.74/132.94 Found (((eq_ref a) ((f h) x2)) P) as proof of (P0 ((f h) x2))
% 132.74/132.94 Found eq_ref000:=(eq_ref00 P):((P ((f h) x2))->(P ((f h) x2)))
% 132.74/132.94 Found (eq_ref00 P) as proof of (P0 ((f h) x2))
% 132.74/132.94 Found ((eq_ref0 ((f h) x2)) P) as proof of (P0 ((f h) x2))
% 132.74/132.94 Found (((eq_ref a) ((f h) x2)) P) as proof of (P0 ((f h) x2))
% 132.74/132.94 Found (((eq_ref a) ((f h) x2)) P) as proof of (P0 ((f h) x2))
% 132.74/132.94 Found x0:(Xq (f h))
% 132.74/132.94 Instantiate: f0:=(f h):(a->a)
% 132.74/132.94 Found x0 as proof of (P f0)
% 132.74/132.94 Found eq_ref00:=(eq_ref0 (f0 x1)):(((eq a) (f0 x1)) (f0 x1))
% 132.74/132.94 Found (eq_ref0 (f0 x1)) as proof of (((eq a) (f0 x1)) ((g j) x1))
% 132.74/132.94 Found ((eq_ref a) (f0 x1)) as proof of (((eq a) (f0 x1)) ((g j) x1))
% 132.74/132.94 Found ((eq_ref a) (f0 x1)) as proof of (((eq a) (f0 x1)) ((g j) x1))
% 132.74/132.94 Found (fun (x1:a)=> ((eq_ref a) (f0 x1))) as proof of (((eq a) (f0 x1)) ((g j) x1))
% 132.74/132.94 Found (fun (x1:a)=> ((eq_ref a) (f0 x1))) as proof of (forall (x:a), (((eq a) (f0 x)) ((g j) x)))
% 132.74/132.94 Found x0:(Xq (f h))
% 132.74/132.94 Instantiate: f0:=(f h):(a->a)
% 132.74/132.94 Found x0 as proof of (P f0)
% 132.74/132.94 Found eq_ref00:=(eq_ref0 (f0 x1)):(((eq a) (f0 x1)) (f0 x1))
% 132.74/132.94 Found (eq_ref0 (f0 x1)) as proof of (((eq a) (f0 x1)) ((g j) x1))
% 132.74/132.94 Found ((eq_ref a) (f0 x1)) as proof of (((eq a) (f0 x1)) ((g j) x1))
% 132.74/132.94 Found ((eq_ref a) (f0 x1)) as proof of (((eq a) (f0 x1)) ((g j) x1))
% 132.74/132.94 Found (fun (x1:a)=> ((eq_ref a) (f0 x1))) as proof of (((eq a) (f0 x1)) ((g j) x1))
% 132.74/132.94 Found (fun (x1:a)=> ((eq_ref a) (f0 x1))) as proof of (forall (x:a), (((eq a) (f0 x)) ((g j) x)))
% 132.74/132.94 Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% 132.74/132.94 Found (eq_ref0 b) as proof of (((eq a) b) ((f j) x0))
% 132.74/132.94 Found ((eq_ref a) b) as proof of (((eq a) b) ((f j) x0))
% 132.74/132.94 Found ((eq_ref a) b) as proof of (((eq a) b) ((f j) x0))
% 132.74/132.94 Found ((eq_ref a) b) as proof of (((eq a) b) ((f j) x0))
% 132.74/132.94 Found eq_ref00:=(eq_ref0 ((f h) x0)):(((eq a) ((f h) x0)) ((f h) x0))
% 132.74/132.94 Found (eq_ref0 ((f h) x0)) as proof of (((eq a) ((f h) x0)) b)
% 132.74/132.94 Found ((eq_ref a) ((f h) x0)) as proof of (((eq a) ((f h) x0)) b)
% 132.74/132.94 Found ((eq_ref a) ((f h) x0)) as proof of (((eq a) ((f h) x0)) b)
% 132.74/132.94 Found ((eq_ref a) ((f h) x0)) as proof of (((eq a) ((f h) x0)) b)
% 132.74/132.94 Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% 132.74/132.94 Found (eq_ref0 b) as proof of (((eq a) b) ((f j) x0))
% 132.74/132.94 Found ((eq_ref a) b) as proof of (((eq a) b) ((f j) x0))
% 132.74/132.94 Found ((eq_ref a) b) as proof of (((eq a) b) ((f j) x0))
% 132.74/132.94 Found ((eq_ref a) b) as proof of (((eq a) b) ((f j) x0))
% 132.74/132.94 Found eq_ref00:=(eq_ref0 ((f h) x0)):(((eq a) ((f h) x0)) ((f h) x0))
% 132.74/132.94 Found (eq_ref0 ((f h) x0)) as proof of (((eq a) ((f h) x0)) b)
% 132.74/132.94 Found ((eq_ref a) ((f h) x0)) as proof of (((eq a) ((f h) x0)) b)
% 132.74/132.94 Found ((eq_ref a) ((f h) x0)) as proof of (((eq a) ((f h) x0)) b)
% 132.74/132.94 Found ((eq_ref a) ((f h) x0)) as proof of (((eq a) ((f h) x0)) b)
% 132.74/132.94 Found x0:(P (f h))
% 132.74/132.94 Instantiate: b:=(f h):(a->a)
% 132.74/132.94 Found x0 as proof of (P0 b)
% 132.74/132.94 Found eta_expansion_dep000:=(eta_expansion_dep00 (g j)):(((eq (a->a)) (g j)) (fun (x:a)=> ((g j) x)))
% 132.74/132.94 Found (eta_expansion_dep00 (g j)) as proof of (((eq (a->a)) (g j)) b)
% 132.74/132.94 Found ((eta_expansion_dep0 (fun (x2:a)=> a)) (g j)) as proof of (((eq (a->a)) (g j)) b)
% 132.74/132.94 Found (((eta_expansion_dep a) (fun (x2:a)=> a)) (g j)) as proof of (((eq (a->a)) (g j)) b)
% 132.74/132.94 Found (((eta_expansion_dep a) (fun (x2:a)=> a)) (g j)) as proof of (((eq (a->a)) (g j)) b)
% 132.74/132.94 Found (((eta_expansion_dep a) (fun (x2:a)=> a)) (g j)) as proof of (((eq (a->a)) (g j)) b)
% 132.74/132.94 Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% 132.74/132.94 Found (eq_ref0 b) as proof of (((eq a) b) ((f j) x0))
% 132.74/132.94 Found ((eq_ref a) b) as proof of (((eq a) b) ((f j) x0))
% 132.74/132.94 Found ((eq_ref a) b) as proof of (((eq a) b) ((f j) x0))
% 132.74/132.94 Found ((eq_ref a) b) as proof of (((eq a) b) ((f j) x0))
% 132.74/132.94 Found eq_ref00:=(eq_ref0 ((f h) x0)):(((eq a) ((f h) x0)) ((f h) x0))
% 144.50/144.72 Found (eq_ref0 ((f h) x0)) as proof of (((eq a) ((f h) x0)) b)
% 144.50/144.72 Found ((eq_ref a) ((f h) x0)) as proof of (((eq a) ((f h) x0)) b)
% 144.50/144.72 Found ((eq_ref a) ((f h) x0)) as proof of (((eq a) ((f h) x0)) b)
% 144.50/144.72 Found ((eq_ref a) ((f h) x0)) as proof of (((eq a) ((f h) x0)) b)
% 144.50/144.72 Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% 144.50/144.72 Found (eq_ref0 b) as proof of (((eq a) b) ((f j) x0))
% 144.50/144.72 Found ((eq_ref a) b) as proof of (((eq a) b) ((f j) x0))
% 144.50/144.72 Found ((eq_ref a) b) as proof of (((eq a) b) ((f j) x0))
% 144.50/144.72 Found ((eq_ref a) b) as proof of (((eq a) b) ((f j) x0))
% 144.50/144.72 Found eq_ref00:=(eq_ref0 ((f h) x0)):(((eq a) ((f h) x0)) ((f h) x0))
% 144.50/144.72 Found (eq_ref0 ((f h) x0)) as proof of (((eq a) ((f h) x0)) b)
% 144.50/144.72 Found ((eq_ref a) ((f h) x0)) as proof of (((eq a) ((f h) x0)) b)
% 144.50/144.72 Found ((eq_ref a) ((f h) x0)) as proof of (((eq a) ((f h) x0)) b)
% 144.50/144.72 Found ((eq_ref a) ((f h) x0)) as proof of (((eq a) ((f h) x0)) b)
% 144.50/144.72 Found eq_ref000:=(eq_ref00 P):((P ((g j) x0))->(P ((g j) x0)))
% 144.50/144.72 Found (eq_ref00 P) as proof of (P0 ((g j) x0))
% 144.50/144.72 Found ((eq_ref0 ((g j) x0)) P) as proof of (P0 ((g j) x0))
% 144.50/144.72 Found (((eq_ref a) ((g j) x0)) P) as proof of (P0 ((g j) x0))
% 144.50/144.72 Found (((eq_ref a) ((g j) x0)) P) as proof of (P0 ((g j) x0))
% 144.50/144.72 Found eq_ref000:=(eq_ref00 P):((P ((g j) x0))->(P ((g j) x0)))
% 144.50/144.72 Found (eq_ref00 P) as proof of (P0 ((g j) x0))
% 144.50/144.72 Found ((eq_ref0 ((g j) x0)) P) as proof of (P0 ((g j) x0))
% 144.50/144.72 Found (((eq_ref a) ((g j) x0)) P) as proof of (P0 ((g j) x0))
% 144.50/144.72 Found (((eq_ref a) ((g j) x0)) P) as proof of (P0 ((g j) x0))
% 144.50/144.72 Found eq_ref000:=(eq_ref00 P):((P ((g j) x2))->(P ((g j) x2)))
% 144.50/144.72 Found (eq_ref00 P) as proof of (P0 ((g j) x2))
% 144.50/144.72 Found ((eq_ref0 ((g j) x2)) P) as proof of (P0 ((g j) x2))
% 144.50/144.72 Found (((eq_ref a) ((g j) x2)) P) as proof of (P0 ((g j) x2))
% 144.50/144.72 Found (((eq_ref a) ((g j) x2)) P) as proof of (P0 ((g j) x2))
% 144.50/144.72 Found eq_ref000:=(eq_ref00 P):((P ((g j) x2))->(P ((g j) x2)))
% 144.50/144.72 Found (eq_ref00 P) as proof of (P0 ((g j) x2))
% 144.50/144.72 Found ((eq_ref0 ((g j) x2)) P) as proof of (P0 ((g j) x2))
% 144.50/144.72 Found (((eq_ref a) ((g j) x2)) P) as proof of (P0 ((g j) x2))
% 144.50/144.72 Found (((eq_ref a) ((g j) x2)) P) as proof of (P0 ((g j) x2))
% 144.50/144.72 Found x0:(Xq (f h))
% 144.50/144.72 Instantiate: b:=(f h):(a->a)
% 144.50/144.72 Found x0 as proof of (P b)
% 144.50/144.72 Found eq_ref00:=(eq_ref0 (g j)):(((eq (a->a)) (g j)) (g j))
% 144.50/144.72 Found (eq_ref0 (g j)) as proof of (((eq (a->a)) (g j)) b)
% 144.50/144.72 Found ((eq_ref (a->a)) (g j)) as proof of (((eq (a->a)) (g j)) b)
% 144.50/144.72 Found ((eq_ref (a->a)) (g j)) as proof of (((eq (a->a)) (g j)) b)
% 144.50/144.72 Found ((eq_ref (a->a)) (g j)) as proof of (((eq (a->a)) (g j)) b)
% 144.50/144.72 Found eq_ref00:=(eq_ref0 b):(((eq (a->a)) b) b)
% 144.50/144.72 Found (eq_ref0 b) as proof of (((eq (a->a)) b) (g j))
% 144.50/144.72 Found ((eq_ref (a->a)) b) as proof of (((eq (a->a)) b) (g j))
% 144.50/144.72 Found ((eq_ref (a->a)) b) as proof of (((eq (a->a)) b) (g j))
% 144.50/144.72 Found ((eq_ref (a->a)) b) as proof of (((eq (a->a)) b) (g j))
% 144.50/144.72 Found eq_ref00:=(eq_ref0 (f h)):(((eq (a->a)) (f h)) (f h))
% 144.50/144.72 Found (eq_ref0 (f h)) as proof of (((eq (a->a)) (f h)) b)
% 144.50/144.72 Found ((eq_ref (a->a)) (f h)) as proof of (((eq (a->a)) (f h)) b)
% 144.50/144.72 Found ((eq_ref (a->a)) (f h)) as proof of (((eq (a->a)) (f h)) b)
% 144.50/144.72 Found ((eq_ref (a->a)) (f h)) as proof of (((eq (a->a)) (f h)) b)
% 144.50/144.72 Found eq_ref00:=(eq_ref0 b):(((eq (a->a)) b) b)
% 144.50/144.72 Found (eq_ref0 b) as proof of (P b)
% 144.50/144.72 Found ((eq_ref (a->a)) b) as proof of (P b)
% 144.50/144.72 Found ((eq_ref (a->a)) b) as proof of (P b)
% 144.50/144.72 Found ((eq_ref (a->a)) b) as proof of (P b)
% 144.50/144.72 Found eta_expansion000:=(eta_expansion00 (g j)):(((eq (a->a)) (g j)) (fun (x:a)=> ((g j) x)))
% 144.50/144.72 Found (eta_expansion00 (g j)) as proof of (((eq (a->a)) (g j)) b)
% 144.50/144.72 Found ((eta_expansion0 a) (g j)) as proof of (((eq (a->a)) (g j)) b)
% 144.50/144.72 Found (((eta_expansion a) a) (g j)) as proof of (((eq (a->a)) (g j)) b)
% 144.50/144.72 Found (((eta_expansion a) a) (g j)) as proof of (((eq (a->a)) (g j)) b)
% 144.50/144.72 Found (((eta_expansion a) a) (g j)) as proof of (((eq (a->a)) (g j)) b)
% 144.50/144.72 Found eq_ref00:=(eq_ref0 ((f h) x0)):(((eq a) ((f h) x0)) ((f h) x0))
% 144.50/144.72 Found (eq_ref0 ((f h) x0)) as proof of (((eq a) ((f h) x0)) b)
% 144.50/144.72 Found ((eq_ref a) ((f h) x0)) as proof of (((eq a) ((f h) x0)) b)
% 144.50/144.72 Found ((eq_ref a) ((f h) x0)) as proof of (((eq a) ((f h) x0)) b)
% 144.50/144.72 Found ((eq_ref a) ((f h) x0)) as proof of (((eq a) ((f h) x0)) b)
% 144.50/144.72 Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% 144.50/144.72 Found (eq_ref0 b) as proof of (((eq a) b) ((g j) x0))
% 149.66/149.95 Found ((eq_ref a) b) as proof of (((eq a) b) ((g j) x0))
% 149.66/149.95 Found ((eq_ref a) b) as proof of (((eq a) b) ((g j) x0))
% 149.66/149.95 Found ((eq_ref a) b) as proof of (((eq a) b) ((g j) x0))
% 149.66/149.95 Found eq_ref00:=(eq_ref0 ((f h) x0)):(((eq a) ((f h) x0)) ((f h) x0))
% 149.66/149.95 Found (eq_ref0 ((f h) x0)) as proof of (((eq a) ((f h) x0)) b)
% 149.66/149.95 Found ((eq_ref a) ((f h) x0)) as proof of (((eq a) ((f h) x0)) b)
% 149.66/149.95 Found ((eq_ref a) ((f h) x0)) as proof of (((eq a) ((f h) x0)) b)
% 149.66/149.95 Found ((eq_ref a) ((f h) x0)) as proof of (((eq a) ((f h) x0)) b)
% 149.66/149.95 Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% 149.66/149.95 Found (eq_ref0 b) as proof of (((eq a) b) ((g j) x0))
% 149.66/149.95 Found ((eq_ref a) b) as proof of (((eq a) b) ((g j) x0))
% 149.66/149.95 Found ((eq_ref a) b) as proof of (((eq a) b) ((g j) x0))
% 149.66/149.95 Found ((eq_ref a) b) as proof of (((eq a) b) ((g j) x0))
% 149.66/149.95 Found eq_ref000:=(eq_ref00 P):((P ((f h) x0))->(P ((f h) x0)))
% 149.66/149.95 Found (eq_ref00 P) as proof of (P0 ((f h) x0))
% 149.66/149.95 Found ((eq_ref0 ((f h) x0)) P) as proof of (P0 ((f h) x0))
% 149.66/149.95 Found (((eq_ref a) ((f h) x0)) P) as proof of (P0 ((f h) x0))
% 149.66/149.95 Found (((eq_ref a) ((f h) x0)) P) as proof of (P0 ((f h) x0))
% 149.66/149.95 Found eq_ref000:=(eq_ref00 P):((P ((f h) x0))->(P ((f h) x0)))
% 149.66/149.95 Found (eq_ref00 P) as proof of (P0 ((f h) x0))
% 149.66/149.95 Found ((eq_ref0 ((f h) x0)) P) as proof of (P0 ((f h) x0))
% 149.66/149.95 Found (((eq_ref a) ((f h) x0)) P) as proof of (P0 ((f h) x0))
% 149.66/149.95 Found (((eq_ref a) ((f h) x0)) P) as proof of (P0 ((f h) x0))
% 149.66/149.95 Found eq_ref000:=(eq_ref00 P):((P ((f h) x0))->(P ((f h) x0)))
% 149.66/149.95 Found (eq_ref00 P) as proof of (P0 ((f h) x0))
% 149.66/149.95 Found ((eq_ref0 ((f h) x0)) P) as proof of (P0 ((f h) x0))
% 149.66/149.95 Found (((eq_ref a) ((f h) x0)) P) as proof of (P0 ((f h) x0))
% 149.66/149.95 Found (((eq_ref a) ((f h) x0)) P) as proof of (P0 ((f h) x0))
% 149.66/149.95 Found eq_ref000:=(eq_ref00 P):((P ((f h) x0))->(P ((f h) x0)))
% 149.66/149.95 Found (eq_ref00 P) as proof of (P0 ((f h) x0))
% 149.66/149.95 Found ((eq_ref0 ((f h) x0)) P) as proof of (P0 ((f h) x0))
% 149.66/149.95 Found (((eq_ref a) ((f h) x0)) P) as proof of (P0 ((f h) x0))
% 149.66/149.95 Found (((eq_ref a) ((f h) x0)) P) as proof of (P0 ((f h) x0))
% 149.66/149.95 Found eq_ref00:=(eq_ref0 ((g j) x2)):(((eq a) ((g j) x2)) ((g j) x2))
% 149.66/149.95 Found (eq_ref0 ((g j) x2)) as proof of (((eq a) ((g j) x2)) b)
% 149.66/149.95 Found ((eq_ref a) ((g j) x2)) as proof of (((eq a) ((g j) x2)) b)
% 149.66/149.95 Found ((eq_ref a) ((g j) x2)) as proof of (((eq a) ((g j) x2)) b)
% 149.66/149.95 Found ((eq_ref a) ((g j) x2)) as proof of (((eq a) ((g j) x2)) b)
% 149.66/149.95 Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% 149.66/149.95 Found (eq_ref0 b) as proof of (((eq a) b) ((f h) x2))
% 149.66/149.95 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x2))
% 149.66/149.95 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x2))
% 149.66/149.95 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x2))
% 149.66/149.95 Found eq_ref00:=(eq_ref0 ((g j) x2)):(((eq a) ((g j) x2)) ((g j) x2))
% 149.66/149.95 Found (eq_ref0 ((g j) x2)) as proof of (((eq a) ((g j) x2)) b)
% 149.66/149.95 Found ((eq_ref a) ((g j) x2)) as proof of (((eq a) ((g j) x2)) b)
% 149.66/149.95 Found ((eq_ref a) ((g j) x2)) as proof of (((eq a) ((g j) x2)) b)
% 149.66/149.95 Found ((eq_ref a) ((g j) x2)) as proof of (((eq a) ((g j) x2)) b)
% 149.66/149.95 Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% 149.66/149.95 Found (eq_ref0 b) as proof of (((eq a) b) ((f h) x2))
% 149.66/149.95 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x2))
% 149.66/149.95 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x2))
% 149.66/149.95 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x2))
% 149.66/149.95 Found eq_ref000:=(eq_ref00 Xq):((Xq (f h))->(Xq (f h)))
% 149.66/149.95 Found (eq_ref00 Xq) as proof of (P (f h))
% 149.66/149.95 Found ((eq_ref0 (f h)) Xq) as proof of (P (f h))
% 149.66/149.95 Found (((eq_ref (a->a)) (f h)) Xq) as proof of (P (f h))
% 149.66/149.95 Found (((eq_ref (a->a)) (f h)) Xq) as proof of (P (f h))
% 149.66/149.95 Found eq_ref00:=(eq_ref0 b):(((eq (a->a)) b) b)
% 149.66/149.95 Found (eq_ref0 b) as proof of (((eq (a->a)) b) (g j))
% 149.66/149.95 Found ((eq_ref (a->a)) b) as proof of (((eq (a->a)) b) (g j))
% 149.66/149.95 Found ((eq_ref (a->a)) b) as proof of (((eq (a->a)) b) (g j))
% 149.66/149.95 Found ((eq_ref (a->a)) b) as proof of (((eq (a->a)) b) (g j))
% 149.66/149.95 Found eq_ref00:=(eq_ref0 (f h)):(((eq (a->a)) (f h)) (f h))
% 149.66/149.95 Found (eq_ref0 (f h)) as proof of (((eq (a->a)) (f h)) b)
% 149.66/149.95 Found ((eq_ref (a->a)) (f h)) as proof of (((eq (a->a)) (f h)) b)
% 149.66/149.95 Found ((eq_ref (a->a)) (f h)) as proof of (((eq (a->a)) (f h)) b)
% 149.66/149.95 Found ((eq_ref (a->a)) (f h)) as proof of (((eq (a->a)) (f h)) b)
% 149.66/149.95 Found x0:(P (g j))
% 149.66/149.95 Instantiate: b:=(g j):(a->a)
% 149.66/149.95 Found x0 as proof of (P0 b)
% 167.36/167.60 Found eta_expansion000:=(eta_expansion00 (f h)):(((eq (a->a)) (f h)) (fun (x:a)=> ((f h) x)))
% 167.36/167.60 Found (eta_expansion00 (f h)) as proof of (((eq (a->a)) (f h)) b)
% 167.36/167.60 Found ((eta_expansion0 a) (f h)) as proof of (((eq (a->a)) (f h)) b)
% 167.36/167.60 Found (((eta_expansion a) a) (f h)) as proof of (((eq (a->a)) (f h)) b)
% 167.36/167.60 Found (((eta_expansion a) a) (f h)) as proof of (((eq (a->a)) (f h)) b)
% 167.36/167.60 Found (((eta_expansion a) a) (f h)) as proof of (((eq (a->a)) (f h)) b)
% 167.36/167.60 Found eq_ref000:=(eq_ref00 P):((P ((f h) x0))->(P ((f h) x0)))
% 167.36/167.60 Found (eq_ref00 P) as proof of (P0 ((f h) x0))
% 167.36/167.60 Found ((eq_ref0 ((f h) x0)) P) as proof of (P0 ((f h) x0))
% 167.36/167.60 Found (((eq_ref a) ((f h) x0)) P) as proof of (P0 ((f h) x0))
% 167.36/167.60 Found (((eq_ref a) ((f h) x0)) P) as proof of (P0 ((f h) x0))
% 167.36/167.60 Found eq_ref000:=(eq_ref00 P):((P ((f h) x0))->(P ((f h) x0)))
% 167.36/167.60 Found (eq_ref00 P) as proof of (P0 ((f h) x0))
% 167.36/167.60 Found ((eq_ref0 ((f h) x0)) P) as proof of (P0 ((f h) x0))
% 167.36/167.60 Found (((eq_ref a) ((f h) x0)) P) as proof of (P0 ((f h) x0))
% 167.36/167.60 Found (((eq_ref a) ((f h) x0)) P) as proof of (P0 ((f h) x0))
% 167.36/167.60 Found eq_ref00:=(eq_ref0 ((g j) x0)):(((eq a) ((g j) x0)) ((g j) x0))
% 167.36/167.60 Found (eq_ref0 ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 167.36/167.60 Found ((eq_ref a) ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 167.36/167.60 Found ((eq_ref a) ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 167.36/167.60 Found ((eq_ref a) ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 167.36/167.60 Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% 167.36/167.60 Found (eq_ref0 b) as proof of (((eq a) b) ((f h) x0))
% 167.36/167.60 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 167.36/167.60 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 167.36/167.60 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 167.36/167.60 Found eq_ref00:=(eq_ref0 ((g j) x0)):(((eq a) ((g j) x0)) ((g j) x0))
% 167.36/167.60 Found (eq_ref0 ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 167.36/167.60 Found ((eq_ref a) ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 167.36/167.60 Found ((eq_ref a) ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 167.36/167.60 Found ((eq_ref a) ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 167.36/167.60 Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% 167.36/167.60 Found (eq_ref0 b) as proof of (((eq a) b) ((f h) x0))
% 167.36/167.60 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 167.36/167.60 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 167.36/167.60 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 167.36/167.60 Found eq_ref00:=(eq_ref0 ((f h) x2)):(((eq a) ((f h) x2)) ((f h) x2))
% 167.36/167.60 Found (eq_ref0 ((f h) x2)) as proof of (((eq a) ((f h) x2)) b)
% 167.36/167.60 Found ((eq_ref a) ((f h) x2)) as proof of (((eq a) ((f h) x2)) b)
% 167.36/167.60 Found ((eq_ref a) ((f h) x2)) as proof of (((eq a) ((f h) x2)) b)
% 167.36/167.60 Found ((eq_ref a) ((f h) x2)) as proof of (((eq a) ((f h) x2)) b)
% 167.36/167.60 Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% 167.36/167.60 Found (eq_ref0 b) as proof of (((eq a) b) ((f j) x2))
% 167.36/167.60 Found ((eq_ref a) b) as proof of (((eq a) b) ((f j) x2))
% 167.36/167.60 Found ((eq_ref a) b) as proof of (((eq a) b) ((f j) x2))
% 167.36/167.60 Found ((eq_ref a) b) as proof of (((eq a) b) ((f j) x2))
% 167.36/167.60 Found eq_ref00:=(eq_ref0 ((f h) x2)):(((eq a) ((f h) x2)) ((f h) x2))
% 167.36/167.60 Found (eq_ref0 ((f h) x2)) as proof of (((eq a) ((f h) x2)) b)
% 167.36/167.60 Found ((eq_ref a) ((f h) x2)) as proof of (((eq a) ((f h) x2)) b)
% 167.36/167.60 Found ((eq_ref a) ((f h) x2)) as proof of (((eq a) ((f h) x2)) b)
% 167.36/167.60 Found ((eq_ref a) ((f h) x2)) as proof of (((eq a) ((f h) x2)) b)
% 167.36/167.60 Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% 167.36/167.60 Found (eq_ref0 b) as proof of (((eq a) b) ((f j) x2))
% 167.36/167.60 Found ((eq_ref a) b) as proof of (((eq a) b) ((f j) x2))
% 167.36/167.60 Found ((eq_ref a) b) as proof of (((eq a) b) ((f j) x2))
% 167.36/167.60 Found ((eq_ref a) b) as proof of (((eq a) b) ((f j) x2))
% 167.36/167.60 Found eq_ref000:=(eq_ref00 P):((P ((f h) x0))->(P ((f h) x0)))
% 167.36/167.60 Found (eq_ref00 P) as proof of (P0 (f h))
% 167.36/167.60 Found ((eq_ref0 ((f h) x0)) P) as proof of (P0 (f h))
% 167.36/167.60 Found (((eq_ref a) ((f h) x0)) P) as proof of (P0 (f h))
% 167.36/167.60 Found (((eq_ref a) ((f h) x0)) P) as proof of (P0 (f h))
% 167.36/167.60 Found eq_ref000:=(eq_ref00 P):((P ((f h) x0))->(P ((f h) x0)))
% 167.36/167.60 Found (eq_ref00 P) as proof of (P0 (f h))
% 167.36/167.60 Found ((eq_ref0 ((f h) x0)) P) as proof of (P0 (f h))
% 167.36/167.60 Found (((eq_ref a) ((f h) x0)) P) as proof of (P0 (f h))
% 167.36/167.60 Found (((eq_ref a) ((f h) x0)) P) as proof of (P0 (f h))
% 167.36/167.60 Found eq_ref000:=(eq_ref00 P):((P ((g j) x2))->(P ((g j) x2)))
% 167.36/167.60 Found (eq_ref00 P) as proof of (P0 ((g j) x2))
% 167.36/167.60 Found ((eq_ref0 ((g j) x2)) P) as proof of (P0 ((g j) x2))
% 185.89/186.21 Found (((eq_ref a) ((g j) x2)) P) as proof of (P0 ((g j) x2))
% 185.89/186.21 Found (((eq_ref a) ((g j) x2)) P) as proof of (P0 ((g j) x2))
% 185.89/186.21 Found eq_ref000:=(eq_ref00 P):((P ((g j) x2))->(P ((g j) x2)))
% 185.89/186.21 Found (eq_ref00 P) as proof of (P0 ((g j) x2))
% 185.89/186.21 Found ((eq_ref0 ((g j) x2)) P) as proof of (P0 ((g j) x2))
% 185.89/186.21 Found (((eq_ref a) ((g j) x2)) P) as proof of (P0 ((g j) x2))
% 185.89/186.21 Found (((eq_ref a) ((g j) x2)) P) as proof of (P0 ((g j) x2))
% 185.89/186.21 Found eq_ref00:=(eq_ref0 ((g j) x0)):(((eq a) ((g j) x0)) ((g j) x0))
% 185.89/186.21 Found (eq_ref0 ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 185.89/186.21 Found ((eq_ref a) ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 185.89/186.21 Found ((eq_ref a) ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 185.89/186.21 Found ((eq_ref a) ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 185.89/186.21 Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% 185.89/186.21 Found (eq_ref0 b) as proof of (((eq a) b) ((f h) x0))
% 185.89/186.21 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 185.89/186.21 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 185.89/186.21 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 185.89/186.21 Found eq_ref00:=(eq_ref0 ((g j) x0)):(((eq a) ((g j) x0)) ((g j) x0))
% 185.89/186.21 Found (eq_ref0 ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 185.89/186.21 Found ((eq_ref a) ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 185.89/186.21 Found ((eq_ref a) ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 185.89/186.21 Found ((eq_ref a) ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 185.89/186.21 Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% 185.89/186.21 Found (eq_ref0 b) as proof of (((eq a) b) ((f h) x0))
% 185.89/186.21 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 185.89/186.21 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 185.89/186.21 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 185.89/186.21 Found x0:(P (f h))
% 185.89/186.21 Instantiate: f0:=(f h):(a->a)
% 185.89/186.21 Found x0 as proof of (P0 f0)
% 185.89/186.21 Found eq_ref00:=(eq_ref0 (f0 x1)):(((eq a) (f0 x1)) (f0 x1))
% 185.89/186.21 Found (eq_ref0 (f0 x1)) as proof of (((eq a) (f0 x1)) ((g j) x1))
% 185.89/186.21 Found ((eq_ref a) (f0 x1)) as proof of (((eq a) (f0 x1)) ((g j) x1))
% 185.89/186.21 Found ((eq_ref a) (f0 x1)) as proof of (((eq a) (f0 x1)) ((g j) x1))
% 185.89/186.21 Found (fun (x1:a)=> ((eq_ref a) (f0 x1))) as proof of (((eq a) (f0 x1)) ((g j) x1))
% 185.89/186.21 Found (fun (x1:a)=> ((eq_ref a) (f0 x1))) as proof of (forall (x:a), (((eq a) (f0 x)) ((g j) x)))
% 185.89/186.21 Found x0:(P (f h))
% 185.89/186.21 Instantiate: f0:=(f h):(a->a)
% 185.89/186.21 Found x0 as proof of (P0 f0)
% 185.89/186.21 Found eq_ref00:=(eq_ref0 (f0 x1)):(((eq a) (f0 x1)) (f0 x1))
% 185.89/186.21 Found (eq_ref0 (f0 x1)) as proof of (((eq a) (f0 x1)) ((g j) x1))
% 185.89/186.21 Found ((eq_ref a) (f0 x1)) as proof of (((eq a) (f0 x1)) ((g j) x1))
% 185.89/186.21 Found ((eq_ref a) (f0 x1)) as proof of (((eq a) (f0 x1)) ((g j) x1))
% 185.89/186.21 Found (fun (x1:a)=> ((eq_ref a) (f0 x1))) as proof of (((eq a) (f0 x1)) ((g j) x1))
% 185.89/186.21 Found (fun (x1:a)=> ((eq_ref a) (f0 x1))) as proof of (forall (x:a), (((eq a) (f0 x)) ((g j) x)))
% 185.89/186.21 Found eq_ref00:=(eq_ref0 ((g j) x0)):(((eq a) ((g j) x0)) ((g j) x0))
% 185.89/186.21 Found (eq_ref0 ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 185.89/186.21 Found ((eq_ref a) ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 185.89/186.21 Found ((eq_ref a) ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 185.89/186.21 Found ((eq_ref a) ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 185.89/186.21 Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% 185.89/186.21 Found (eq_ref0 b) as proof of (((eq a) b) ((f h) x0))
% 185.89/186.21 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 185.89/186.21 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 185.89/186.21 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 185.89/186.21 Found eq_ref00:=(eq_ref0 ((g j) x0)):(((eq a) ((g j) x0)) ((g j) x0))
% 185.89/186.21 Found (eq_ref0 ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 185.89/186.21 Found ((eq_ref a) ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 185.89/186.21 Found ((eq_ref a) ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 185.89/186.21 Found ((eq_ref a) ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 185.89/186.21 Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% 185.89/186.21 Found (eq_ref0 b) as proof of (((eq a) b) ((f h) x0))
% 185.89/186.21 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 185.89/186.21 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 185.89/186.21 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 185.89/186.21 Found x1:(P ((f h) x0))
% 185.89/186.21 Instantiate: b:=((f h) x0):a
% 185.89/186.21 Found x1 as proof of (P0 b)
% 185.89/186.21 Found eq_ref00:=(eq_ref0 ((g j) x0)):(((eq a) ((g j) x0)) ((g j) x0))
% 185.89/186.21 Found (eq_ref0 ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 197.24/197.54 Found ((eq_ref a) ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 197.24/197.54 Found ((eq_ref a) ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 197.24/197.54 Found ((eq_ref a) ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 197.24/197.54 Found x1:(P ((f h) x0))
% 197.24/197.54 Instantiate: b:=((f h) x0):a
% 197.24/197.54 Found x1 as proof of (P0 b)
% 197.24/197.54 Found eq_ref00:=(eq_ref0 ((g j) x0)):(((eq a) ((g j) x0)) ((g j) x0))
% 197.24/197.54 Found (eq_ref0 ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 197.24/197.54 Found ((eq_ref a) ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 197.24/197.54 Found ((eq_ref a) ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 197.24/197.54 Found ((eq_ref a) ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 197.24/197.54 Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% 197.24/197.54 Found (eq_ref0 b) as proof of (((eq a) b) ((f h) x2))
% 197.24/197.54 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x2))
% 197.24/197.54 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x2))
% 197.24/197.54 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x2))
% 197.24/197.54 Found eq_ref00:=(eq_ref0 ((g j) x2)):(((eq a) ((g j) x2)) ((g j) x2))
% 197.24/197.54 Found (eq_ref0 ((g j) x2)) as proof of (((eq a) ((g j) x2)) b)
% 197.24/197.54 Found ((eq_ref a) ((g j) x2)) as proof of (((eq a) ((g j) x2)) b)
% 197.24/197.54 Found ((eq_ref a) ((g j) x2)) as proof of (((eq a) ((g j) x2)) b)
% 197.24/197.54 Found ((eq_ref a) ((g j) x2)) as proof of (((eq a) ((g j) x2)) b)
% 197.24/197.54 Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% 197.24/197.54 Found (eq_ref0 b) as proof of (((eq a) b) ((f h) x2))
% 197.24/197.54 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x2))
% 197.24/197.54 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x2))
% 197.24/197.54 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x2))
% 197.24/197.54 Found eq_ref00:=(eq_ref0 ((g j) x2)):(((eq a) ((g j) x2)) ((g j) x2))
% 197.24/197.54 Found (eq_ref0 ((g j) x2)) as proof of (((eq a) ((g j) x2)) b)
% 197.24/197.54 Found ((eq_ref a) ((g j) x2)) as proof of (((eq a) ((g j) x2)) b)
% 197.24/197.54 Found ((eq_ref a) ((g j) x2)) as proof of (((eq a) ((g j) x2)) b)
% 197.24/197.54 Found ((eq_ref a) ((g j) x2)) as proof of (((eq a) ((g j) x2)) b)
% 197.24/197.54 Found eq_ref00:=(eq_ref0 ((g j) x2)):(((eq a) ((g j) x2)) ((g j) x2))
% 197.24/197.54 Found (eq_ref0 ((g j) x2)) as proof of (((eq a) ((g j) x2)) b)
% 197.24/197.54 Found ((eq_ref a) ((g j) x2)) as proof of (((eq a) ((g j) x2)) b)
% 197.24/197.54 Found ((eq_ref a) ((g j) x2)) as proof of (((eq a) ((g j) x2)) b)
% 197.24/197.54 Found ((eq_ref a) ((g j) x2)) as proof of (((eq a) ((g j) x2)) b)
% 197.24/197.54 Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% 197.24/197.54 Found (eq_ref0 b) as proof of (((eq a) b) ((f h) x2))
% 197.24/197.54 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x2))
% 197.24/197.54 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x2))
% 197.24/197.54 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x2))
% 197.24/197.54 Found eq_ref00:=(eq_ref0 ((g j) x2)):(((eq a) ((g j) x2)) ((g j) x2))
% 197.24/197.54 Found (eq_ref0 ((g j) x2)) as proof of (((eq a) ((g j) x2)) b)
% 197.24/197.54 Found ((eq_ref a) ((g j) x2)) as proof of (((eq a) ((g j) x2)) b)
% 197.24/197.54 Found ((eq_ref a) ((g j) x2)) as proof of (((eq a) ((g j) x2)) b)
% 197.24/197.54 Found ((eq_ref a) ((g j) x2)) as proof of (((eq a) ((g j) x2)) b)
% 197.24/197.54 Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% 197.24/197.54 Found (eq_ref0 b) as proof of (((eq a) b) ((f h) x2))
% 197.24/197.54 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x2))
% 197.24/197.54 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x2))
% 197.24/197.54 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x2))
% 197.24/197.54 Found x2:(P (f h))
% 197.24/197.54 Instantiate: b:=(f h):(a->a)
% 197.24/197.54 Found x2 as proof of (P0 b)
% 197.24/197.54 Found eq_ref00:=(eq_ref0 (g j)):(((eq (a->a)) (g j)) (g j))
% 197.24/197.54 Found (eq_ref0 (g j)) as proof of (((eq (a->a)) (g j)) b)
% 197.24/197.54 Found ((eq_ref (a->a)) (g j)) as proof of (((eq (a->a)) (g j)) b)
% 197.24/197.54 Found ((eq_ref (a->a)) (g j)) as proof of (((eq (a->a)) (g j)) b)
% 197.24/197.54 Found ((eq_ref (a->a)) (g j)) as proof of (((eq (a->a)) (g j)) b)
% 197.24/197.54 Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% 197.24/197.54 Found (eq_ref0 b) as proof of (((eq a) b) ((f j) x0))
% 197.24/197.54 Found ((eq_ref a) b) as proof of (((eq a) b) ((f j) x0))
% 197.24/197.54 Found ((eq_ref a) b) as proof of (((eq a) b) ((f j) x0))
% 197.24/197.54 Found ((eq_ref a) b) as proof of (((eq a) b) ((f j) x0))
% 197.24/197.54 Found eq_ref00:=(eq_ref0 ((f h) x0)):(((eq a) ((f h) x0)) ((f h) x0))
% 197.24/197.54 Found (eq_ref0 ((f h) x0)) as proof of (((eq a) ((f h) x0)) b)
% 197.24/197.54 Found ((eq_ref a) ((f h) x0)) as proof of (((eq a) ((f h) x0)) b)
% 197.24/197.54 Found ((eq_ref a) ((f h) x0)) as proof of (((eq a) ((f h) x0)) b)
% 197.24/197.54 Found ((eq_ref a) ((f h) x0)) as proof of (((eq a) ((f h) x0)) b)
% 197.24/197.54 Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% 197.24/197.54 Found (eq_ref0 b) as proof of (((eq a) b) ((f j) x0))
% 207.74/208.03 Found ((eq_ref a) b) as proof of (((eq a) b) ((f j) x0))
% 207.74/208.03 Found ((eq_ref a) b) as proof of (((eq a) b) ((f j) x0))
% 207.74/208.03 Found ((eq_ref a) b) as proof of (((eq a) b) ((f j) x0))
% 207.74/208.03 Found eq_ref00:=(eq_ref0 ((f h) x0)):(((eq a) ((f h) x0)) ((f h) x0))
% 207.74/208.03 Found (eq_ref0 ((f h) x0)) as proof of (((eq a) ((f h) x0)) b)
% 207.74/208.03 Found ((eq_ref a) ((f h) x0)) as proof of (((eq a) ((f h) x0)) b)
% 207.74/208.03 Found ((eq_ref a) ((f h) x0)) as proof of (((eq a) ((f h) x0)) b)
% 207.74/208.03 Found ((eq_ref a) ((f h) x0)) as proof of (((eq a) ((f h) x0)) b)
% 207.74/208.03 Found eq_ref000:=(eq_ref00 P):((P ((f h) x2))->(P ((f h) x2)))
% 207.74/208.03 Found (eq_ref00 P) as proof of (P0 (f h))
% 207.74/208.03 Found ((eq_ref0 ((f h) x2)) P) as proof of (P0 (f h))
% 207.74/208.03 Found (((eq_ref a) ((f h) x2)) P) as proof of (P0 (f h))
% 207.74/208.03 Found (((eq_ref a) ((f h) x2)) P) as proof of (P0 (f h))
% 207.74/208.03 Found eq_ref000:=(eq_ref00 P):((P ((f h) x2))->(P ((f h) x2)))
% 207.74/208.03 Found (eq_ref00 P) as proof of (P0 (f h))
% 207.74/208.03 Found ((eq_ref0 ((f h) x2)) P) as proof of (P0 (f h))
% 207.74/208.03 Found (((eq_ref a) ((f h) x2)) P) as proof of (P0 (f h))
% 207.74/208.03 Found (((eq_ref a) ((f h) x2)) P) as proof of (P0 (f h))
% 207.74/208.03 Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% 207.74/208.03 Found (eq_ref0 b) as proof of (((eq a) b) ((f j) x0))
% 207.74/208.03 Found ((eq_ref a) b) as proof of (((eq a) b) ((f j) x0))
% 207.74/208.03 Found ((eq_ref a) b) as proof of (((eq a) b) ((f j) x0))
% 207.74/208.03 Found ((eq_ref a) b) as proof of (((eq a) b) ((f j) x0))
% 207.74/208.03 Found eq_ref00:=(eq_ref0 ((f h) x0)):(((eq a) ((f h) x0)) ((f h) x0))
% 207.74/208.03 Found (eq_ref0 ((f h) x0)) as proof of (((eq a) ((f h) x0)) b)
% 207.74/208.03 Found ((eq_ref a) ((f h) x0)) as proof of (((eq a) ((f h) x0)) b)
% 207.74/208.03 Found ((eq_ref a) ((f h) x0)) as proof of (((eq a) ((f h) x0)) b)
% 207.74/208.03 Found ((eq_ref a) ((f h) x0)) as proof of (((eq a) ((f h) x0)) b)
% 207.74/208.03 Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% 207.74/208.03 Found (eq_ref0 b) as proof of (((eq a) b) ((f j) x0))
% 207.74/208.03 Found ((eq_ref a) b) as proof of (((eq a) b) ((f j) x0))
% 207.74/208.03 Found ((eq_ref a) b) as proof of (((eq a) b) ((f j) x0))
% 207.74/208.03 Found ((eq_ref a) b) as proof of (((eq a) b) ((f j) x0))
% 207.74/208.03 Found eq_ref00:=(eq_ref0 ((f h) x0)):(((eq a) ((f h) x0)) ((f h) x0))
% 207.74/208.03 Found (eq_ref0 ((f h) x0)) as proof of (((eq a) ((f h) x0)) b)
% 207.74/208.03 Found ((eq_ref a) ((f h) x0)) as proof of (((eq a) ((f h) x0)) b)
% 207.74/208.03 Found ((eq_ref a) ((f h) x0)) as proof of (((eq a) ((f h) x0)) b)
% 207.74/208.03 Found ((eq_ref a) ((f h) x0)) as proof of (((eq a) ((f h) x0)) b)
% 207.74/208.03 Found eq_ref000:=(eq_ref00 P):((P ((f j) x0))->(P ((f j) x0)))
% 207.74/208.03 Found (eq_ref00 P) as proof of (P0 ((f j) x0))
% 207.74/208.03 Found ((eq_ref0 ((f j) x0)) P) as proof of (P0 ((f j) x0))
% 207.74/208.03 Found (((eq_ref a) ((f j) x0)) P) as proof of (P0 ((f j) x0))
% 207.74/208.03 Found (((eq_ref a) ((f j) x0)) P) as proof of (P0 ((f j) x0))
% 207.74/208.03 Found eq_ref000:=(eq_ref00 P):((P ((f j) x0))->(P ((f j) x0)))
% 207.74/208.03 Found (eq_ref00 P) as proof of (P0 ((f j) x0))
% 207.74/208.03 Found ((eq_ref0 ((f j) x0)) P) as proof of (P0 ((f j) x0))
% 207.74/208.03 Found (((eq_ref a) ((f j) x0)) P) as proof of (P0 ((f j) x0))
% 207.74/208.03 Found (((eq_ref a) ((f j) x0)) P) as proof of (P0 ((f j) x0))
% 207.74/208.03 Found x0:(Xq (f h))
% 207.74/208.03 Instantiate: f0:=(f h):(a->a)
% 207.74/208.03 Found x0 as proof of (P f0)
% 207.74/208.03 Found eq_ref00:=(eq_ref0 (f0 x3)):(((eq a) (f0 x3)) (f0 x3))
% 207.74/208.03 Found (eq_ref0 (f0 x3)) as proof of (((eq a) (f0 x3)) ((g j) x3))
% 207.74/208.03 Found ((eq_ref a) (f0 x3)) as proof of (((eq a) (f0 x3)) ((g j) x3))
% 207.74/208.03 Found ((eq_ref a) (f0 x3)) as proof of (((eq a) (f0 x3)) ((g j) x3))
% 207.74/208.03 Found (fun (x3:a)=> ((eq_ref a) (f0 x3))) as proof of (((eq a) (f0 x3)) ((g j) x3))
% 207.74/208.03 Found (fun (x3:a)=> ((eq_ref a) (f0 x3))) as proof of (forall (x:a), (((eq a) (f0 x)) ((g j) x)))
% 207.74/208.03 Found x0:(Xq (f h))
% 207.74/208.03 Instantiate: f0:=(f h):(a->a)
% 207.74/208.03 Found x0 as proof of (P f0)
% 207.74/208.03 Found eq_ref00:=(eq_ref0 (f0 x3)):(((eq a) (f0 x3)) (f0 x3))
% 207.74/208.03 Found (eq_ref0 (f0 x3)) as proof of (((eq a) (f0 x3)) ((g j) x3))
% 207.74/208.03 Found ((eq_ref a) (f0 x3)) as proof of (((eq a) (f0 x3)) ((g j) x3))
% 207.74/208.03 Found ((eq_ref a) (f0 x3)) as proof of (((eq a) (f0 x3)) ((g j) x3))
% 207.74/208.03 Found (fun (x3:a)=> ((eq_ref a) (f0 x3))) as proof of (((eq a) (f0 x3)) ((g j) x3))
% 207.74/208.03 Found (fun (x3:a)=> ((eq_ref a) (f0 x3))) as proof of (forall (x:a), (((eq a) (f0 x)) ((g j) x)))
% 207.74/208.03 Found eq_ref000:=(eq_ref00 P):((P ((g j) x0))->(P ((g j) x0)))
% 207.74/208.03 Found (eq_ref00 P) as proof of (P0 ((g j) x0))
% 207.74/208.03 Found ((eq_ref0 ((g j) x0)) P) as proof of (P0 ((g j) x0))
% 207.74/208.03 Found (((eq_ref a) ((g j) x0)) P) as proof of (P0 ((g j) x0))
% 214.98/215.29 Found (((eq_ref a) ((g j) x0)) P) as proof of (P0 ((g j) x0))
% 214.98/215.29 Found eq_ref000:=(eq_ref00 P):((P ((g j) x0))->(P ((g j) x0)))
% 214.98/215.29 Found (eq_ref00 P) as proof of (P0 ((g j) x0))
% 214.98/215.29 Found ((eq_ref0 ((g j) x0)) P) as proof of (P0 ((g j) x0))
% 214.98/215.29 Found (((eq_ref a) ((g j) x0)) P) as proof of (P0 ((g j) x0))
% 214.98/215.29 Found (((eq_ref a) ((g j) x0)) P) as proof of (P0 ((g j) x0))
% 214.98/215.29 Found x0:(P (f h))
% 214.98/215.29 Instantiate: b:=(f h):(a->a)
% 214.98/215.29 Found x0 as proof of (P0 b)
% 214.98/215.29 Found eq_ref00:=(eq_ref0 (g j)):(((eq (a->a)) (g j)) (g j))
% 214.98/215.29 Found (eq_ref0 (g j)) as proof of (((eq (a->a)) (g j)) b)
% 214.98/215.29 Found ((eq_ref (a->a)) (g j)) as proof of (((eq (a->a)) (g j)) b)
% 214.98/215.29 Found ((eq_ref (a->a)) (g j)) as proof of (((eq (a->a)) (g j)) b)
% 214.98/215.29 Found ((eq_ref (a->a)) (g j)) as proof of (((eq (a->a)) (g j)) b)
% 214.98/215.29 Found eq_ref00:=(eq_ref0 b):(((eq (a->a)) b) b)
% 214.98/215.29 Found (eq_ref0 b) as proof of (((eq (a->a)) b) (g j))
% 214.98/215.29 Found ((eq_ref (a->a)) b) as proof of (((eq (a->a)) b) (g j))
% 214.98/215.29 Found ((eq_ref (a->a)) b) as proof of (((eq (a->a)) b) (g j))
% 214.98/215.29 Found ((eq_ref (a->a)) b) as proof of (((eq (a->a)) b) (g j))
% 214.98/215.29 Found eq_ref00:=(eq_ref0 (f h)):(((eq (a->a)) (f h)) (f h))
% 214.98/215.29 Found (eq_ref0 (f h)) as proof of (((eq (a->a)) (f h)) b)
% 214.98/215.29 Found ((eq_ref (a->a)) (f h)) as proof of (((eq (a->a)) (f h)) b)
% 214.98/215.29 Found ((eq_ref (a->a)) (f h)) as proof of (((eq (a->a)) (f h)) b)
% 214.98/215.29 Found ((eq_ref (a->a)) (f h)) as proof of (((eq (a->a)) (f h)) b)
% 214.98/215.29 Found eq_ref00:=(eq_ref0 b):(((eq (a->a)) b) b)
% 214.98/215.29 Found (eq_ref0 b) as proof of (P b)
% 214.98/215.29 Found ((eq_ref (a->a)) b) as proof of (P b)
% 214.98/215.29 Found ((eq_ref (a->a)) b) as proof of (P b)
% 214.98/215.29 Found ((eq_ref (a->a)) b) as proof of (P b)
% 214.98/215.29 Found eta_expansion000:=(eta_expansion00 (g j)):(((eq (a->a)) (g j)) (fun (x:a)=> ((g j) x)))
% 214.98/215.29 Found (eta_expansion00 (g j)) as proof of (((eq (a->a)) (g j)) b)
% 214.98/215.29 Found ((eta_expansion0 a) (g j)) as proof of (((eq (a->a)) (g j)) b)
% 214.98/215.29 Found (((eta_expansion a) a) (g j)) as proof of (((eq (a->a)) (g j)) b)
% 214.98/215.29 Found (((eta_expansion a) a) (g j)) as proof of (((eq (a->a)) (g j)) b)
% 214.98/215.29 Found (((eta_expansion a) a) (g j)) as proof of (((eq (a->a)) (g j)) b)
% 214.98/215.29 Found eq_ref000:=(eq_ref00 P0):((P0 (g j))->(P0 (g j)))
% 214.98/215.29 Found (eq_ref00 P0) as proof of (P1 (g j))
% 214.98/215.29 Found ((eq_ref0 (g j)) P0) as proof of (P1 (g j))
% 214.98/215.29 Found (((eq_ref (a->a)) (g j)) P0) as proof of (P1 (g j))
% 214.98/215.29 Found (((eq_ref (a->a)) (g j)) P0) as proof of (P1 (g j))
% 214.98/215.29 Found eq_ref000:=(eq_ref00 P0):((P0 (g j))->(P0 (g j)))
% 214.98/215.29 Found (eq_ref00 P0) as proof of (P1 (g j))
% 214.98/215.29 Found ((eq_ref0 (g j)) P0) as proof of (P1 (g j))
% 214.98/215.29 Found (((eq_ref (a->a)) (g j)) P0) as proof of (P1 (g j))
% 214.98/215.29 Found (((eq_ref (a->a)) (g j)) P0) as proof of (P1 (g j))
% 214.98/215.29 Found eq_ref000:=(eq_ref00 P0):((P0 (g j))->(P0 (g j)))
% 214.98/215.29 Found (eq_ref00 P0) as proof of (P1 (g j))
% 214.98/215.29 Found ((eq_ref0 (g j)) P0) as proof of (P1 (g j))
% 214.98/215.29 Found (((eq_ref (a->a)) (g j)) P0) as proof of (P1 (g j))
% 214.98/215.29 Found (((eq_ref (a->a)) (g j)) P0) as proof of (P1 (g j))
% 214.98/215.29 Found eq_ref000:=(eq_ref00 P0):((P0 (g j))->(P0 (g j)))
% 214.98/215.29 Found (eq_ref00 P0) as proof of (P1 (g j))
% 214.98/215.29 Found ((eq_ref0 (g j)) P0) as proof of (P1 (g j))
% 214.98/215.29 Found (((eq_ref (a->a)) (g j)) P0) as proof of (P1 (g j))
% 214.98/215.29 Found (((eq_ref (a->a)) (g j)) P0) as proof of (P1 (g j))
% 214.98/215.29 Found eq_ref000:=(eq_ref00 P):((P (f h))->(P (f h)))
% 214.98/215.29 Found (eq_ref00 P) as proof of (P0 (f h))
% 214.98/215.29 Found ((eq_ref0 (f h)) P) as proof of (P0 (f h))
% 214.98/215.29 Found (((eq_ref (a->a)) (f h)) P) as proof of (P0 (f h))
% 214.98/215.29 Found (((eq_ref (a->a)) (f h)) P) as proof of (P0 (f h))
% 214.98/215.29 Found eq_ref00:=(eq_ref0 b):(((eq (a->a)) b) b)
% 214.98/215.29 Found (eq_ref0 b) as proof of (((eq (a->a)) b) (g j))
% 214.98/215.29 Found ((eq_ref (a->a)) b) as proof of (((eq (a->a)) b) (g j))
% 214.98/215.29 Found ((eq_ref (a->a)) b) as proof of (((eq (a->a)) b) (g j))
% 214.98/215.29 Found ((eq_ref (a->a)) b) as proof of (((eq (a->a)) b) (g j))
% 214.98/215.29 Found eq_ref00:=(eq_ref0 (f h)):(((eq (a->a)) (f h)) (f h))
% 214.98/215.29 Found (eq_ref0 (f h)) as proof of (((eq (a->a)) (f h)) b)
% 214.98/215.29 Found ((eq_ref (a->a)) (f h)) as proof of (((eq (a->a)) (f h)) b)
% 214.98/215.29 Found ((eq_ref (a->a)) (f h)) as proof of (((eq (a->a)) (f h)) b)
% 214.98/215.29 Found ((eq_ref (a->a)) (f h)) as proof of (((eq (a->a)) (f h)) b)
% 214.98/215.29 Found eq_ref00:=(eq_ref0 a0):(((eq (a->a)) a0) a0)
% 214.98/215.29 Found (eq_ref0 a0) as proof of (((eq (a->a)) a0) j)
% 214.98/215.29 Found ((eq_ref (a->a)) a0) as proof of (((eq (a->a)) a0) j)
% 223.84/224.14 Found ((eq_ref (a->a)) a0) as proof of (((eq (a->a)) a0) j)
% 223.84/224.14 Found ((eq_ref (a->a)) a0) as proof of (((eq (a->a)) a0) j)
% 223.84/224.14 Found x0:(P (g j))
% 223.84/224.14 Instantiate: b:=(g j):(a->a)
% 223.84/224.14 Found x0 as proof of (P0 b)
% 223.84/224.14 Found eta_expansion000:=(eta_expansion00 (f h)):(((eq (a->a)) (f h)) (fun (x:a)=> ((f h) x)))
% 223.84/224.14 Found (eta_expansion00 (f h)) as proof of (((eq (a->a)) (f h)) b)
% 223.84/224.14 Found ((eta_expansion0 a) (f h)) as proof of (((eq (a->a)) (f h)) b)
% 223.84/224.14 Found (((eta_expansion a) a) (f h)) as proof of (((eq (a->a)) (f h)) b)
% 223.84/224.14 Found (((eta_expansion a) a) (f h)) as proof of (((eq (a->a)) (f h)) b)
% 223.84/224.14 Found (((eta_expansion a) a) (f h)) as proof of (((eq (a->a)) (f h)) b)
% 223.84/224.14 Found eq_ref00:=(eq_ref0 a0):(((eq (a->a)) a0) a0)
% 223.84/224.14 Found (eq_ref0 a0) as proof of (((eq (a->a)) a0) j)
% 223.84/224.14 Found ((eq_ref (a->a)) a0) as proof of (((eq (a->a)) a0) j)
% 223.84/224.14 Found ((eq_ref (a->a)) a0) as proof of (((eq (a->a)) a0) j)
% 223.84/224.14 Found ((eq_ref (a->a)) a0) as proof of (((eq (a->a)) a0) j)
% 223.84/224.14 Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% 223.84/224.14 Found (eq_ref0 b) as proof of (((eq a) b) ((g j) x0))
% 223.84/224.14 Found ((eq_ref a) b) as proof of (((eq a) b) ((g j) x0))
% 223.84/224.14 Found ((eq_ref a) b) as proof of (((eq a) b) ((g j) x0))
% 223.84/224.14 Found ((eq_ref a) b) as proof of (((eq a) b) ((g j) x0))
% 223.84/224.14 Found eq_ref00:=(eq_ref0 ((f h) x0)):(((eq a) ((f h) x0)) ((f h) x0))
% 223.84/224.14 Found (eq_ref0 ((f h) x0)) as proof of (((eq a) ((f h) x0)) b)
% 223.84/224.14 Found ((eq_ref a) ((f h) x0)) as proof of (((eq a) ((f h) x0)) b)
% 223.84/224.14 Found ((eq_ref a) ((f h) x0)) as proof of (((eq a) ((f h) x0)) b)
% 223.84/224.14 Found ((eq_ref a) ((f h) x0)) as proof of (((eq a) ((f h) x0)) b)
% 223.84/224.14 Found eq_ref00:=(eq_ref0 ((f h) x0)):(((eq a) ((f h) x0)) ((f h) x0))
% 223.84/224.14 Found (eq_ref0 ((f h) x0)) as proof of (((eq a) ((f h) x0)) b)
% 223.84/224.14 Found ((eq_ref a) ((f h) x0)) as proof of (((eq a) ((f h) x0)) b)
% 223.84/224.14 Found ((eq_ref a) ((f h) x0)) as proof of (((eq a) ((f h) x0)) b)
% 223.84/224.14 Found ((eq_ref a) ((f h) x0)) as proof of (((eq a) ((f h) x0)) b)
% 223.84/224.14 Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% 223.84/224.14 Found (eq_ref0 b) as proof of (((eq a) b) ((g j) x0))
% 223.84/224.14 Found ((eq_ref a) b) as proof of (((eq a) b) ((g j) x0))
% 223.84/224.14 Found ((eq_ref a) b) as proof of (((eq a) b) ((g j) x0))
% 223.84/224.14 Found ((eq_ref a) b) as proof of (((eq a) b) ((g j) x0))
% 223.84/224.14 Found eq_ref000:=(eq_ref00 P0):((P0 ((f h) x0))->(P0 ((f h) x0)))
% 223.84/224.14 Found (eq_ref00 P0) as proof of (P1 ((f h) x0))
% 223.84/224.14 Found ((eq_ref0 ((f h) x0)) P0) as proof of (P1 ((f h) x0))
% 223.84/224.14 Found (((eq_ref a) ((f h) x0)) P0) as proof of (P1 ((f h) x0))
% 223.84/224.14 Found (((eq_ref a) ((f h) x0)) P0) as proof of (P1 ((f h) x0))
% 223.84/224.14 Found eq_ref000:=(eq_ref00 P0):((P0 ((f h) x0))->(P0 ((f h) x0)))
% 223.84/224.14 Found (eq_ref00 P0) as proof of (P1 ((f h) x0))
% 223.84/224.14 Found ((eq_ref0 ((f h) x0)) P0) as proof of (P1 ((f h) x0))
% 223.84/224.14 Found (((eq_ref a) ((f h) x0)) P0) as proof of (P1 ((f h) x0))
% 223.84/224.14 Found (((eq_ref a) ((f h) x0)) P0) as proof of (P1 ((f h) x0))
% 223.84/224.14 Found eq_ref000:=(eq_ref00 P0):((P0 ((f h) x0))->(P0 ((f h) x0)))
% 223.84/224.14 Found (eq_ref00 P0) as proof of (P1 ((f h) x0))
% 223.84/224.14 Found ((eq_ref0 ((f h) x0)) P0) as proof of (P1 ((f h) x0))
% 223.84/224.14 Found (((eq_ref a) ((f h) x0)) P0) as proof of (P1 ((f h) x0))
% 223.84/224.14 Found (((eq_ref a) ((f h) x0)) P0) as proof of (P1 ((f h) x0))
% 223.84/224.14 Found eq_ref000:=(eq_ref00 P0):((P0 ((f h) x0))->(P0 ((f h) x0)))
% 223.84/224.14 Found (eq_ref00 P0) as proof of (P1 ((f h) x0))
% 223.84/224.14 Found ((eq_ref0 ((f h) x0)) P0) as proof of (P1 ((f h) x0))
% 223.84/224.14 Found (((eq_ref a) ((f h) x0)) P0) as proof of (P1 ((f h) x0))
% 223.84/224.14 Found (((eq_ref a) ((f h) x0)) P0) as proof of (P1 ((f h) x0))
% 223.84/224.14 Found eq_ref000:=(eq_ref00 P):((P ((f j) x2))->(P ((f j) x2)))
% 223.84/224.14 Found (eq_ref00 P) as proof of (P0 ((f j) x2))
% 223.84/224.14 Found ((eq_ref0 ((f j) x2)) P) as proof of (P0 ((f j) x2))
% 223.84/224.14 Found (((eq_ref a) ((f j) x2)) P) as proof of (P0 ((f j) x2))
% 223.84/224.14 Found (((eq_ref a) ((f j) x2)) P) as proof of (P0 ((f j) x2))
% 223.84/224.14 Found eq_ref000:=(eq_ref00 P):((P ((f j) x2))->(P ((f j) x2)))
% 223.84/224.14 Found (eq_ref00 P) as proof of (P0 ((f j) x2))
% 223.84/224.14 Found ((eq_ref0 ((f j) x2)) P) as proof of (P0 ((f j) x2))
% 223.84/224.14 Found (((eq_ref a) ((f j) x2)) P) as proof of (P0 ((f j) x2))
% 223.84/224.14 Found (((eq_ref a) ((f j) x2)) P) as proof of (P0 ((f j) x2))
% 223.84/224.14 Found eq_ref00:=(eq_ref0 ((g j) x2)):(((eq a) ((g j) x2)) ((g j) x2))
% 223.84/224.14 Found (eq_ref0 ((g j) x2)) as proof of (((eq a) ((g j) x2)) b)
% 223.84/224.14 Found ((eq_ref a) ((g j) x2)) as proof of (((eq a) ((g j) x2)) b)
% 233.14/233.48 Found ((eq_ref a) ((g j) x2)) as proof of (((eq a) ((g j) x2)) b)
% 233.14/233.48 Found ((eq_ref a) ((g j) x2)) as proof of (((eq a) ((g j) x2)) b)
% 233.14/233.48 Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% 233.14/233.48 Found (eq_ref0 b) as proof of (((eq a) b) ((f h) x2))
% 233.14/233.48 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x2))
% 233.14/233.48 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x2))
% 233.14/233.48 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x2))
% 233.14/233.48 Found eq_ref00:=(eq_ref0 ((g j) x2)):(((eq a) ((g j) x2)) ((g j) x2))
% 233.14/233.48 Found (eq_ref0 ((g j) x2)) as proof of (((eq a) ((g j) x2)) b)
% 233.14/233.48 Found ((eq_ref a) ((g j) x2)) as proof of (((eq a) ((g j) x2)) b)
% 233.14/233.48 Found ((eq_ref a) ((g j) x2)) as proof of (((eq a) ((g j) x2)) b)
% 233.14/233.48 Found ((eq_ref a) ((g j) x2)) as proof of (((eq a) ((g j) x2)) b)
% 233.14/233.48 Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% 233.14/233.48 Found (eq_ref0 b) as proof of (((eq a) b) ((f h) x2))
% 233.14/233.48 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x2))
% 233.14/233.48 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x2))
% 233.14/233.48 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x2))
% 233.14/233.48 Found eq_ref000:=(eq_ref00 P):((P (f h))->(P (f h)))
% 233.14/233.48 Found (eq_ref00 P) as proof of (P0 (f h))
% 233.14/233.48 Found ((eq_ref0 (f h)) P) as proof of (P0 (f h))
% 233.14/233.48 Found (((eq_ref (a->a)) (f h)) P) as proof of (P0 (f h))
% 233.14/233.48 Found (((eq_ref (a->a)) (f h)) P) as proof of (P0 (f h))
% 233.14/233.48 Found x000:=(x00 x2):(((eq a) ((f j) x2)) ((g j) x2))
% 233.14/233.48 Instantiate: b:=((g j) x2):a
% 233.14/233.48 Found x000 as proof of (((eq a) ((f j) x2)) b)
% 233.14/233.48 Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% 233.14/233.48 Found (eq_ref0 b) as proof of (((eq a) b) ((f h) x2))
% 233.14/233.48 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x2))
% 233.14/233.48 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x2))
% 233.14/233.48 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x2))
% 233.14/233.48 Found x000:=(x00 x2):(((eq a) ((f j) x2)) ((g j) x2))
% 233.14/233.48 Instantiate: b:=((g j) x2):a
% 233.14/233.48 Found x000 as proof of (((eq a) ((f j) x2)) b)
% 233.14/233.48 Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% 233.14/233.48 Found (eq_ref0 b) as proof of (((eq a) b) ((f h) x2))
% 233.14/233.48 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x2))
% 233.14/233.48 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x2))
% 233.14/233.48 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x2))
% 233.14/233.48 Found x0:(P (g j))
% 233.14/233.48 Instantiate: f0:=(g j):(a->a)
% 233.14/233.48 Found x0 as proof of (P0 f0)
% 233.14/233.48 Found eq_ref00:=(eq_ref0 (f0 x1)):(((eq a) (f0 x1)) (f0 x1))
% 233.14/233.48 Found (eq_ref0 (f0 x1)) as proof of (((eq a) (f0 x1)) ((f h) x1))
% 233.14/233.48 Found ((eq_ref a) (f0 x1)) as proof of (((eq a) (f0 x1)) ((f h) x1))
% 233.14/233.48 Found ((eq_ref a) (f0 x1)) as proof of (((eq a) (f0 x1)) ((f h) x1))
% 233.14/233.48 Found (fun (x1:a)=> ((eq_ref a) (f0 x1))) as proof of (((eq a) (f0 x1)) ((f h) x1))
% 233.14/233.48 Found (fun (x1:a)=> ((eq_ref a) (f0 x1))) as proof of (forall (x:a), (((eq a) (f0 x)) ((f h) x)))
% 233.14/233.48 Found x0:(P (g j))
% 233.14/233.48 Instantiate: f0:=(g j):(a->a)
% 233.14/233.48 Found x0 as proof of (P0 f0)
% 233.14/233.48 Found eq_ref00:=(eq_ref0 (f0 x1)):(((eq a) (f0 x1)) (f0 x1))
% 233.14/233.48 Found (eq_ref0 (f0 x1)) as proof of (((eq a) (f0 x1)) ((f h) x1))
% 233.14/233.48 Found ((eq_ref a) (f0 x1)) as proof of (((eq a) (f0 x1)) ((f h) x1))
% 233.14/233.48 Found ((eq_ref a) (f0 x1)) as proof of (((eq a) (f0 x1)) ((f h) x1))
% 233.14/233.48 Found (fun (x1:a)=> ((eq_ref a) (f0 x1))) as proof of (((eq a) (f0 x1)) ((f h) x1))
% 233.14/233.48 Found (fun (x1:a)=> ((eq_ref a) (f0 x1))) as proof of (forall (x:a), (((eq a) (f0 x)) ((f h) x)))
% 233.14/233.48 Found eq_ref000:=(eq_ref00 P):((P ((f j) x0))->(P ((f j) x0)))
% 233.14/233.48 Found (eq_ref00 P) as proof of (P0 ((f j) x0))
% 233.14/233.48 Found ((eq_ref0 ((f j) x0)) P) as proof of (P0 ((f j) x0))
% 233.14/233.48 Found (((eq_ref a) ((f j) x0)) P) as proof of (P0 ((f j) x0))
% 233.14/233.48 Found (((eq_ref a) ((f j) x0)) P) as proof of (P0 ((f j) x0))
% 233.14/233.48 Found eq_ref000:=(eq_ref00 P):((P ((f j) x0))->(P ((f j) x0)))
% 233.14/233.48 Found (eq_ref00 P) as proof of (P0 ((f j) x0))
% 233.14/233.48 Found ((eq_ref0 ((f j) x0)) P) as proof of (P0 ((f j) x0))
% 233.14/233.48 Found (((eq_ref a) ((f j) x0)) P) as proof of (P0 ((f j) x0))
% 233.14/233.48 Found (((eq_ref a) ((f j) x0)) P) as proof of (P0 ((f j) x0))
% 233.14/233.48 Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% 233.14/233.48 Found (eq_ref0 b) as proof of (((eq a) b) ((f h) x0))
% 233.14/233.48 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 233.14/233.48 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 233.14/233.48 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 233.14/233.48 Found eq_ref00:=(eq_ref0 ((g j) x0)):(((eq a) ((g j) x0)) ((g j) x0))
% 233.14/233.48 Found (eq_ref0 ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 245.24/245.56 Found ((eq_ref a) ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 245.24/245.56 Found ((eq_ref a) ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 245.24/245.56 Found ((eq_ref a) ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 245.24/245.56 Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% 245.24/245.56 Found (eq_ref0 b) as proof of (((eq a) b) ((f h) x0))
% 245.24/245.56 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 245.24/245.56 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 245.24/245.56 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 245.24/245.56 Found eq_ref00:=(eq_ref0 ((g j) x0)):(((eq a) ((g j) x0)) ((g j) x0))
% 245.24/245.56 Found (eq_ref0 ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 245.24/245.56 Found ((eq_ref a) ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 245.24/245.56 Found ((eq_ref a) ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 245.24/245.56 Found ((eq_ref a) ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 245.24/245.56 Found x100:=(x10 x0):(((eq a) ((f j) x0)) ((g j) x0))
% 245.24/245.56 Instantiate: b:=((g j) x0):a
% 245.24/245.56 Found x100 as proof of (((eq a) ((f j) x0)) b)
% 245.24/245.56 Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% 245.24/245.56 Found (eq_ref0 b) as proof of (((eq a) b) ((f h) x0))
% 245.24/245.56 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 245.24/245.56 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 245.24/245.56 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 245.24/245.56 Found x100:=(x10 x0):(((eq a) ((f j) x0)) ((g j) x0))
% 245.24/245.56 Instantiate: b:=((g j) x0):a
% 245.24/245.56 Found x100 as proof of (((eq a) ((f j) x0)) b)
% 245.24/245.56 Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% 245.24/245.56 Found (eq_ref0 b) as proof of (((eq a) b) ((f h) x0))
% 245.24/245.56 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 245.24/245.56 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 245.24/245.56 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 245.24/245.56 Found eq_ref000:=(eq_ref00 P):((P ((f j) x0))->(P ((f j) x0)))
% 245.24/245.56 Found (eq_ref00 P) as proof of (P0 ((f j) x0))
% 245.24/245.56 Found ((eq_ref0 ((f j) x0)) P) as proof of (P0 ((f j) x0))
% 245.24/245.56 Found (((eq_ref a) ((f j) x0)) P) as proof of (P0 ((f j) x0))
% 245.24/245.56 Found (((eq_ref a) ((f j) x0)) P) as proof of (P0 ((f j) x0))
% 245.24/245.56 Found eq_ref000:=(eq_ref00 P):((P ((f j) x0))->(P ((f j) x0)))
% 245.24/245.56 Found (eq_ref00 P) as proof of (P0 ((f j) x0))
% 245.24/245.56 Found ((eq_ref0 ((f j) x0)) P) as proof of (P0 ((f j) x0))
% 245.24/245.56 Found (((eq_ref a) ((f j) x0)) P) as proof of (P0 ((f j) x0))
% 245.24/245.56 Found (((eq_ref a) ((f j) x0)) P) as proof of (P0 ((f j) x0))
% 245.24/245.56 Found x100:=(x10 x0):(((eq a) ((f j) x0)) ((g j) x0))
% 245.24/245.56 Instantiate: b:=((g j) x0):a
% 245.24/245.56 Found x100 as proof of (((eq a) ((f j) x0)) b)
% 245.24/245.56 Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% 245.24/245.56 Found (eq_ref0 b) as proof of (((eq a) b) ((f h) x0))
% 245.24/245.56 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 245.24/245.56 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 245.24/245.56 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 245.24/245.56 Found x100:=(x10 x0):(((eq a) ((f j) x0)) ((g j) x0))
% 245.24/245.56 Instantiate: b:=((g j) x0):a
% 245.24/245.56 Found x100 as proof of (((eq a) ((f j) x0)) b)
% 245.24/245.56 Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% 245.24/245.56 Found (eq_ref0 b) as proof of (((eq a) b) ((f h) x0))
% 245.24/245.56 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 245.24/245.56 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 245.24/245.56 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 245.24/245.56 Found x100:=(x10 x0):(((eq a) ((f j) x0)) ((g j) x0))
% 245.24/245.56 Instantiate: b:=((g j) x0):a
% 245.24/245.56 Found x100 as proof of (((eq a) ((f j) x0)) b)
% 245.24/245.56 Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% 245.24/245.56 Found (eq_ref0 b) as proof of (((eq a) b) ((f h) x0))
% 245.24/245.56 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 245.24/245.56 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 245.24/245.56 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 245.24/245.56 Found x100:=(x10 x0):(((eq a) ((f j) x0)) ((g j) x0))
% 245.24/245.56 Instantiate: b:=((g j) x0):a
% 245.24/245.56 Found x100 as proof of (((eq a) ((f j) x0)) b)
% 245.24/245.56 Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% 245.24/245.56 Found (eq_ref0 b) as proof of (((eq a) b) ((f h) x0))
% 245.24/245.56 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 245.24/245.56 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 245.24/245.56 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 245.24/245.56 Found eq_ref000:=(eq_ref00 P):((P ((f h) x0))->(P ((f h) x0)))
% 245.24/245.56 Found (eq_ref00 P) as proof of (P0 (f h))
% 245.24/245.56 Found ((eq_ref0 ((f h) x0)) P) as proof of (P0 (f h))
% 245.24/245.56 Found (((eq_ref a) ((f h) x0)) P) as proof of (P0 (f h))
% 245.24/245.56 Found (((eq_ref a) ((f h) x0)) P) as proof of (P0 (f h))
% 260.63/260.99 Found eq_ref000:=(eq_ref00 P):((P ((f h) x0))->(P ((f h) x0)))
% 260.63/260.99 Found (eq_ref00 P) as proof of (P0 (f h))
% 260.63/260.99 Found ((eq_ref0 ((f h) x0)) P) as proof of (P0 (f h))
% 260.63/260.99 Found (((eq_ref a) ((f h) x0)) P) as proof of (P0 (f h))
% 260.63/260.99 Found (((eq_ref a) ((f h) x0)) P) as proof of (P0 (f h))
% 260.63/260.99 Found eq_ref000:=(eq_ref00 P):((P ((f j) x2))->(P ((f j) x2)))
% 260.63/260.99 Found (eq_ref00 P) as proof of (P0 ((f j) x2))
% 260.63/260.99 Found ((eq_ref0 ((f j) x2)) P) as proof of (P0 ((f j) x2))
% 260.63/260.99 Found (((eq_ref a) ((f j) x2)) P) as proof of (P0 ((f j) x2))
% 260.63/260.99 Found (((eq_ref a) ((f j) x2)) P) as proof of (P0 ((f j) x2))
% 260.63/260.99 Found eq_ref000:=(eq_ref00 P):((P ((f j) x2))->(P ((f j) x2)))
% 260.63/260.99 Found (eq_ref00 P) as proof of (P0 ((f j) x2))
% 260.63/260.99 Found ((eq_ref0 ((f j) x2)) P) as proof of (P0 ((f j) x2))
% 260.63/260.99 Found (((eq_ref a) ((f j) x2)) P) as proof of (P0 ((f j) x2))
% 260.63/260.99 Found (((eq_ref a) ((f j) x2)) P) as proof of (P0 ((f j) x2))
% 260.63/260.99 Found eq_ref000:=(eq_ref00 P):((P (f h))->(P (f h)))
% 260.63/260.99 Found (eq_ref00 P) as proof of (P0 (f h))
% 260.63/260.99 Found ((eq_ref0 (f h)) P) as proof of (P0 (f h))
% 260.63/260.99 Found (((eq_ref (a->a)) (f h)) P) as proof of (P0 (f h))
% 260.63/260.99 Found (((eq_ref (a->a)) (f h)) P) as proof of (P0 (f h))
% 260.63/260.99 Found eq_ref000:=(eq_ref00 P):((P (f h))->(P (f h)))
% 260.63/260.99 Found (eq_ref00 P) as proof of (P0 (f h))
% 260.63/260.99 Found ((eq_ref0 (f h)) P) as proof of (P0 (f h))
% 260.63/260.99 Found (((eq_ref (a->a)) (f h)) P) as proof of (P0 (f h))
% 260.63/260.99 Found (((eq_ref (a->a)) (f h)) P) as proof of (P0 (f h))
% 260.63/260.99 Found eq_ref00:=(eq_ref0 b):(((eq (a->a)) b) b)
% 260.63/260.99 Found (eq_ref0 b) as proof of (((eq (a->a)) b) (f h))
% 260.63/260.99 Found ((eq_ref (a->a)) b) as proof of (((eq (a->a)) b) (f h))
% 260.63/260.99 Found ((eq_ref (a->a)) b) as proof of (((eq (a->a)) b) (f h))
% 260.63/260.99 Found ((eq_ref (a->a)) b) as proof of (((eq (a->a)) b) (f h))
% 260.63/260.99 Found eq_ref00:=(eq_ref0 (g j)):(((eq (a->a)) (g j)) (g j))
% 260.63/260.99 Found (eq_ref0 (g j)) as proof of (((eq (a->a)) (g j)) b)
% 260.63/260.99 Found ((eq_ref (a->a)) (g j)) as proof of (((eq (a->a)) (g j)) b)
% 260.63/260.99 Found ((eq_ref (a->a)) (g j)) as proof of (((eq (a->a)) (g j)) b)
% 260.63/260.99 Found ((eq_ref (a->a)) (g j)) as proof of (((eq (a->a)) (g j)) b)
% 260.63/260.99 Found eq_ref000:=(eq_ref00 P):((P (g j))->(P (g j)))
% 260.63/260.99 Found (eq_ref00 P) as proof of (P0 (g j))
% 260.63/260.99 Found ((eq_ref0 (g j)) P) as proof of (P0 (g j))
% 260.63/260.99 Found (((eq_ref (a->a)) (g j)) P) as proof of (P0 (g j))
% 260.63/260.99 Found (((eq_ref (a->a)) (g j)) P) as proof of (P0 (g j))
% 260.63/260.99 Found eq_ref00:=(eq_ref0 b):(((eq (a->a)) b) b)
% 260.63/260.99 Found (eq_ref0 b) as proof of (((eq (a->a)) b) (f h))
% 260.63/260.99 Found ((eq_ref (a->a)) b) as proof of (((eq (a->a)) b) (f h))
% 260.63/260.99 Found ((eq_ref (a->a)) b) as proof of (((eq (a->a)) b) (f h))
% 260.63/260.99 Found ((eq_ref (a->a)) b) as proof of (((eq (a->a)) b) (f h))
% 260.63/260.99 Found eq_ref00:=(eq_ref0 (g j)):(((eq (a->a)) (g j)) (g j))
% 260.63/260.99 Found (eq_ref0 (g j)) as proof of (((eq (a->a)) (g j)) b)
% 260.63/260.99 Found ((eq_ref (a->a)) (g j)) as proof of (((eq (a->a)) (g j)) b)
% 260.63/260.99 Found ((eq_ref (a->a)) (g j)) as proof of (((eq (a->a)) (g j)) b)
% 260.63/260.99 Found ((eq_ref (a->a)) (g j)) as proof of (((eq (a->a)) (g j)) b)
% 260.63/260.99 Found eq_ref00:=(eq_ref0 b):(((eq (a->a)) b) b)
% 260.63/260.99 Found (eq_ref0 b) as proof of (((eq (a->a)) b) (f h))
% 260.63/260.99 Found ((eq_ref (a->a)) b) as proof of (((eq (a->a)) b) (f h))
% 260.63/260.99 Found ((eq_ref (a->a)) b) as proof of (((eq (a->a)) b) (f h))
% 260.63/260.99 Found ((eq_ref (a->a)) b) as proof of (((eq (a->a)) b) (f h))
% 260.63/260.99 Found eta_expansion000:=(eta_expansion00 (g j)):(((eq (a->a)) (g j)) (fun (x:a)=> ((g j) x)))
% 260.63/260.99 Found (eta_expansion00 (g j)) as proof of (((eq (a->a)) (g j)) b)
% 260.63/260.99 Found ((eta_expansion0 a) (g j)) as proof of (((eq (a->a)) (g j)) b)
% 260.63/260.99 Found (((eta_expansion a) a) (g j)) as proof of (((eq (a->a)) (g j)) b)
% 260.63/260.99 Found (((eta_expansion a) a) (g j)) as proof of (((eq (a->a)) (g j)) b)
% 260.63/260.99 Found (((eta_expansion a) a) (g j)) as proof of (((eq (a->a)) (g j)) b)
% 260.63/260.99 Found eq_ref00:=(eq_ref0 b):(((eq (a->a)) b) b)
% 260.63/260.99 Found (eq_ref0 b) as proof of (((eq (a->a)) b) (f h))
% 260.63/260.99 Found ((eq_ref (a->a)) b) as proof of (((eq (a->a)) b) (f h))
% 260.63/260.99 Found ((eq_ref (a->a)) b) as proof of (((eq (a->a)) b) (f h))
% 260.63/260.99 Found ((eq_ref (a->a)) b) as proof of (((eq (a->a)) b) (f h))
% 260.63/260.99 Found eta_expansion000:=(eta_expansion00 (g j)):(((eq (a->a)) (g j)) (fun (x:a)=> ((g j) x)))
% 260.63/260.99 Found (eta_expansion00 (g j)) as proof of (((eq (a->a)) (g j)) b)
% 260.63/260.99 Found ((eta_expansion0 a) (g j)) as proof of (((eq (a->a)) (g j)) b)
% 260.63/260.99 Found (((eta_expansion a) a) (g j)) as proof of (((eq (a->a)) (g j)) b)
% 272.12/272.49 Found (((eta_expansion a) a) (g j)) as proof of (((eq (a->a)) (g j)) b)
% 272.12/272.49 Found (((eta_expansion a) a) (g j)) as proof of (((eq (a->a)) (g j)) b)
% 272.12/272.49 Found eq_ref00:=(eq_ref0 b0):(((eq (a->a)) b0) b0)
% 272.12/272.49 Found (eq_ref0 b0) as proof of (((eq (a->a)) b0) (g j))
% 272.12/272.49 Found ((eq_ref (a->a)) b0) as proof of (((eq (a->a)) b0) (g j))
% 272.12/272.49 Found ((eq_ref (a->a)) b0) as proof of (((eq (a->a)) b0) (g j))
% 272.12/272.49 Found ((eq_ref (a->a)) b0) as proof of (((eq (a->a)) b0) (g j))
% 272.12/272.49 Found eq_ref00:=(eq_ref0 (f h)):(((eq (a->a)) (f h)) (f h))
% 272.12/272.49 Found (eq_ref0 (f h)) as proof of (((eq (a->a)) (f h)) b0)
% 272.12/272.49 Found ((eq_ref (a->a)) (f h)) as proof of (((eq (a->a)) (f h)) b0)
% 272.12/272.49 Found ((eq_ref (a->a)) (f h)) as proof of (((eq (a->a)) (f h)) b0)
% 272.12/272.49 Found ((eq_ref (a->a)) (f h)) as proof of (((eq (a->a)) (f h)) b0)
% 272.12/272.49 Found eq_ref00:=(eq_ref0 b):(((eq (a->a)) b) b)
% 272.12/272.49 Found (eq_ref0 b) as proof of (P b)
% 272.12/272.49 Found ((eq_ref (a->a)) b) as proof of (P b)
% 272.12/272.49 Found ((eq_ref (a->a)) b) as proof of (P b)
% 272.12/272.49 Found ((eq_ref (a->a)) b) as proof of (P b)
% 272.12/272.49 Found eq_ref00:=(eq_ref0 (g j)):(((eq (a->a)) (g j)) (g j))
% 272.12/272.49 Found (eq_ref0 (g j)) as proof of (((eq (a->a)) (g j)) b)
% 272.12/272.49 Found ((eq_ref (a->a)) (g j)) as proof of (((eq (a->a)) (g j)) b)
% 272.12/272.49 Found ((eq_ref (a->a)) (g j)) as proof of (((eq (a->a)) (g j)) b)
% 272.12/272.49 Found ((eq_ref (a->a)) (g j)) as proof of (((eq (a->a)) (g j)) b)
% 272.12/272.49 Found eq_ref000:=(eq_ref00 P):((P ((f j) x0))->(P ((f j) x0)))
% 272.12/272.49 Found (eq_ref00 P) as proof of (P0 ((f j) x0))
% 272.12/272.49 Found ((eq_ref0 ((f j) x0)) P) as proof of (P0 ((f j) x0))
% 272.12/272.49 Found (((eq_ref a) ((f j) x0)) P) as proof of (P0 ((f j) x0))
% 272.12/272.49 Found (((eq_ref a) ((f j) x0)) P) as proof of (P0 ((f j) x0))
% 272.12/272.49 Found eq_ref000:=(eq_ref00 P):((P ((f j) x0))->(P ((f j) x0)))
% 272.12/272.49 Found (eq_ref00 P) as proof of (P0 ((f j) x0))
% 272.12/272.49 Found ((eq_ref0 ((f j) x0)) P) as proof of (P0 ((f j) x0))
% 272.12/272.49 Found (((eq_ref a) ((f j) x0)) P) as proof of (P0 ((f j) x0))
% 272.12/272.49 Found (((eq_ref a) ((f j) x0)) P) as proof of (P0 ((f j) x0))
% 272.12/272.49 Found x1:(P ((f h) x0))
% 272.12/272.49 Instantiate: b:=((f h) x0):a
% 272.12/272.49 Found x1 as proof of (P0 b)
% 272.12/272.49 Found eq_ref00:=(eq_ref0 ((g j) x0)):(((eq a) ((g j) x0)) ((g j) x0))
% 272.12/272.49 Found (eq_ref0 ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 272.12/272.49 Found ((eq_ref a) ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 272.12/272.49 Found ((eq_ref a) ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 272.12/272.49 Found ((eq_ref a) ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 272.12/272.49 Found x1:(P ((f h) x0))
% 272.12/272.49 Instantiate: b:=((f h) x0):a
% 272.12/272.49 Found x1 as proof of (P0 b)
% 272.12/272.49 Found eq_ref00:=(eq_ref0 ((g j) x0)):(((eq a) ((g j) x0)) ((g j) x0))
% 272.12/272.49 Found (eq_ref0 ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 272.12/272.49 Found ((eq_ref a) ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 272.12/272.49 Found ((eq_ref a) ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 272.12/272.49 Found ((eq_ref a) ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 272.12/272.49 Found x100:=(x10 x0):(((eq a) ((f j) x0)) ((g j) x0))
% 272.12/272.49 Instantiate: b:=((g j) x0):a
% 272.12/272.49 Found x100 as proof of (((eq a) ((f j) x0)) b)
% 272.12/272.49 Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% 272.12/272.49 Found (eq_ref0 b) as proof of (((eq a) b) ((f h) x0))
% 272.12/272.49 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 272.12/272.49 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 272.12/272.49 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 272.12/272.49 Found x100:=(x10 x0):(((eq a) ((f j) x0)) ((g j) x0))
% 272.12/272.49 Instantiate: b:=((g j) x0):a
% 272.12/272.49 Found x100 as proof of (((eq a) ((f j) x0)) b)
% 272.12/272.49 Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% 272.12/272.49 Found (eq_ref0 b) as proof of (((eq a) b) ((f h) x0))
% 272.12/272.49 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 272.12/272.49 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 272.12/272.49 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 272.12/272.49 Found eq_ref000:=(eq_ref00 P):((P ((f j) x0))->(P ((f j) x0)))
% 272.12/272.49 Found (eq_ref00 P) as proof of (P0 ((f j) x0))
% 272.12/272.49 Found ((eq_ref0 ((f j) x0)) P) as proof of (P0 ((f j) x0))
% 272.12/272.49 Found (((eq_ref a) ((f j) x0)) P) as proof of (P0 ((f j) x0))
% 272.12/272.49 Found (((eq_ref a) ((f j) x0)) P) as proof of (P0 ((f j) x0))
% 272.12/272.49 Found eq_ref00:=(eq_ref0 ((g j) x0)):(((eq a) ((g j) x0)) ((g j) x0))
% 272.12/272.49 Found (eq_ref0 ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 272.12/272.49 Found ((eq_ref a) ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 272.12/272.49 Found ((eq_ref a) ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 277.62/277.95 Found ((eq_ref a) ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 277.62/277.95 Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% 277.62/277.95 Found (eq_ref0 b) as proof of (((eq a) b) ((f h) x0))
% 277.62/277.95 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 277.62/277.95 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 277.62/277.95 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 277.62/277.95 Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% 277.62/277.95 Found (eq_ref0 b) as proof of (((eq a) b) ((f h) x0))
% 277.62/277.95 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 277.62/277.95 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 277.62/277.95 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 277.62/277.95 Found eq_ref00:=(eq_ref0 ((g j) x0)):(((eq a) ((g j) x0)) ((g j) x0))
% 277.62/277.95 Found (eq_ref0 ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 277.62/277.95 Found ((eq_ref a) ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 277.62/277.95 Found ((eq_ref a) ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 277.62/277.95 Found ((eq_ref a) ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 277.62/277.95 Found eq_ref000:=(eq_ref00 P):((P ((f j) x0))->(P ((f j) x0)))
% 277.62/277.95 Found (eq_ref00 P) as proof of (P0 ((f j) x0))
% 277.62/277.95 Found ((eq_ref0 ((f j) x0)) P) as proof of (P0 ((f j) x0))
% 277.62/277.95 Found (((eq_ref a) ((f j) x0)) P) as proof of (P0 ((f j) x0))
% 277.62/277.95 Found (((eq_ref a) ((f j) x0)) P) as proof of (P0 ((f j) x0))
% 277.62/277.95 Found x2:(P (g j))
% 277.62/277.95 Instantiate: b:=(g j):(a->a)
% 277.62/277.95 Found x2 as proof of (P0 b)
% 277.62/277.95 Found eta_expansion_dep000:=(eta_expansion_dep00 (f h)):(((eq (a->a)) (f h)) (fun (x:a)=> ((f h) x)))
% 277.62/277.95 Found (eta_expansion_dep00 (f h)) as proof of (((eq (a->a)) (f h)) b)
% 277.62/277.95 Found ((eta_expansion_dep0 (fun (x4:a)=> a)) (f h)) as proof of (((eq (a->a)) (f h)) b)
% 277.62/277.95 Found (((eta_expansion_dep a) (fun (x4:a)=> a)) (f h)) as proof of (((eq (a->a)) (f h)) b)
% 277.62/277.95 Found (((eta_expansion_dep a) (fun (x4:a)=> a)) (f h)) as proof of (((eq (a->a)) (f h)) b)
% 277.62/277.95 Found (((eta_expansion_dep a) (fun (x4:a)=> a)) (f h)) as proof of (((eq (a->a)) (f h)) b)
% 277.62/277.95 Found eq_ref00:=(eq_ref0 ((g j) x0)):(((eq a) ((g j) x0)) ((g j) x0))
% 277.62/277.95 Found (eq_ref0 ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 277.62/277.95 Found ((eq_ref a) ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 277.62/277.95 Found ((eq_ref a) ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 277.62/277.95 Found ((eq_ref a) ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 277.62/277.95 Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% 277.62/277.95 Found (eq_ref0 b) as proof of (((eq a) b) ((f h) x0))
% 277.62/277.95 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 277.62/277.95 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 277.62/277.95 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 277.62/277.95 Found x100:=(x10 x0):(((eq a) ((f j) x0)) ((g j) x0))
% 277.62/277.95 Instantiate: b:=((g j) x0):a
% 277.62/277.95 Found x100 as proof of (((eq a) ((f j) x0)) b)
% 277.62/277.95 Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% 277.62/277.95 Found (eq_ref0 b) as proof of (((eq a) b) ((f h) x0))
% 277.62/277.95 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 277.62/277.95 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 277.62/277.95 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 277.62/277.95 Found eq_ref00:=(eq_ref0 ((g j) x0)):(((eq a) ((g j) x0)) ((g j) x0))
% 277.62/277.95 Found (eq_ref0 ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 277.62/277.95 Found ((eq_ref a) ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 277.62/277.95 Found ((eq_ref a) ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 277.62/277.95 Found ((eq_ref a) ((g j) x0)) as proof of (((eq a) ((g j) x0)) b)
% 277.62/277.95 Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% 277.62/277.95 Found (eq_ref0 b) as proof of (((eq a) b) ((f h) x0))
% 277.62/277.95 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 277.62/277.95 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 277.62/277.95 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 277.62/277.95 Found x100:=(x10 x0):(((eq a) ((f j) x0)) ((g j) x0))
% 277.62/277.95 Instantiate: b:=((g j) x0):a
% 277.62/277.95 Found x100 as proof of (((eq a) ((f j) x0)) b)
% 277.62/277.95 Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% 277.62/277.95 Found (eq_ref0 b) as proof of (((eq a) b) ((f h) x0))
% 277.62/277.95 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 277.62/277.95 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 277.62/277.95 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 277.62/277.95 Found x2:(P (f h))
% 277.62/277.95 Instantiate: f0:=(f h):(a->a)
% 277.62/277.95 Found x2 as proof of (P0 f0)
% 277.62/277.95 Found eq_ref00:=(eq_ref0 (f0 x3)):(((eq a) (f0 x3)) (f0 x3))
% 277.62/277.95 Found (eq_ref0 (f0 x3)) as proof of (((eq a) (f0 x3)) ((g j) x3))
% 277.62/277.95 Found ((eq_ref a) (f0 x3)) as proof of (((eq a) (f0 x3)) ((g j) x3))
% 291.98/292.32 Found ((eq_ref a) (f0 x3)) as proof of (((eq a) (f0 x3)) ((g j) x3))
% 291.98/292.32 Found (fun (x3:a)=> ((eq_ref a) (f0 x3))) as proof of (((eq a) (f0 x3)) ((g j) x3))
% 291.98/292.32 Found (fun (x3:a)=> ((eq_ref a) (f0 x3))) as proof of (forall (x:a), (((eq a) (f0 x)) ((g j) x)))
% 291.98/292.32 Found x2:(P (f h))
% 291.98/292.32 Instantiate: f0:=(f h):(a->a)
% 291.98/292.32 Found x2 as proof of (P0 f0)
% 291.98/292.32 Found eq_ref00:=(eq_ref0 (f0 x3)):(((eq a) (f0 x3)) (f0 x3))
% 291.98/292.32 Found (eq_ref0 (f0 x3)) as proof of (((eq a) (f0 x3)) ((g j) x3))
% 291.98/292.32 Found ((eq_ref a) (f0 x3)) as proof of (((eq a) (f0 x3)) ((g j) x3))
% 291.98/292.32 Found ((eq_ref a) (f0 x3)) as proof of (((eq a) (f0 x3)) ((g j) x3))
% 291.98/292.32 Found (fun (x3:a)=> ((eq_ref a) (f0 x3))) as proof of (((eq a) (f0 x3)) ((g j) x3))
% 291.98/292.32 Found (fun (x3:a)=> ((eq_ref a) (f0 x3))) as proof of (forall (x:a), (((eq a) (f0 x)) ((g j) x)))
% 291.98/292.32 Found x100:=(x10 x0):(((eq a) ((f j) x0)) ((g j) x0))
% 291.98/292.32 Instantiate: b:=((g j) x0):a
% 291.98/292.32 Found x100 as proof of (((eq a) ((f j) x0)) b)
% 291.98/292.32 Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% 291.98/292.32 Found (eq_ref0 b) as proof of (((eq a) b) ((f h) x0))
% 292.00/292.32 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 292.00/292.32 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 292.00/292.32 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 292.00/292.32 Found x100:=(x10 x0):(((eq a) ((f j) x0)) ((g j) x0))
% 292.00/292.32 Instantiate: b:=((g j) x0):a
% 292.00/292.32 Found x100 as proof of (((eq a) ((f j) x0)) b)
% 292.00/292.32 Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% 292.00/292.32 Found (eq_ref0 b) as proof of (((eq a) b) ((f h) x0))
% 292.00/292.32 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 292.00/292.32 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 292.00/292.32 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 292.00/292.32 Found x100:=(x10 x0):(((eq a) ((f j) x0)) ((g j) x0))
% 292.00/292.32 Instantiate: b:=((g j) x0):a
% 292.00/292.32 Found x100 as proof of (((eq a) ((f j) x0)) b)
% 292.00/292.32 Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% 292.00/292.32 Found (eq_ref0 b) as proof of (((eq a) b) ((f h) x0))
% 292.00/292.32 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 292.00/292.32 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 292.00/292.32 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 292.00/292.32 Found x100:=(x10 x0):(((eq a) ((f j) x0)) ((g j) x0))
% 292.00/292.32 Instantiate: b:=((g j) x0):a
% 292.00/292.32 Found x100 as proof of (((eq a) ((f j) x0)) b)
% 292.00/292.32 Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% 292.00/292.32 Found (eq_ref0 b) as proof of (((eq a) b) ((f h) x0))
% 292.00/292.32 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 292.00/292.32 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 292.00/292.32 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x0))
% 292.00/292.32 Found eq_ref000:=(eq_ref00 P):((P ((f j) x2))->(P ((f j) x2)))
% 292.00/292.32 Found (eq_ref00 P) as proof of (P0 ((f j) x2))
% 292.00/292.32 Found ((eq_ref0 ((f j) x2)) P) as proof of (P0 ((f j) x2))
% 292.00/292.32 Found (((eq_ref a) ((f j) x2)) P) as proof of (P0 ((f j) x2))
% 292.00/292.32 Found (((eq_ref a) ((f j) x2)) P) as proof of (P0 ((f j) x2))
% 292.00/292.32 Found eq_ref000:=(eq_ref00 P):((P ((f j) x2))->(P ((f j) x2)))
% 292.00/292.32 Found (eq_ref00 P) as proof of (P0 ((f j) x2))
% 292.00/292.32 Found ((eq_ref0 ((f j) x2)) P) as proof of (P0 ((f j) x2))
% 292.00/292.32 Found (((eq_ref a) ((f j) x2)) P) as proof of (P0 ((f j) x2))
% 292.00/292.32 Found (((eq_ref a) ((f j) x2)) P) as proof of (P0 ((f j) x2))
% 292.00/292.32 Found x0:(P (g j))
% 292.00/292.32 Instantiate: b:=(g j):(a->a)
% 292.00/292.32 Found x0 as proof of (P0 b)
% 292.00/292.32 Found eta_expansion_dep000:=(eta_expansion_dep00 (f h)):(((eq (a->a)) (f h)) (fun (x:a)=> ((f h) x)))
% 292.00/292.32 Found (eta_expansion_dep00 (f h)) as proof of (((eq (a->a)) (f h)) b)
% 292.00/292.32 Found ((eta_expansion_dep0 (fun (x4:a)=> a)) (f h)) as proof of (((eq (a->a)) (f h)) b)
% 292.00/292.32 Found (((eta_expansion_dep a) (fun (x4:a)=> a)) (f h)) as proof of (((eq (a->a)) (f h)) b)
% 292.00/292.32 Found (((eta_expansion_dep a) (fun (x4:a)=> a)) (f h)) as proof of (((eq (a->a)) (f h)) b)
% 292.00/292.32 Found (((eta_expansion_dep a) (fun (x4:a)=> a)) (f h)) as proof of (((eq (a->a)) (f h)) b)
% 292.00/292.32 Found x000:=(x00 x2):(((eq a) ((f j) x2)) ((g j) x2))
% 292.00/292.32 Instantiate: b:=((g j) x2):a
% 292.00/292.32 Found x000 as proof of (((eq a) ((f j) x2)) b)
% 292.00/292.32 Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% 292.00/292.32 Found (eq_ref0 b) as proof of (((eq a) b) ((f h) x2))
% 292.00/292.32 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x2))
% 292.00/292.32 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x2))
% 292.00/292.32 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x2))
% 292.00/292.32 Found x000:=(x00 x2):(((eq a) ((f j) x2)) ((g j) x2))
% 292.00/292.32 Instantiate: b:=((g j) x2):a
% 292.00/292.32 Found x000 as proof of (((eq a) ((f j) x2)) b)
% 297.40/297.75 Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% 297.40/297.75 Found (eq_ref0 b) as proof of (((eq a) b) ((f h) x2))
% 297.40/297.75 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x2))
% 297.40/297.75 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x2))
% 297.40/297.75 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x2))
% 297.40/297.75 Found x000:=(x00 x2):(((eq a) ((f j) x2)) ((g j) x2))
% 297.40/297.75 Instantiate: b:=((g j) x2):a
% 297.40/297.75 Found x000 as proof of (((eq a) ((f j) x2)) b)
% 297.40/297.75 Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% 297.40/297.75 Found (eq_ref0 b) as proof of (((eq a) b) ((f h) x2))
% 297.40/297.75 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x2))
% 297.40/297.75 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x2))
% 297.40/297.75 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x2))
% 297.40/297.75 Found x000:=(x00 x2):(((eq a) ((f j) x2)) ((g j) x2))
% 297.40/297.75 Instantiate: b:=((g j) x2):a
% 297.40/297.75 Found x000 as proof of (((eq a) ((f j) x2)) b)
% 297.40/297.75 Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% 297.40/297.75 Found (eq_ref0 b) as proof of (((eq a) b) ((f h) x2))
% 297.40/297.75 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x2))
% 297.40/297.75 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x2))
% 297.40/297.75 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x2))
% 297.40/297.75 Found x0:(P (f h))
% 297.40/297.75 Instantiate: f0:=(f h):(a->a)
% 297.40/297.75 Found x0 as proof of (P0 f0)
% 297.40/297.75 Found eq_ref00:=(eq_ref0 (f0 x3)):(((eq a) (f0 x3)) (f0 x3))
% 297.40/297.75 Found (eq_ref0 (f0 x3)) as proof of (((eq a) (f0 x3)) ((g j) x3))
% 297.40/297.75 Found ((eq_ref a) (f0 x3)) as proof of (((eq a) (f0 x3)) ((g j) x3))
% 297.40/297.75 Found ((eq_ref a) (f0 x3)) as proof of (((eq a) (f0 x3)) ((g j) x3))
% 297.40/297.75 Found (fun (x3:a)=> ((eq_ref a) (f0 x3))) as proof of (((eq a) (f0 x3)) ((g j) x3))
% 297.40/297.75 Found (fun (x3:a)=> ((eq_ref a) (f0 x3))) as proof of (forall (x:a), (((eq a) (f0 x)) ((g j) x)))
% 297.40/297.75 Found x0:(P (f h))
% 297.40/297.75 Instantiate: f0:=(f h):(a->a)
% 297.40/297.75 Found x0 as proof of (P0 f0)
% 297.40/297.75 Found eq_ref00:=(eq_ref0 (f0 x3)):(((eq a) (f0 x3)) (f0 x3))
% 297.40/297.75 Found (eq_ref0 (f0 x3)) as proof of (((eq a) (f0 x3)) ((g j) x3))
% 297.40/297.75 Found ((eq_ref a) (f0 x3)) as proof of (((eq a) (f0 x3)) ((g j) x3))
% 297.40/297.75 Found ((eq_ref a) (f0 x3)) as proof of (((eq a) (f0 x3)) ((g j) x3))
% 297.40/297.75 Found (fun (x3:a)=> ((eq_ref a) (f0 x3))) as proof of (((eq a) (f0 x3)) ((g j) x3))
% 297.40/297.75 Found (fun (x3:a)=> ((eq_ref a) (f0 x3))) as proof of (forall (x:a), (((eq a) (f0 x)) ((g j) x)))
% 297.40/297.75 Found x000:=(x00 x2):(((eq a) ((f j) x2)) ((g j) x2))
% 297.40/297.75 Instantiate: b:=((g j) x2):a
% 297.40/297.75 Found x000 as proof of (((eq a) ((f j) x2)) b)
% 297.40/297.75 Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% 297.40/297.75 Found (eq_ref0 b) as proof of (((eq a) b) ((f h) x2))
% 297.40/297.75 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x2))
% 297.40/297.75 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x2))
% 297.40/297.75 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x2))
% 297.40/297.75 Found x000:=(x00 x2):(((eq a) ((f j) x2)) ((g j) x2))
% 297.40/297.75 Instantiate: b:=((g j) x2):a
% 297.40/297.75 Found x000 as proof of (((eq a) ((f j) x2)) b)
% 297.40/297.75 Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% 297.40/297.75 Found (eq_ref0 b) as proof of (((eq a) b) ((f h) x2))
% 297.40/297.75 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x2))
% 297.40/297.75 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x2))
% 297.40/297.75 Found ((eq_ref a) b) as proof of (((eq a) b) ((f h) x2))
% 297.40/297.75 Found eq_ref00:=(eq_ref0 ((f h) x0)):(((eq a) ((f h) x0)) ((f h) x0))
% 297.40/297.75 Found (eq_ref0 ((f h) x0)) as proof of (((eq a) ((f h) x0)) b)
% 297.40/297.75 Found ((eq_ref a) ((f h) x0)) as proof of (((eq a) ((f h) x0)) b)
% 297.40/297.75 Found ((eq_ref a) ((f h) x0)) as proof of (((eq a) ((f h) x0)) b)
% 297.40/297.75 Found ((eq_ref a) ((f h) x0)) as proof of (((eq a) ((f h) x0)) b)
% 297.40/297.75 Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% 297.40/297.75 Found (eq_ref0 b) as proof of (((eq a) b) ((g j) x0))
% 297.40/297.75 Found ((eq_ref a) b) as proof of (((eq a) b) ((g j) x0))
% 297.40/297.75 Found ((eq_ref a) b) as proof of (((eq a) b) ((g j) x0))
% 297.40/297.75 Found ((eq_ref a) b) as proof of (((eq a) b) ((g j) x0))
% 297.40/297.75 Found eq_ref00:=(eq_ref0 ((f h) x0)):(((eq a) ((f h) x0)) ((f h) x0))
% 297.40/297.75 Found (eq_ref0 ((f h) x0)) as proof of (((eq a) ((f h) x0)) b)
% 297.40/297.75 Found ((eq_ref a) ((f h) x0)) as proof of (((eq a) ((f h) x0)) b)
% 297.40/297.75 Found ((eq_ref a) ((f h) x0)) as proof of (((eq a) ((f h) x0)) b)
% 297.40/297.75 Found ((eq_ref a) ((f h) x0)) as proof of (((eq a) ((f h) x0)) b)
% 297.40/297.75 Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% 297.40/297.75 Found (eq_ref0 b) as proof of (((eq a) b) ((g j) x0))
% 297.40/297.75 Found ((eq_ref a) b) as proof of (((eq a) b) ((g j) x0))
% 297.40/297.75 Found ((eq_ref a) b) as proof of (((eq a) b) ((g j) x0))
% 297.40/297.75 Found ((eq
%------------------------------------------------------------------------------