TSTP Solution File: SYO271^5 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SYO271^5 : TPTP v7.5.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 00:51:03 EDT 2022
% Result : Timeout 293.61s 294.01s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.11 % Problem : SYO271^5 : TPTP v7.5.0. Released v4.0.0.
% 0.04/0.12 % Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n001.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 00:14:42 EST 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.12/0.34 Python 2.7.5
% 13.74/13.91 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox2/benchmark/', '/export/starexec/sandbox2/benchmark/']
% 13.74/13.91 FOF formula (<kernel.Constant object at 0x1a33998>, <kernel.Type object at 0x2b50cc4351b8>) of role type named b_type
% 13.74/13.91 Using role type
% 13.74/13.91 Declaring b:Type
% 13.74/13.91 FOF formula (<kernel.Constant object at 0x1793878>, <kernel.Type object at 0x2b50cc4351b8>) of role type named a_type
% 13.74/13.91 Using role type
% 13.74/13.91 Declaring a:Type
% 13.74/13.91 FOF formula (<kernel.Constant object at 0x178acf8>, <kernel.DependentProduct object at 0x2b50c493c710>) of role type named cJ
% 13.74/13.91 Using role type
% 13.74/13.91 Declaring cJ:((b->Prop)->b)
% 13.74/13.91 FOF formula ((forall (P:(b->Prop)), (((ex b) (fun (Xx:b)=> (P Xx)))->(P (cJ P))))->(forall (Xf:(b->a)) (Xg:(b->a)), ((((eq a) (Xf (cJ (fun (Xx:b)=> (not (((eq a) (Xf Xx)) (Xg Xx))))))) (Xg (cJ (fun (Xx:b)=> (not (((eq a) (Xf Xx)) (Xg Xx)))))))->(((eq (b->a)) Xf) Xg)))) of role conjecture named cX5500
% 13.74/13.91 Conjecture to prove = ((forall (P:(b->Prop)), (((ex b) (fun (Xx:b)=> (P Xx)))->(P (cJ P))))->(forall (Xf:(b->a)) (Xg:(b->a)), ((((eq a) (Xf (cJ (fun (Xx:b)=> (not (((eq a) (Xf Xx)) (Xg Xx))))))) (Xg (cJ (fun (Xx:b)=> (not (((eq a) (Xf Xx)) (Xg Xx)))))))->(((eq (b->a)) Xf) Xg)))):Prop
% 13.74/13.91 Parameter b_DUMMY:b.
% 13.74/13.91 Parameter a_DUMMY:a.
% 13.74/13.91 We need to prove ['((forall (P:(b->Prop)), (((ex b) (fun (Xx:b)=> (P Xx)))->(P (cJ P))))->(forall (Xf:(b->a)) (Xg:(b->a)), ((((eq a) (Xf (cJ (fun (Xx:b)=> (not (((eq a) (Xf Xx)) (Xg Xx))))))) (Xg (cJ (fun (Xx:b)=> (not (((eq a) (Xf Xx)) (Xg Xx)))))))->(((eq (b->a)) Xf) Xg))))']
% 13.74/13.91 Parameter b:Type.
% 13.74/13.91 Parameter a:Type.
% 13.74/13.91 Parameter cJ:((b->Prop)->b).
% 13.74/13.91 Trying to prove ((forall (P:(b->Prop)), (((ex b) (fun (Xx:b)=> (P Xx)))->(P (cJ P))))->(forall (Xf:(b->a)) (Xg:(b->a)), ((((eq a) (Xf (cJ (fun (Xx:b)=> (not (((eq a) (Xf Xx)) (Xg Xx))))))) (Xg (cJ (fun (Xx:b)=> (not (((eq a) (Xf Xx)) (Xg Xx)))))))->(((eq (b->a)) Xf) Xg))))
% 13.74/13.91 Found x00:=(x0 (fun (x1:a)=> (P Xf))):((P Xf)->(P Xf))
% 13.74/13.91 Found (x0 (fun (x1:a)=> (P Xf))) as proof of (P0 Xf)
% 13.74/13.91 Found (x0 (fun (x1:a)=> (P Xf))) as proof of (P0 Xf)
% 13.74/13.91 Found x00:=(x0 (fun (x1:a)=> (P Xf))):((P Xf)->(P Xf))
% 13.74/13.91 Found (x0 (fun (x1:a)=> (P Xf))) as proof of (P0 Xf)
% 13.74/13.91 Found (x0 (fun (x1:a)=> (P Xf))) as proof of (P0 Xf)
% 13.74/13.91 Found x00:=(x0 (fun (x1:a)=> (P Xf))):((P Xf)->(P Xf))
% 13.74/13.91 Found (x0 (fun (x1:a)=> (P Xf))) as proof of (P0 Xf)
% 13.74/13.91 Found (x0 (fun (x1:a)=> (P Xf))) as proof of (P0 Xf)
% 13.74/13.91 Found eq_ref00:=(eq_ref0 b0):(((eq (b->a)) b0) b0)
% 13.74/13.91 Found (eq_ref0 b0) as proof of (((eq (b->a)) b0) Xg)
% 13.74/13.91 Found ((eq_ref (b->a)) b0) as proof of (((eq (b->a)) b0) Xg)
% 13.74/13.91 Found ((eq_ref (b->a)) b0) as proof of (((eq (b->a)) b0) Xg)
% 13.74/13.91 Found ((eq_ref (b->a)) b0) as proof of (((eq (b->a)) b0) Xg)
% 13.74/13.91 Found eta_expansion000:=(eta_expansion00 Xf):(((eq (b->a)) Xf) (fun (x:b)=> (Xf x)))
% 13.74/13.91 Found (eta_expansion00 Xf) as proof of (((eq (b->a)) Xf) b0)
% 13.74/13.91 Found ((eta_expansion0 a) Xf) as proof of (((eq (b->a)) Xf) b0)
% 13.74/13.91 Found (((eta_expansion b) a) Xf) as proof of (((eq (b->a)) Xf) b0)
% 13.74/13.91 Found (((eta_expansion b) a) Xf) as proof of (((eq (b->a)) Xf) b0)
% 13.74/13.91 Found (((eta_expansion b) a) Xf) as proof of (((eq (b->a)) Xf) b0)
% 13.74/13.91 Found x00:=(x0 (fun (x1:a)=> (P Xg))):((P Xg)->(P Xg))
% 13.74/13.91 Found (x0 (fun (x1:a)=> (P Xg))) as proof of (P0 Xg)
% 13.74/13.91 Found (x0 (fun (x1:a)=> (P Xg))) as proof of (P0 Xg)
% 13.74/13.91 Found x00:=(x0 (fun (x1:a)=> (P Xg))):((P Xg)->(P Xg))
% 13.74/13.91 Found (x0 (fun (x1:a)=> (P Xg))) as proof of (P0 Xg)
% 13.74/13.91 Found (x0 (fun (x1:a)=> (P Xg))) as proof of (P0 Xg)
% 13.74/13.91 Found x00:=(x0 (fun (x2:a)=> (P (Xf x1)))):((P (Xf x1))->(P (Xf x1)))
% 13.74/13.91 Found (x0 (fun (x2:a)=> (P (Xf x1)))) as proof of (P0 (Xf x1))
% 13.74/13.91 Found (x0 (fun (x2:a)=> (P (Xf x1)))) as proof of (P0 (Xf x1))
% 13.74/13.91 Found x00:=(x0 (fun (x2:a)=> (P (Xf x1)))):((P (Xf x1))->(P (Xf x1)))
% 13.74/13.91 Found (x0 (fun (x2:a)=> (P (Xf x1)))) as proof of (P0 (Xf x1))
% 13.74/13.91 Found (x0 (fun (x2:a)=> (P (Xf x1)))) as proof of (P0 (Xf x1))
% 13.74/13.91 Found eq_ref00:=(eq_ref0 b0):(((eq (b->a)) b0) b0)
% 13.74/13.91 Found (eq_ref0 b0) as proof of (((eq (b->a)) b0) Xf)
% 13.74/13.91 Found ((eq_ref (b->a)) b0) as proof of (((eq (b->a)) b0) Xf)
% 13.74/13.91 Found ((eq_ref (b->a)) b0) as proof of (((eq (b->a)) b0) Xf)
% 13.74/13.91 Found ((eq_ref (b->a)) b0) as proof of (((eq (b->a)) b0) Xf)
% 13.74/13.91 Found eta_expansion000:=(eta_expansion00 Xg):(((eq (b->a)) Xg) (fun (x:b)=> (Xg x)))
% 28.39/28.58 Found (eta_expansion00 Xg) as proof of (((eq (b->a)) Xg) b0)
% 28.39/28.58 Found ((eta_expansion0 a) Xg) as proof of (((eq (b->a)) Xg) b0)
% 28.39/28.58 Found (((eta_expansion b) a) Xg) as proof of (((eq (b->a)) Xg) b0)
% 28.39/28.58 Found (((eta_expansion b) a) Xg) as proof of (((eq (b->a)) Xg) b0)
% 28.39/28.58 Found (((eta_expansion b) a) Xg) as proof of (((eq (b->a)) Xg) b0)
% 28.39/28.58 Found eq_ref00:=(eq_ref0 (Xf x1)):(((eq a) (Xf x1)) (Xf x1))
% 28.39/28.58 Found (eq_ref0 (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 28.39/28.58 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 28.39/28.58 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 28.39/28.58 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 28.39/28.58 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 28.39/28.58 Found (eq_ref0 b0) as proof of (((eq a) b0) (Xg x1))
% 28.39/28.58 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 28.39/28.58 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 28.39/28.58 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 28.39/28.58 Found eq_ref00:=(eq_ref0 (Xf x1)):(((eq a) (Xf x1)) (Xf x1))
% 28.39/28.58 Found (eq_ref0 (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 28.39/28.58 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 28.39/28.58 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 28.39/28.58 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 28.39/28.58 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 28.39/28.58 Found (eq_ref0 b0) as proof of (((eq a) b0) (Xg x1))
% 28.39/28.58 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 28.39/28.58 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 28.39/28.58 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 28.39/28.58 Found x00:=(x0 (fun (x2:a)=> (P (Xg x1)))):((P (Xg x1))->(P (Xg x1)))
% 28.39/28.58 Found (x0 (fun (x2:a)=> (P (Xg x1)))) as proof of (P0 (Xg x1))
% 28.39/28.58 Found (x0 (fun (x2:a)=> (P (Xg x1)))) as proof of (P0 (Xg x1))
% 28.39/28.58 Found x00:=(x0 (fun (x2:a)=> (P (Xg x1)))):((P (Xg x1))->(P (Xg x1)))
% 28.39/28.58 Found (x0 (fun (x2:a)=> (P (Xg x1)))) as proof of (P0 (Xg x1))
% 28.39/28.58 Found (x0 (fun (x2:a)=> (P (Xg x1)))) as proof of (P0 (Xg x1))
% 28.39/28.58 Found eq_ref00:=(eq_ref0 (Xg x1)):(((eq a) (Xg x1)) (Xg x1))
% 28.39/28.58 Found (eq_ref0 (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 28.39/28.58 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 28.39/28.58 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 28.39/28.58 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 28.39/28.58 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 28.39/28.58 Found (eq_ref0 b0) as proof of (((eq a) b0) (Xf x1))
% 28.39/28.58 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 28.39/28.58 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 28.39/28.58 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 28.39/28.58 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 28.39/28.58 Found (eq_ref0 b0) as proof of (((eq a) b0) (Xf x1))
% 28.39/28.58 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 28.39/28.58 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 28.39/28.58 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 28.39/28.58 Found eq_ref00:=(eq_ref0 (Xg x1)):(((eq a) (Xg x1)) (Xg x1))
% 28.39/28.58 Found (eq_ref0 (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 28.39/28.58 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 28.39/28.58 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 28.39/28.58 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 28.39/28.58 Found eq_ref00:=(eq_ref0 (Xg x1)):(((eq a) (Xg x1)) (Xg x1))
% 28.39/28.58 Found (eq_ref0 (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 28.39/28.58 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 28.39/28.58 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 28.39/28.58 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 28.39/28.58 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 28.39/28.58 Found (eq_ref0 b0) as proof of (((eq a) b0) (Xf x1))
% 28.39/28.58 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 28.39/28.58 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 28.39/28.58 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 28.39/28.58 Found eq_ref00:=(eq_ref0 (Xg x1)):(((eq a) (Xg x1)) (Xg x1))
% 28.39/28.58 Found (eq_ref0 (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 28.39/28.58 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 28.39/28.58 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 28.39/28.58 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 28.39/28.58 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 28.39/28.58 Found (eq_ref0 b0) as proof of (((eq a) b0) (Xf x1))
% 28.39/28.58 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 28.39/28.58 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 33.33/33.51 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 33.33/33.51 Found x1:(P Xf)
% 33.33/33.51 Instantiate: b0:=Xf:(b->a)
% 33.33/33.51 Found x1 as proof of (P0 b0)
% 33.33/33.51 Found eta_expansion000:=(eta_expansion00 Xg):(((eq (b->a)) Xg) (fun (x:b)=> (Xg x)))
% 33.33/33.51 Found (eta_expansion00 Xg) as proof of (((eq (b->a)) Xg) b0)
% 33.33/33.51 Found ((eta_expansion0 a) Xg) as proof of (((eq (b->a)) Xg) b0)
% 33.33/33.51 Found (((eta_expansion b) a) Xg) as proof of (((eq (b->a)) Xg) b0)
% 33.33/33.51 Found (((eta_expansion b) a) Xg) as proof of (((eq (b->a)) Xg) b0)
% 33.33/33.51 Found (((eta_expansion b) a) Xg) as proof of (((eq (b->a)) Xg) b0)
% 33.33/33.51 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xx:b)=> (forall (Xf:(b->a)) (Xg:(b->a)), ((((eq a) (Xf (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0))))))) (Xg (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0)))))))->(((eq (b->a)) Xf) Xg))))):(((eq (b->Prop)) (fun (Xx:b)=> (forall (Xf:(b->a)) (Xg:(b->a)), ((((eq a) (Xf (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0))))))) (Xg (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0)))))))->(((eq (b->a)) Xf) Xg))))) (fun (x:b)=> (forall (Xf:(b->a)) (Xg:(b->a)), ((((eq a) (Xf (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0))))))) (Xg (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0)))))))->(((eq (b->a)) Xf) Xg)))))
% 33.33/33.51 Found (eta_expansion_dep00 (fun (Xx:b)=> (forall (Xf:(b->a)) (Xg:(b->a)), ((((eq a) (Xf (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0))))))) (Xg (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0)))))))->(((eq (b->a)) Xf) Xg))))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (forall (Xf:(b->a)) (Xg:(b->a)), ((((eq a) (Xf (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0))))))) (Xg (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0)))))))->(((eq (b->a)) Xf) Xg))))) b0)
% 33.33/33.51 Found ((eta_expansion_dep0 (fun (x2:b)=> Prop)) (fun (Xx:b)=> (forall (Xf:(b->a)) (Xg:(b->a)), ((((eq a) (Xf (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0))))))) (Xg (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0)))))))->(((eq (b->a)) Xf) Xg))))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (forall (Xf:(b->a)) (Xg:(b->a)), ((((eq a) (Xf (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0))))))) (Xg (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0)))))))->(((eq (b->a)) Xf) Xg))))) b0)
% 33.33/33.51 Found (((eta_expansion_dep b) (fun (x2:b)=> Prop)) (fun (Xx:b)=> (forall (Xf:(b->a)) (Xg:(b->a)), ((((eq a) (Xf (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0))))))) (Xg (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0)))))))->(((eq (b->a)) Xf) Xg))))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (forall (Xf:(b->a)) (Xg:(b->a)), ((((eq a) (Xf (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0))))))) (Xg (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0)))))))->(((eq (b->a)) Xf) Xg))))) b0)
% 33.33/33.51 Found (((eta_expansion_dep b) (fun (x2:b)=> Prop)) (fun (Xx:b)=> (forall (Xf:(b->a)) (Xg:(b->a)), ((((eq a) (Xf (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0))))))) (Xg (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0)))))))->(((eq (b->a)) Xf) Xg))))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (forall (Xf:(b->a)) (Xg:(b->a)), ((((eq a) (Xf (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0))))))) (Xg (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0)))))))->(((eq (b->a)) Xf) Xg))))) b0)
% 33.33/33.51 Found (((eta_expansion_dep b) (fun (x2:b)=> Prop)) (fun (Xx:b)=> (forall (Xf:(b->a)) (Xg:(b->a)), ((((eq a) (Xf (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0))))))) (Xg (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0)))))))->(((eq (b->a)) Xf) Xg))))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (forall (Xf:(b->a)) (Xg:(b->a)), ((((eq a) (Xf (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0))))))) (Xg (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0)))))))->(((eq (b->a)) Xf) Xg))))) b0)
% 33.33/33.51 Found eq_ref00:=(eq_ref0 (fun (Xx:b)=> (forall (Xg:(b->a)), ((((eq a) (Xf (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0))))))) (Xg (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0)))))))->(((eq (b->a)) Xf) Xg))))):(((eq (b->Prop)) (fun (Xx:b)=> (forall (Xg:(b->a)), ((((eq a) (Xf (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0))))))) (Xg (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0)))))))->(((eq (b->a)) Xf) Xg))))) (fun (Xx:b)=> (forall (Xg:(b->a)), ((((eq a) (Xf (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0))))))) (Xg (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0)))))))->(((eq (b->a)) Xf) Xg)))))
% 34.64/34.82 Found (eq_ref0 (fun (Xx:b)=> (forall (Xg:(b->a)), ((((eq a) (Xf (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0))))))) (Xg (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0)))))))->(((eq (b->a)) Xf) Xg))))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (forall (Xg:(b->a)), ((((eq a) (Xf (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0))))))) (Xg (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0)))))))->(((eq (b->a)) Xf) Xg))))) b0)
% 34.64/34.82 Found ((eq_ref (b->Prop)) (fun (Xx:b)=> (forall (Xg:(b->a)), ((((eq a) (Xf (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0))))))) (Xg (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0)))))))->(((eq (b->a)) Xf) Xg))))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (forall (Xg:(b->a)), ((((eq a) (Xf (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0))))))) (Xg (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0)))))))->(((eq (b->a)) Xf) Xg))))) b0)
% 34.64/34.82 Found ((eq_ref (b->Prop)) (fun (Xx:b)=> (forall (Xg:(b->a)), ((((eq a) (Xf (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0))))))) (Xg (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0)))))))->(((eq (b->a)) Xf) Xg))))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (forall (Xg:(b->a)), ((((eq a) (Xf (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0))))))) (Xg (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0)))))))->(((eq (b->a)) Xf) Xg))))) b0)
% 34.64/34.82 Found ((eq_ref (b->Prop)) (fun (Xx:b)=> (forall (Xg:(b->a)), ((((eq a) (Xf (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0))))))) (Xg (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0)))))))->(((eq (b->a)) Xf) Xg))))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (forall (Xg:(b->a)), ((((eq a) (Xf (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0))))))) (Xg (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0)))))))->(((eq (b->a)) Xf) Xg))))) b0)
% 34.64/34.82 Found eta_expansion000:=(eta_expansion00 (fun (Xx:b)=> ((((eq a) (Xf (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0))))))) (Xg (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0)))))))->(((eq (b->a)) Xf) Xg)))):(((eq (b->Prop)) (fun (Xx:b)=> ((((eq a) (Xf (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0))))))) (Xg (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0)))))))->(((eq (b->a)) Xf) Xg)))) (fun (x:b)=> ((((eq a) (Xf (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0))))))) (Xg (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0)))))))->(((eq (b->a)) Xf) Xg))))
% 34.64/34.82 Found (eta_expansion00 (fun (Xx:b)=> ((((eq a) (Xf (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0))))))) (Xg (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0)))))))->(((eq (b->a)) Xf) Xg)))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> ((((eq a) (Xf (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0))))))) (Xg (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0)))))))->(((eq (b->a)) Xf) Xg)))) b0)
% 34.64/34.82 Found ((eta_expansion0 Prop) (fun (Xx:b)=> ((((eq a) (Xf (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0))))))) (Xg (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0)))))))->(((eq (b->a)) Xf) Xg)))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> ((((eq a) (Xf (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0))))))) (Xg (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0)))))))->(((eq (b->a)) Xf) Xg)))) b0)
% 34.64/34.82 Found (((eta_expansion b) Prop) (fun (Xx:b)=> ((((eq a) (Xf (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0))))))) (Xg (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0)))))))->(((eq (b->a)) Xf) Xg)))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> ((((eq a) (Xf (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0))))))) (Xg (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0)))))))->(((eq (b->a)) Xf) Xg)))) b0)
% 34.64/34.82 Found (((eta_expansion b) Prop) (fun (Xx:b)=> ((((eq a) (Xf (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0))))))) (Xg (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0)))))))->(((eq (b->a)) Xf) Xg)))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> ((((eq a) (Xf (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0))))))) (Xg (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0)))))))->(((eq (b->a)) Xf) Xg)))) b0)
% 37.64/37.83 Found (((eta_expansion b) Prop) (fun (Xx:b)=> ((((eq a) (Xf (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0))))))) (Xg (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0)))))))->(((eq (b->a)) Xf) Xg)))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> ((((eq a) (Xf (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0))))))) (Xg (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0)))))))->(((eq (b->a)) Xf) Xg)))) b0)
% 37.64/37.83 Found eq_ref00:=(eq_ref0 (fun (Xx:b)=> (((eq (b->a)) Xf) Xg))):(((eq (b->Prop)) (fun (Xx:b)=> (((eq (b->a)) Xf) Xg))) (fun (Xx:b)=> (((eq (b->a)) Xf) Xg)))
% 37.64/37.83 Found (eq_ref0 (fun (Xx:b)=> (((eq (b->a)) Xf) Xg))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (((eq (b->a)) Xf) Xg))) b0)
% 37.64/37.83 Found ((eq_ref (b->Prop)) (fun (Xx:b)=> (((eq (b->a)) Xf) Xg))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (((eq (b->a)) Xf) Xg))) b0)
% 37.64/37.83 Found ((eq_ref (b->Prop)) (fun (Xx:b)=> (((eq (b->a)) Xf) Xg))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (((eq (b->a)) Xf) Xg))) b0)
% 37.64/37.83 Found ((eq_ref (b->Prop)) (fun (Xx:b)=> (((eq (b->a)) Xf) Xg))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (((eq (b->a)) Xf) Xg))) b0)
% 37.64/37.83 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 37.64/37.83 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (forall (Xf:(b->a)) (Xg:(b->a)), ((((eq a) (Xf (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0))))))) (Xg (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0)))))))->(((eq (b->a)) Xf) Xg))))
% 37.64/37.83 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (forall (Xf:(b->a)) (Xg:(b->a)), ((((eq a) (Xf (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0))))))) (Xg (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0)))))))->(((eq (b->a)) Xf) Xg))))
% 37.64/37.83 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (forall (Xf:(b->a)) (Xg:(b->a)), ((((eq a) (Xf (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0))))))) (Xg (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0)))))))->(((eq (b->a)) Xf) Xg))))
% 37.64/37.83 Found (fun (x1:b)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (forall (Xf:(b->a)) (Xg:(b->a)), ((((eq a) (Xf (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0))))))) (Xg (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0)))))))->(((eq (b->a)) Xf) Xg))))
% 37.64/37.83 Found (fun (x1:b)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:b), (((eq Prop) (f x)) (forall (Xf:(b->a)) (Xg:(b->a)), ((((eq a) (Xf (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0))))))) (Xg (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0)))))))->(((eq (b->a)) Xf) Xg)))))
% 37.64/37.83 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 37.64/37.83 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (forall (Xf:(b->a)) (Xg:(b->a)), ((((eq a) (Xf (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0))))))) (Xg (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0)))))))->(((eq (b->a)) Xf) Xg))))
% 37.64/37.83 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (forall (Xf:(b->a)) (Xg:(b->a)), ((((eq a) (Xf (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0))))))) (Xg (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0)))))))->(((eq (b->a)) Xf) Xg))))
% 37.64/37.83 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (forall (Xf:(b->a)) (Xg:(b->a)), ((((eq a) (Xf (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0))))))) (Xg (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0)))))))->(((eq (b->a)) Xf) Xg))))
% 37.64/37.83 Found (fun (x1:b)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (forall (Xf:(b->a)) (Xg:(b->a)), ((((eq a) (Xf (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0))))))) (Xg (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0)))))))->(((eq (b->a)) Xf) Xg))))
% 37.64/37.83 Found (fun (x1:b)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:b), (((eq Prop) (f x)) (forall (Xf:(b->a)) (Xg:(b->a)), ((((eq a) (Xf (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0))))))) (Xg (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0)))))))->(((eq (b->a)) Xf) Xg)))))
% 37.64/37.83 Found eq_ref00:=(eq_ref0 (fun (Xx:b)=> ((P Xf)->(P Xg)))):(((eq (b->Prop)) (fun (Xx:b)=> ((P Xf)->(P Xg)))) (fun (Xx:b)=> ((P Xf)->(P Xg))))
% 38.16/38.36 Found (eq_ref0 (fun (Xx:b)=> ((P Xf)->(P Xg)))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> ((P Xf)->(P Xg)))) b0)
% 38.16/38.36 Found ((eq_ref (b->Prop)) (fun (Xx:b)=> ((P Xf)->(P Xg)))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> ((P Xf)->(P Xg)))) b0)
% 38.16/38.36 Found ((eq_ref (b->Prop)) (fun (Xx:b)=> ((P Xf)->(P Xg)))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> ((P Xf)->(P Xg)))) b0)
% 38.16/38.36 Found ((eq_ref (b->Prop)) (fun (Xx:b)=> ((P Xf)->(P Xg)))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> ((P Xf)->(P Xg)))) b0)
% 38.16/38.36 Found x1:(P Xf)
% 38.16/38.36 Instantiate: f:=Xf:(b->a)
% 38.16/38.36 Found x1 as proof of (P0 f)
% 38.16/38.36 Found eq_ref00:=(eq_ref0 (f x2)):(((eq a) (f x2)) (f x2))
% 38.16/38.36 Found (eq_ref0 (f x2)) as proof of (((eq a) (f x2)) (Xg x2))
% 38.16/38.36 Found ((eq_ref a) (f x2)) as proof of (((eq a) (f x2)) (Xg x2))
% 38.16/38.36 Found ((eq_ref a) (f x2)) as proof of (((eq a) (f x2)) (Xg x2))
% 38.16/38.36 Found (fun (x2:b)=> ((eq_ref a) (f x2))) as proof of (((eq a) (f x2)) (Xg x2))
% 38.16/38.36 Found (fun (x2:b)=> ((eq_ref a) (f x2))) as proof of (forall (x:b), (((eq a) (f x)) (Xg x)))
% 38.16/38.36 Found x1:(P Xf)
% 38.16/38.36 Instantiate: f:=Xf:(b->a)
% 38.16/38.36 Found x1 as proof of (P0 f)
% 38.16/38.36 Found eq_ref00:=(eq_ref0 (f x2)):(((eq a) (f x2)) (f x2))
% 38.16/38.36 Found (eq_ref0 (f x2)) as proof of (((eq a) (f x2)) (Xg x2))
% 38.16/38.36 Found ((eq_ref a) (f x2)) as proof of (((eq a) (f x2)) (Xg x2))
% 38.16/38.36 Found ((eq_ref a) (f x2)) as proof of (((eq a) (f x2)) (Xg x2))
% 38.16/38.36 Found (fun (x2:b)=> ((eq_ref a) (f x2))) as proof of (((eq a) (f x2)) (Xg x2))
% 38.16/38.36 Found (fun (x2:b)=> ((eq_ref a) (f x2))) as proof of (forall (x:b), (((eq a) (f x)) (Xg x)))
% 38.16/38.36 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 38.16/38.36 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (forall (Xg:(b->a)), ((((eq a) (Xf (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0))))))) (Xg (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0)))))))->(((eq (b->a)) Xf) Xg))))
% 38.16/38.36 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (forall (Xg:(b->a)), ((((eq a) (Xf (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0))))))) (Xg (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0)))))))->(((eq (b->a)) Xf) Xg))))
% 38.16/38.36 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (forall (Xg:(b->a)), ((((eq a) (Xf (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0))))))) (Xg (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0)))))))->(((eq (b->a)) Xf) Xg))))
% 38.16/38.36 Found (fun (x1:b)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (forall (Xg:(b->a)), ((((eq a) (Xf (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0))))))) (Xg (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0)))))))->(((eq (b->a)) Xf) Xg))))
% 38.16/38.36 Found (fun (x1:b)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:b), (((eq Prop) (f x)) (forall (Xg:(b->a)), ((((eq a) (Xf (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0))))))) (Xg (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0)))))))->(((eq (b->a)) Xf) Xg)))))
% 38.16/38.36 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 38.16/38.36 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (forall (Xg:(b->a)), ((((eq a) (Xf (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0))))))) (Xg (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0)))))))->(((eq (b->a)) Xf) Xg))))
% 38.16/38.36 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (forall (Xg:(b->a)), ((((eq a) (Xf (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0))))))) (Xg (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0)))))))->(((eq (b->a)) Xf) Xg))))
% 38.16/38.36 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (forall (Xg:(b->a)), ((((eq a) (Xf (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0))))))) (Xg (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0)))))))->(((eq (b->a)) Xf) Xg))))
% 38.16/38.36 Found (fun (x1:b)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (forall (Xg:(b->a)), ((((eq a) (Xf (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0))))))) (Xg (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0)))))))->(((eq (b->a)) Xf) Xg))))
% 38.16/38.36 Found (fun (x1:b)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:b), (((eq Prop) (f x)) (forall (Xg:(b->a)), ((((eq a) (Xf (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0))))))) (Xg (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0)))))))->(((eq (b->a)) Xf) Xg)))))
% 41.57/41.75 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 41.57/41.75 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) ((((eq a) (Xf (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0))))))) (Xg (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0)))))))->(((eq (b->a)) Xf) Xg)))
% 41.57/41.75 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) ((((eq a) (Xf (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0))))))) (Xg (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0)))))))->(((eq (b->a)) Xf) Xg)))
% 41.57/41.75 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) ((((eq a) (Xf (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0))))))) (Xg (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0)))))))->(((eq (b->a)) Xf) Xg)))
% 41.57/41.75 Found (fun (x1:b)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) ((((eq a) (Xf (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0))))))) (Xg (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0)))))))->(((eq (b->a)) Xf) Xg)))
% 41.57/41.75 Found (fun (x1:b)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:b), (((eq Prop) (f x)) ((((eq a) (Xf (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0))))))) (Xg (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0)))))))->(((eq (b->a)) Xf) Xg))))
% 41.57/41.75 Found eq_ref00:=(eq_ref0 (fun (Xx:b)=> (P Xg))):(((eq (b->Prop)) (fun (Xx:b)=> (P Xg))) (fun (Xx:b)=> (P Xg)))
% 41.57/41.75 Found (eq_ref0 (fun (Xx:b)=> (P Xg))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (P Xg))) b0)
% 41.57/41.75 Found ((eq_ref (b->Prop)) (fun (Xx:b)=> (P Xg))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (P Xg))) b0)
% 41.57/41.75 Found ((eq_ref (b->Prop)) (fun (Xx:b)=> (P Xg))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (P Xg))) b0)
% 41.57/41.75 Found ((eq_ref (b->Prop)) (fun (Xx:b)=> (P Xg))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (P Xg))) b0)
% 41.57/41.75 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 41.57/41.75 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) ((((eq a) (Xf (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0))))))) (Xg (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0)))))))->(((eq (b->a)) Xf) Xg)))
% 41.57/41.75 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) ((((eq a) (Xf (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0))))))) (Xg (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0)))))))->(((eq (b->a)) Xf) Xg)))
% 41.57/41.75 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) ((((eq a) (Xf (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0))))))) (Xg (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0)))))))->(((eq (b->a)) Xf) Xg)))
% 41.57/41.75 Found (fun (x1:b)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) ((((eq a) (Xf (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0))))))) (Xg (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0)))))))->(((eq (b->a)) Xf) Xg)))
% 41.57/41.75 Found (fun (x1:b)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:b), (((eq Prop) (f x)) ((((eq a) (Xf (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0))))))) (Xg (cJ (fun (Xx0:b)=> (not (((eq a) (Xf Xx0)) (Xg Xx0)))))))->(((eq (b->a)) Xf) Xg))))
% 41.57/41.75 Found eq_ref00:=(eq_ref0 b0):(((eq (b->a)) b0) b0)
% 41.57/41.75 Found (eq_ref0 b0) as proof of (((eq (b->a)) b0) Xg)
% 41.57/41.75 Found ((eq_ref (b->a)) b0) as proof of (((eq (b->a)) b0) Xg)
% 41.57/41.75 Found ((eq_ref (b->a)) b0) as proof of (((eq (b->a)) b0) Xg)
% 41.57/41.75 Found ((eq_ref (b->a)) b0) as proof of (((eq (b->a)) b0) Xg)
% 41.57/41.75 Found eta_expansion000:=(eta_expansion00 Xf):(((eq (b->a)) Xf) (fun (x:b)=> (Xf x)))
% 41.57/41.75 Found (eta_expansion00 Xf) as proof of (((eq (b->a)) Xf) b0)
% 41.57/41.75 Found ((eta_expansion0 a) Xf) as proof of (((eq (b->a)) Xf) b0)
% 41.57/41.75 Found (((eta_expansion b) a) Xf) as proof of (((eq (b->a)) Xf) b0)
% 41.57/41.75 Found (((eta_expansion b) a) Xf) as proof of (((eq (b->a)) Xf) b0)
% 41.57/41.75 Found (((eta_expansion b) a) Xf) as proof of (((eq (b->a)) Xf) b0)
% 41.57/41.75 Found x00:=(x0 (fun (x1:a)=> (P Xf))):((P Xf)->(P Xf))
% 41.57/41.75 Found (x0 (fun (x1:a)=> (P Xf))) as proof of (P0 Xf)
% 41.57/41.75 Found (x0 (fun (x1:a)=> (P Xf))) as proof of (P0 Xf)
% 41.57/41.75 Found eq_ref00:=(eq_ref0 b0):(((eq (b->a)) b0) b0)
% 41.57/41.75 Found (eq_ref0 b0) as proof of (((eq (b->a)) b0) Xg)
% 41.57/41.75 Found ((eq_ref (b->a)) b0) as proof of (((eq (b->a)) b0) Xg)
% 41.57/41.75 Found ((eq_ref (b->a)) b0) as proof of (((eq (b->a)) b0) Xg)
% 41.57/41.75 Found ((eq_ref (b->a)) b0) as proof of (((eq (b->a)) b0) Xg)
% 41.57/41.75 Found eta_expansion_dep000:=(eta_expansion_dep00 Xf):(((eq (b->a)) Xf) (fun (x:b)=> (Xf x)))
% 45.16/45.40 Found (eta_expansion_dep00 Xf) as proof of (((eq (b->a)) Xf) b0)
% 45.16/45.40 Found ((eta_expansion_dep0 (fun (x2:b)=> a)) Xf) as proof of (((eq (b->a)) Xf) b0)
% 45.16/45.40 Found (((eta_expansion_dep b) (fun (x2:b)=> a)) Xf) as proof of (((eq (b->a)) Xf) b0)
% 45.16/45.40 Found (((eta_expansion_dep b) (fun (x2:b)=> a)) Xf) as proof of (((eq (b->a)) Xf) b0)
% 45.16/45.40 Found (((eta_expansion_dep b) (fun (x2:b)=> a)) Xf) as proof of (((eq (b->a)) Xf) b0)
% 45.16/45.40 Found eq_ref00:=(eq_ref0 b0):(((eq (b->a)) b0) b0)
% 45.16/45.40 Found (eq_ref0 b0) as proof of (P b0)
% 45.16/45.40 Found ((eq_ref (b->a)) b0) as proof of (P b0)
% 45.16/45.40 Found ((eq_ref (b->a)) b0) as proof of (P b0)
% 45.16/45.40 Found ((eq_ref (b->a)) b0) as proof of (P b0)
% 45.16/45.40 Found eq_ref00:=(eq_ref0 Xg):(((eq (b->a)) Xg) Xg)
% 45.16/45.40 Found (eq_ref0 Xg) as proof of (((eq (b->a)) Xg) b0)
% 45.16/45.40 Found ((eq_ref (b->a)) Xg) as proof of (((eq (b->a)) Xg) b0)
% 45.16/45.40 Found ((eq_ref (b->a)) Xg) as proof of (((eq (b->a)) Xg) b0)
% 45.16/45.40 Found ((eq_ref (b->a)) Xg) as proof of (((eq (b->a)) Xg) b0)
% 45.16/45.40 Found eq_ref00:=(eq_ref0 (f x2)):(((eq Prop) (f x2)) (f x2))
% 45.16/45.40 Found (eq_ref0 (f x2)) as proof of (((eq Prop) (f x2)) (((eq (b->a)) Xf) Xg))
% 45.16/45.40 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) (((eq (b->a)) Xf) Xg))
% 45.16/45.40 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) (((eq (b->a)) Xf) Xg))
% 45.16/45.40 Found (fun (x2:b)=> ((eq_ref Prop) (f x2))) as proof of (((eq Prop) (f x2)) (((eq (b->a)) Xf) Xg))
% 45.16/45.40 Found (fun (x2:b)=> ((eq_ref Prop) (f x2))) as proof of (forall (x:b), (((eq Prop) (f x)) (((eq (b->a)) Xf) Xg)))
% 45.16/45.40 Found eq_ref00:=(eq_ref0 (f x2)):(((eq Prop) (f x2)) (f x2))
% 45.16/45.40 Found (eq_ref0 (f x2)) as proof of (((eq Prop) (f x2)) (((eq (b->a)) Xf) Xg))
% 45.16/45.40 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) (((eq (b->a)) Xf) Xg))
% 45.16/45.40 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) (((eq (b->a)) Xf) Xg))
% 45.16/45.40 Found (fun (x2:b)=> ((eq_ref Prop) (f x2))) as proof of (((eq Prop) (f x2)) (((eq (b->a)) Xf) Xg))
% 45.16/45.40 Found (fun (x2:b)=> ((eq_ref Prop) (f x2))) as proof of (forall (x:b), (((eq Prop) (f x)) (((eq (b->a)) Xf) Xg)))
% 45.16/45.40 Found x1:(P Xg)
% 45.16/45.40 Instantiate: b0:=Xg:(b->a)
% 45.16/45.40 Found x1 as proof of (P0 b0)
% 45.16/45.40 Found eq_ref00:=(eq_ref0 Xf):(((eq (b->a)) Xf) Xf)
% 45.16/45.40 Found (eq_ref0 Xf) as proof of (((eq (b->a)) Xf) b0)
% 45.16/45.40 Found ((eq_ref (b->a)) Xf) as proof of (((eq (b->a)) Xf) b0)
% 45.16/45.40 Found ((eq_ref (b->a)) Xf) as proof of (((eq (b->a)) Xf) b0)
% 45.16/45.40 Found ((eq_ref (b->a)) Xf) as proof of (((eq (b->a)) Xf) b0)
% 45.16/45.40 Found eq_ref00:=(eq_ref0 (f x2)):(((eq Prop) (f x2)) (f x2))
% 45.16/45.40 Found (eq_ref0 (f x2)) as proof of (((eq Prop) (f x2)) ((P Xf)->(P Xg)))
% 45.16/45.40 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) ((P Xf)->(P Xg)))
% 45.16/45.40 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) ((P Xf)->(P Xg)))
% 45.16/45.40 Found (fun (x2:b)=> ((eq_ref Prop) (f x2))) as proof of (((eq Prop) (f x2)) ((P Xf)->(P Xg)))
% 45.16/45.40 Found (fun (x2:b)=> ((eq_ref Prop) (f x2))) as proof of (forall (x:b), (((eq Prop) (f x)) ((P Xf)->(P Xg))))
% 45.16/45.40 Found eq_ref00:=(eq_ref0 (f x2)):(((eq Prop) (f x2)) (f x2))
% 45.16/45.40 Found (eq_ref0 (f x2)) as proof of (((eq Prop) (f x2)) ((P Xf)->(P Xg)))
% 45.16/45.40 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) ((P Xf)->(P Xg)))
% 45.16/45.40 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) ((P Xf)->(P Xg)))
% 45.16/45.40 Found (fun (x2:b)=> ((eq_ref Prop) (f x2))) as proof of (((eq Prop) (f x2)) ((P Xf)->(P Xg)))
% 45.16/45.40 Found (fun (x2:b)=> ((eq_ref Prop) (f x2))) as proof of (forall (x:b), (((eq Prop) (f x)) ((P Xf)->(P Xg))))
% 45.16/45.40 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 45.16/45.40 Found (eq_ref0 b0) as proof of (((eq a) b0) (Xg x1))
% 45.16/45.40 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 45.16/45.40 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 45.16/45.40 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 45.16/45.40 Found eq_ref00:=(eq_ref0 (Xf x1)):(((eq a) (Xf x1)) (Xf x1))
% 45.16/45.40 Found (eq_ref0 (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 45.16/45.40 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 45.16/45.40 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 45.16/45.40 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 45.16/45.40 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 45.16/45.40 Found (eq_ref0 b0) as proof of (((eq a) b0) (Xg x1))
% 45.16/45.40 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 57.55/57.76 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 57.55/57.76 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 57.55/57.76 Found eq_ref00:=(eq_ref0 (Xf x1)):(((eq a) (Xf x1)) (Xf x1))
% 57.55/57.76 Found (eq_ref0 (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 57.55/57.76 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 57.55/57.76 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 57.55/57.76 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 57.55/57.76 Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% 57.55/57.76 Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) (P Xg))
% 57.55/57.76 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (P Xg))
% 57.55/57.76 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (P Xg))
% 57.55/57.76 Found (fun (x3:b)=> ((eq_ref Prop) (f x3))) as proof of (((eq Prop) (f x3)) (P Xg))
% 57.55/57.76 Found (fun (x3:b)=> ((eq_ref Prop) (f x3))) as proof of (forall (x:b), (((eq Prop) (f x)) (P Xg)))
% 57.55/57.76 Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% 57.55/57.76 Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) (P Xg))
% 57.55/57.76 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (P Xg))
% 57.55/57.76 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (P Xg))
% 57.55/57.76 Found (fun (x3:b)=> ((eq_ref Prop) (f x3))) as proof of (((eq Prop) (f x3)) (P Xg))
% 57.55/57.76 Found (fun (x3:b)=> ((eq_ref Prop) (f x3))) as proof of (forall (x:b), (((eq Prop) (f x)) (P Xg)))
% 57.55/57.76 Found eq_ref00:=(eq_ref0 Xg):(((eq (b->a)) Xg) Xg)
% 57.55/57.76 Found (eq_ref0 Xg) as proof of (((eq (b->a)) Xg) b0)
% 57.55/57.76 Found ((eq_ref (b->a)) Xg) as proof of (((eq (b->a)) Xg) b0)
% 57.55/57.76 Found ((eq_ref (b->a)) Xg) as proof of (((eq (b->a)) Xg) b0)
% 57.55/57.76 Found ((eq_ref (b->a)) Xg) as proof of (((eq (b->a)) Xg) b0)
% 57.55/57.76 Found x2:(P (Xf x1))
% 57.55/57.76 Instantiate: b0:=(Xf x1):a
% 57.55/57.76 Found x2 as proof of (P0 b0)
% 57.55/57.76 Found eq_ref00:=(eq_ref0 (Xg x1)):(((eq a) (Xg x1)) (Xg x1))
% 57.55/57.76 Found (eq_ref0 (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 57.55/57.76 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 57.55/57.76 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 57.55/57.76 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 57.55/57.76 Found x2:(P (Xf x1))
% 57.55/57.76 Instantiate: b0:=(Xf x1):a
% 57.55/57.76 Found x2 as proof of (P0 b0)
% 57.55/57.76 Found eq_ref00:=(eq_ref0 (Xg x1)):(((eq a) (Xg x1)) (Xg x1))
% 57.55/57.76 Found (eq_ref0 (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 57.55/57.76 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 57.55/57.76 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 57.55/57.76 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 57.55/57.76 Found eq_ref00:=(eq_ref0 b00):(((eq (b->a)) b00) b00)
% 57.55/57.76 Found (eq_ref0 b00) as proof of (((eq (b->a)) b00) Xg)
% 57.55/57.76 Found ((eq_ref (b->a)) b00) as proof of (((eq (b->a)) b00) Xg)
% 57.55/57.76 Found ((eq_ref (b->a)) b00) as proof of (((eq (b->a)) b00) Xg)
% 57.55/57.76 Found ((eq_ref (b->a)) b00) as proof of (((eq (b->a)) b00) Xg)
% 57.55/57.76 Found eq_ref00:=(eq_ref0 Xf):(((eq (b->a)) Xf) Xf)
% 57.55/57.76 Found (eq_ref0 Xf) as proof of (((eq (b->a)) Xf) b00)
% 57.55/57.76 Found ((eq_ref (b->a)) Xf) as proof of (((eq (b->a)) Xf) b00)
% 57.55/57.76 Found ((eq_ref (b->a)) Xf) as proof of (((eq (b->a)) Xf) b00)
% 57.55/57.76 Found ((eq_ref (b->a)) Xf) as proof of (((eq (b->a)) Xf) b00)
% 57.55/57.76 Found x00:=(x0 (fun (x1:a)=> (P1 Xg))):((P1 Xg)->(P1 Xg))
% 57.55/57.76 Found (x0 (fun (x1:a)=> (P1 Xg))) as proof of (P2 Xg)
% 57.55/57.76 Found (x0 (fun (x1:a)=> (P1 Xg))) as proof of (P2 Xg)
% 57.55/57.76 Found x00:=(x0 (fun (x1:a)=> (P1 Xg))):((P1 Xg)->(P1 Xg))
% 57.55/57.76 Found (x0 (fun (x1:a)=> (P1 Xg))) as proof of (P2 Xg)
% 57.55/57.76 Found (x0 (fun (x1:a)=> (P1 Xg))) as proof of (P2 Xg)
% 57.55/57.76 Found x00:=(x0 (fun (x1:a)=> (P1 Xg))):((P1 Xg)->(P1 Xg))
% 57.55/57.76 Found (x0 (fun (x1:a)=> (P1 Xg))) as proof of (P2 Xg)
% 57.55/57.76 Found (x0 (fun (x1:a)=> (P1 Xg))) as proof of (P2 Xg)
% 57.55/57.76 Found x00:=(x0 (fun (x1:a)=> (P1 Xg))):((P1 Xg)->(P1 Xg))
% 57.55/57.76 Found (x0 (fun (x1:a)=> (P1 Xg))) as proof of (P2 Xg)
% 57.55/57.76 Found (x0 (fun (x1:a)=> (P1 Xg))) as proof of (P2 Xg)
% 57.55/57.76 Found eq_ref00:=(eq_ref0 (fun (Xx:b)=> (((eq (b->a)) Xg) Xf))):(((eq (b->Prop)) (fun (Xx:b)=> (((eq (b->a)) Xg) Xf))) (fun (Xx:b)=> (((eq (b->a)) Xg) Xf)))
% 57.55/57.76 Found (eq_ref0 (fun (Xx:b)=> (((eq (b->a)) Xg) Xf))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (((eq (b->a)) Xg) Xf))) b0)
% 57.55/57.76 Found ((eq_ref (b->Prop)) (fun (Xx:b)=> (((eq (b->a)) Xg) Xf))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (((eq (b->a)) Xg) Xf))) b0)
% 57.55/57.76 Found ((eq_ref (b->Prop)) (fun (Xx:b)=> (((eq (b->a)) Xg) Xf))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (((eq (b->a)) Xg) Xf))) b0)
% 62.49/62.72 Found ((eq_ref (b->Prop)) (fun (Xx:b)=> (((eq (b->a)) Xg) Xf))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (((eq (b->a)) Xg) Xf))) b0)
% 62.49/62.72 Found x00:=(x0 (fun (x1:a)=> (P Xf))):((P Xf)->(P Xf))
% 62.49/62.72 Found (x0 (fun (x1:a)=> (P Xf))) as proof of (P0 Xf)
% 62.49/62.72 Found (x0 (fun (x1:a)=> (P Xf))) as proof of (P0 Xf)
% 62.49/62.72 Found x1:(P Xg)
% 62.49/62.72 Instantiate: f:=Xg:(b->a)
% 62.49/62.72 Found x1 as proof of (P0 f)
% 62.49/62.72 Found eq_ref00:=(eq_ref0 (f x2)):(((eq a) (f x2)) (f x2))
% 62.49/62.72 Found (eq_ref0 (f x2)) as proof of (((eq a) (f x2)) (Xf x2))
% 62.49/62.72 Found ((eq_ref a) (f x2)) as proof of (((eq a) (f x2)) (Xf x2))
% 62.49/62.72 Found ((eq_ref a) (f x2)) as proof of (((eq a) (f x2)) (Xf x2))
% 62.49/62.72 Found (fun (x2:b)=> ((eq_ref a) (f x2))) as proof of (((eq a) (f x2)) (Xf x2))
% 62.49/62.72 Found (fun (x2:b)=> ((eq_ref a) (f x2))) as proof of (forall (x:b), (((eq a) (f x)) (Xf x)))
% 62.49/62.72 Found x1:(P Xg)
% 62.49/62.72 Instantiate: f:=Xg:(b->a)
% 62.49/62.72 Found x1 as proof of (P0 f)
% 62.49/62.72 Found eq_ref00:=(eq_ref0 (f x2)):(((eq a) (f x2)) (f x2))
% 62.49/62.72 Found (eq_ref0 (f x2)) as proof of (((eq a) (f x2)) (Xf x2))
% 62.49/62.72 Found ((eq_ref a) (f x2)) as proof of (((eq a) (f x2)) (Xf x2))
% 62.49/62.72 Found ((eq_ref a) (f x2)) as proof of (((eq a) (f x2)) (Xf x2))
% 62.49/62.72 Found (fun (x2:b)=> ((eq_ref a) (f x2))) as proof of (((eq a) (f x2)) (Xf x2))
% 62.49/62.72 Found (fun (x2:b)=> ((eq_ref a) (f x2))) as proof of (forall (x:b), (((eq a) (f x)) (Xf x)))
% 62.49/62.72 Found x00:=(x0 (fun (x2:a)=> (P1 (Xf x1)))):((P1 (Xf x1))->(P1 (Xf x1)))
% 62.49/62.72 Found (x0 (fun (x2:a)=> (P1 (Xf x1)))) as proof of (P2 (Xf x1))
% 62.49/62.72 Found (x0 (fun (x2:a)=> (P1 (Xf x1)))) as proof of (P2 (Xf x1))
% 62.49/62.72 Found x00:=(x0 (fun (x2:a)=> (P1 (Xf x1)))):((P1 (Xf x1))->(P1 (Xf x1)))
% 62.49/62.72 Found (x0 (fun (x2:a)=> (P1 (Xf x1)))) as proof of (P2 (Xf x1))
% 62.49/62.72 Found (x0 (fun (x2:a)=> (P1 (Xf x1)))) as proof of (P2 (Xf x1))
% 62.49/62.72 Found x00:=(x0 (fun (x2:a)=> (P1 (Xf x1)))):((P1 (Xf x1))->(P1 (Xf x1)))
% 62.49/62.72 Found (x0 (fun (x2:a)=> (P1 (Xf x1)))) as proof of (P2 (Xf x1))
% 62.49/62.72 Found (x0 (fun (x2:a)=> (P1 (Xf x1)))) as proof of (P2 (Xf x1))
% 62.49/62.72 Found x00:=(x0 (fun (x2:a)=> (P1 (Xf x1)))):((P1 (Xf x1))->(P1 (Xf x1)))
% 62.49/62.72 Found (x0 (fun (x2:a)=> (P1 (Xf x1)))) as proof of (P2 (Xf x1))
% 62.49/62.72 Found (x0 (fun (x2:a)=> (P1 (Xf x1)))) as proof of (P2 (Xf x1))
% 62.49/62.72 Found eta_expansion000:=(eta_expansion00 (fun (Xx:b)=> ((P Xg)->(P Xf)))):(((eq (b->Prop)) (fun (Xx:b)=> ((P Xg)->(P Xf)))) (fun (x:b)=> ((P Xg)->(P Xf))))
% 62.49/62.72 Found (eta_expansion00 (fun (Xx:b)=> ((P Xg)->(P Xf)))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> ((P Xg)->(P Xf)))) b0)
% 62.49/62.72 Found ((eta_expansion0 Prop) (fun (Xx:b)=> ((P Xg)->(P Xf)))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> ((P Xg)->(P Xf)))) b0)
% 62.49/62.72 Found (((eta_expansion b) Prop) (fun (Xx:b)=> ((P Xg)->(P Xf)))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> ((P Xg)->(P Xf)))) b0)
% 62.49/62.72 Found (((eta_expansion b) Prop) (fun (Xx:b)=> ((P Xg)->(P Xf)))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> ((P Xg)->(P Xf)))) b0)
% 62.49/62.72 Found (((eta_expansion b) Prop) (fun (Xx:b)=> ((P Xg)->(P Xf)))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> ((P Xg)->(P Xf)))) b0)
% 62.49/62.72 Found eta_expansion000:=(eta_expansion00 (fun (Xx:b)=> (forall (x10:b), (((eq a) (Xf x10)) (Xg x10))))):(((eq (b->Prop)) (fun (Xx:b)=> (forall (x10:b), (((eq a) (Xf x10)) (Xg x10))))) (fun (x:b)=> (forall (x10:b), (((eq a) (Xf x10)) (Xg x10)))))
% 62.49/62.72 Found (eta_expansion00 (fun (Xx:b)=> (forall (x10:b), (((eq a) (Xf x10)) (Xg x10))))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (forall (x10:b), (((eq a) (Xf x10)) (Xg x10))))) b0)
% 62.49/62.72 Found ((eta_expansion0 Prop) (fun (Xx:b)=> (forall (x10:b), (((eq a) (Xf x10)) (Xg x10))))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (forall (x10:b), (((eq a) (Xf x10)) (Xg x10))))) b0)
% 62.49/62.72 Found (((eta_expansion b) Prop) (fun (Xx:b)=> (forall (x10:b), (((eq a) (Xf x10)) (Xg x10))))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (forall (x10:b), (((eq a) (Xf x10)) (Xg x10))))) b0)
% 62.49/62.72 Found (((eta_expansion b) Prop) (fun (Xx:b)=> (forall (x10:b), (((eq a) (Xf x10)) (Xg x10))))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (forall (x10:b), (((eq a) (Xf x10)) (Xg x10))))) b0)
% 62.49/62.72 Found (((eta_expansion b) Prop) (fun (Xx:b)=> (forall (x10:b), (((eq a) (Xf x10)) (Xg x10))))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (forall (x10:b), (((eq a) (Xf x10)) (Xg x10))))) b0)
% 68.46/68.66 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xx:b)=> (forall (x10:b), (((eq a) (Xf x10)) (Xg x10))))):(((eq (b->Prop)) (fun (Xx:b)=> (forall (x10:b), (((eq a) (Xf x10)) (Xg x10))))) (fun (x:b)=> (forall (x10:b), (((eq a) (Xf x10)) (Xg x10)))))
% 68.46/68.66 Found (eta_expansion_dep00 (fun (Xx:b)=> (forall (x10:b), (((eq a) (Xf x10)) (Xg x10))))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (forall (x10:b), (((eq a) (Xf x10)) (Xg x10))))) b0)
% 68.46/68.66 Found ((eta_expansion_dep0 (fun (x3:b)=> Prop)) (fun (Xx:b)=> (forall (x10:b), (((eq a) (Xf x10)) (Xg x10))))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (forall (x10:b), (((eq a) (Xf x10)) (Xg x10))))) b0)
% 68.46/68.66 Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) (fun (Xx:b)=> (forall (x10:b), (((eq a) (Xf x10)) (Xg x10))))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (forall (x10:b), (((eq a) (Xf x10)) (Xg x10))))) b0)
% 68.46/68.66 Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) (fun (Xx:b)=> (forall (x10:b), (((eq a) (Xf x10)) (Xg x10))))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (forall (x10:b), (((eq a) (Xf x10)) (Xg x10))))) b0)
% 68.46/68.66 Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) (fun (Xx:b)=> (forall (x10:b), (((eq a) (Xf x10)) (Xg x10))))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (forall (x10:b), (((eq a) (Xf x10)) (Xg x10))))) b0)
% 68.46/68.66 Found x00:=(x0 (fun (x1:a)=> (P Xf))):((P Xf)->(P Xf))
% 68.46/68.66 Found (x0 (fun (x1:a)=> (P Xf))) as proof of (P0 Xf)
% 68.46/68.66 Found (x0 (fun (x1:a)=> (P Xf))) as proof of (P0 Xf)
% 68.46/68.66 Found x00:=(x0 (fun (x1:a)=> (P Xf))):((P Xf)->(P Xf))
% 68.46/68.66 Found (x0 (fun (x1:a)=> (P Xf))) as proof of (P0 Xf)
% 68.46/68.66 Found (x0 (fun (x1:a)=> (P Xf))) as proof of (P0 Xf)
% 68.46/68.66 Found b_DUMMY:b
% 68.46/68.66 Found b_DUMMY as proof of b
% 68.46/68.66 Found eq_ref00:=(eq_ref0 b0):(((eq (b->a)) b0) b0)
% 68.46/68.66 Found (eq_ref0 b0) as proof of (((eq (b->a)) b0) Xf)
% 68.46/68.66 Found ((eq_ref (b->a)) b0) as proof of (((eq (b->a)) b0) Xf)
% 68.46/68.66 Found ((eq_ref (b->a)) b0) as proof of (((eq (b->a)) b0) Xf)
% 68.46/68.66 Found ((eq_ref (b->a)) b0) as proof of (((eq (b->a)) b0) Xf)
% 68.46/68.66 Found ((ex_intro00 b_DUMMY) ((eq_ref (b->a)) b0)) as proof of (P b0)
% 68.46/68.66 Found (((ex_intro0 (fun (Xx:b)=> (((eq (b->a)) b0) Xf))) b_DUMMY) ((eq_ref (b->a)) b0)) as proof of (P b0)
% 68.46/68.66 Found ((((ex_intro b) (fun (Xx:b)=> (((eq (b->a)) b0) Xf))) b_DUMMY) ((eq_ref (b->a)) b0)) as proof of (P b0)
% 68.46/68.66 Found ((((ex_intro b) (fun (Xx:b)=> (((eq (b->a)) b0) Xf))) b_DUMMY) ((eq_ref (b->a)) b0)) as proof of (P b0)
% 68.46/68.66 Found x00:=(x0 (fun (x1:a)=> (P Xg))):((P Xg)->(P Xg))
% 68.46/68.66 Found (x0 (fun (x1:a)=> (P Xg))) as proof of (P0 Xg)
% 68.46/68.66 Found (x0 (fun (x1:a)=> (P Xg))) as proof of (P0 Xg)
% 68.46/68.66 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xx:b)=> (P Xf))):(((eq (b->Prop)) (fun (Xx:b)=> (P Xf))) (fun (x:b)=> (P Xf)))
% 68.46/68.66 Found (eta_expansion_dep00 (fun (Xx:b)=> (P Xf))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (P Xf))) b0)
% 68.46/68.66 Found ((eta_expansion_dep0 (fun (x4:b)=> Prop)) (fun (Xx:b)=> (P Xf))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (P Xf))) b0)
% 68.46/68.66 Found (((eta_expansion_dep b) (fun (x4:b)=> Prop)) (fun (Xx:b)=> (P Xf))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (P Xf))) b0)
% 68.46/68.66 Found (((eta_expansion_dep b) (fun (x4:b)=> Prop)) (fun (Xx:b)=> (P Xf))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (P Xf))) b0)
% 68.46/68.66 Found (((eta_expansion_dep b) (fun (x4:b)=> Prop)) (fun (Xx:b)=> (P Xf))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (P Xf))) b0)
% 68.46/68.66 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xx:b)=> (((eq a) (Xf x1)) (Xg x1)))):(((eq (b->Prop)) (fun (Xx:b)=> (((eq a) (Xf x1)) (Xg x1)))) (fun (x:b)=> (((eq a) (Xf x1)) (Xg x1))))
% 68.46/68.66 Found (eta_expansion_dep00 (fun (Xx:b)=> (((eq a) (Xf x1)) (Xg x1)))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (((eq a) (Xf x1)) (Xg x1)))) b0)
% 68.46/68.66 Found ((eta_expansion_dep0 (fun (x4:b)=> Prop)) (fun (Xx:b)=> (((eq a) (Xf x1)) (Xg x1)))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (((eq a) (Xf x1)) (Xg x1)))) b0)
% 68.46/68.66 Found (((eta_expansion_dep b) (fun (x4:b)=> Prop)) (fun (Xx:b)=> (((eq a) (Xf x1)) (Xg x1)))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (((eq a) (Xf x1)) (Xg x1)))) b0)
% 68.46/68.66 Found (((eta_expansion_dep b) (fun (x4:b)=> Prop)) (fun (Xx:b)=> (((eq a) (Xf x1)) (Xg x1)))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (((eq a) (Xf x1)) (Xg x1)))) b0)
% 70.16/70.38 Found (((eta_expansion_dep b) (fun (x4:b)=> Prop)) (fun (Xx:b)=> (((eq a) (Xf x1)) (Xg x1)))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (((eq a) (Xf x1)) (Xg x1)))) b0)
% 70.16/70.38 Found eta_expansion000:=(eta_expansion00 (fun (Xx:b)=> (((eq a) (Xf x1)) (Xg x1)))):(((eq (b->Prop)) (fun (Xx:b)=> (((eq a) (Xf x1)) (Xg x1)))) (fun (x:b)=> (((eq a) (Xf x1)) (Xg x1))))
% 70.16/70.38 Found (eta_expansion00 (fun (Xx:b)=> (((eq a) (Xf x1)) (Xg x1)))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (((eq a) (Xf x1)) (Xg x1)))) b0)
% 70.16/70.38 Found ((eta_expansion0 Prop) (fun (Xx:b)=> (((eq a) (Xf x1)) (Xg x1)))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (((eq a) (Xf x1)) (Xg x1)))) b0)
% 70.16/70.38 Found (((eta_expansion b) Prop) (fun (Xx:b)=> (((eq a) (Xf x1)) (Xg x1)))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (((eq a) (Xf x1)) (Xg x1)))) b0)
% 70.16/70.38 Found (((eta_expansion b) Prop) (fun (Xx:b)=> (((eq a) (Xf x1)) (Xg x1)))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (((eq a) (Xf x1)) (Xg x1)))) b0)
% 70.16/70.38 Found (((eta_expansion b) Prop) (fun (Xx:b)=> (((eq a) (Xf x1)) (Xg x1)))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (((eq a) (Xf x1)) (Xg x1)))) b0)
% 70.16/70.38 Found eq_ref00:=(eq_ref0 b0):(((eq (b->a)) b0) b0)
% 70.16/70.38 Found (eq_ref0 b0) as proof of (((eq (b->a)) b0) Xf)
% 70.16/70.38 Found ((eq_ref (b->a)) b0) as proof of (((eq (b->a)) b0) Xf)
% 70.16/70.38 Found ((eq_ref (b->a)) b0) as proof of (((eq (b->a)) b0) Xf)
% 70.16/70.38 Found ((eq_ref (b->a)) b0) as proof of (((eq (b->a)) b0) Xf)
% 70.16/70.38 Found eta_expansion_dep000:=(eta_expansion_dep00 Xg):(((eq (b->a)) Xg) (fun (x:b)=> (Xg x)))
% 70.16/70.38 Found (eta_expansion_dep00 Xg) as proof of (((eq (b->a)) Xg) b0)
% 70.16/70.38 Found ((eta_expansion_dep0 (fun (x2:b)=> a)) Xg) as proof of (((eq (b->a)) Xg) b0)
% 70.16/70.38 Found (((eta_expansion_dep b) (fun (x2:b)=> a)) Xg) as proof of (((eq (b->a)) Xg) b0)
% 70.16/70.38 Found (((eta_expansion_dep b) (fun (x2:b)=> a)) Xg) as proof of (((eq (b->a)) Xg) b0)
% 70.16/70.38 Found (((eta_expansion_dep b) (fun (x2:b)=> a)) Xg) as proof of (((eq (b->a)) Xg) b0)
% 70.16/70.38 Found eq_ref00:=(eq_ref0 b0):(((eq (b->a)) b0) b0)
% 70.16/70.38 Found (eq_ref0 b0) as proof of (((eq (b->a)) b0) Xf)
% 70.16/70.38 Found ((eq_ref (b->a)) b0) as proof of (((eq (b->a)) b0) Xf)
% 70.16/70.38 Found ((eq_ref (b->a)) b0) as proof of (((eq (b->a)) b0) Xf)
% 70.16/70.38 Found ((eq_ref (b->a)) b0) as proof of (((eq (b->a)) b0) Xf)
% 70.16/70.38 Found eta_expansion_dep000:=(eta_expansion_dep00 Xg):(((eq (b->a)) Xg) (fun (x:b)=> (Xg x)))
% 70.16/70.38 Found (eta_expansion_dep00 Xg) as proof of (((eq (b->a)) Xg) b0)
% 70.16/70.38 Found ((eta_expansion_dep0 (fun (x2:b)=> a)) Xg) as proof of (((eq (b->a)) Xg) b0)
% 70.16/70.38 Found (((eta_expansion_dep b) (fun (x2:b)=> a)) Xg) as proof of (((eq (b->a)) Xg) b0)
% 70.16/70.38 Found (((eta_expansion_dep b) (fun (x2:b)=> a)) Xg) as proof of (((eq (b->a)) Xg) b0)
% 70.16/70.38 Found (((eta_expansion_dep b) (fun (x2:b)=> a)) Xg) as proof of (((eq (b->a)) Xg) b0)
% 70.16/70.38 Found eq_ref00:=(eq_ref0 b0):(((eq (b->a)) b0) b0)
% 70.16/70.38 Found (eq_ref0 b0) as proof of (((eq (b->a)) b0) Xf)
% 70.16/70.38 Found ((eq_ref (b->a)) b0) as proof of (((eq (b->a)) b0) Xf)
% 70.16/70.38 Found ((eq_ref (b->a)) b0) as proof of (((eq (b->a)) b0) Xf)
% 70.16/70.38 Found ((eq_ref (b->a)) b0) as proof of (((eq (b->a)) b0) Xf)
% 70.16/70.38 Found eta_expansion_dep000:=(eta_expansion_dep00 Xg):(((eq (b->a)) Xg) (fun (x:b)=> (Xg x)))
% 70.16/70.38 Found (eta_expansion_dep00 Xg) as proof of (((eq (b->a)) Xg) b0)
% 70.16/70.38 Found ((eta_expansion_dep0 (fun (x2:b)=> a)) Xg) as proof of (((eq (b->a)) Xg) b0)
% 70.16/70.38 Found (((eta_expansion_dep b) (fun (x2:b)=> a)) Xg) as proof of (((eq (b->a)) Xg) b0)
% 70.16/70.38 Found (((eta_expansion_dep b) (fun (x2:b)=> a)) Xg) as proof of (((eq (b->a)) Xg) b0)
% 70.16/70.38 Found (((eta_expansion_dep b) (fun (x2:b)=> a)) Xg) as proof of (((eq (b->a)) Xg) b0)
% 70.16/70.38 Found eq_ref00:=(eq_ref0 b0):(((eq (b->a)) b0) b0)
% 70.16/70.38 Found (eq_ref0 b0) as proof of (((eq (b->a)) b0) Xf)
% 70.16/70.38 Found ((eq_ref (b->a)) b0) as proof of (((eq (b->a)) b0) Xf)
% 70.16/70.38 Found ((eq_ref (b->a)) b0) as proof of (((eq (b->a)) b0) Xf)
% 70.16/70.38 Found ((eq_ref (b->a)) b0) as proof of (((eq (b->a)) b0) Xf)
% 70.16/70.38 Found eta_expansion_dep000:=(eta_expansion_dep00 Xg):(((eq (b->a)) Xg) (fun (x:b)=> (Xg x)))
% 70.16/70.38 Found (eta_expansion_dep00 Xg) as proof of (((eq (b->a)) Xg) b0)
% 70.16/70.38 Found ((eta_expansion_dep0 (fun (x2:b)=> a)) Xg) as proof of (((eq (b->a)) Xg) b0)
% 70.16/70.38 Found (((eta_expansion_dep b) (fun (x2:b)=> a)) Xg) as proof of (((eq (b->a)) Xg) b0)
% 74.91/75.16 Found (((eta_expansion_dep b) (fun (x2:b)=> a)) Xg) as proof of (((eq (b->a)) Xg) b0)
% 74.91/75.16 Found (((eta_expansion_dep b) (fun (x2:b)=> a)) Xg) as proof of (((eq (b->a)) Xg) b0)
% 74.91/75.16 Found b_DUMMY:b
% 74.91/75.16 Found b_DUMMY as proof of b
% 74.91/75.16 Found eq_ref00:=(eq_ref0 (f x2)):(((eq Prop) (f x2)) (f x2))
% 74.91/75.16 Found (eq_ref0 (f x2)) as proof of (((eq Prop) (f x2)) (forall (x10:b), (((eq a) (Xf x10)) (Xg x10))))
% 74.91/75.16 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) (forall (x10:b), (((eq a) (Xf x10)) (Xg x10))))
% 74.91/75.16 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) (forall (x10:b), (((eq a) (Xf x10)) (Xg x10))))
% 74.91/75.16 Found (fun (x2:b)=> ((eq_ref Prop) (f x2))) as proof of (((eq Prop) (f x2)) (forall (x10:b), (((eq a) (Xf x10)) (Xg x10))))
% 74.91/75.16 Found (fun (x2:b)=> ((eq_ref Prop) (f x2))) as proof of (forall (x:b), (((eq Prop) (f x)) (forall (x10:b), (((eq a) (Xf x10)) (Xg x10)))))
% 74.91/75.16 Found eq_ref00:=(eq_ref0 (f x2)):(((eq Prop) (f x2)) (f x2))
% 74.91/75.16 Found (eq_ref0 (f x2)) as proof of (((eq Prop) (f x2)) (forall (x10:b), (((eq a) (Xf x10)) (Xg x10))))
% 74.91/75.16 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) (forall (x10:b), (((eq a) (Xf x10)) (Xg x10))))
% 74.91/75.16 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) (forall (x10:b), (((eq a) (Xf x10)) (Xg x10))))
% 74.91/75.16 Found (fun (x2:b)=> ((eq_ref Prop) (f x2))) as proof of (((eq Prop) (f x2)) (forall (x10:b), (((eq a) (Xf x10)) (Xg x10))))
% 74.91/75.16 Found (fun (x2:b)=> ((eq_ref Prop) (f x2))) as proof of (forall (x:b), (((eq Prop) (f x)) (forall (x10:b), (((eq a) (Xf x10)) (Xg x10)))))
% 74.91/75.16 Found eta_expansion000:=(eta_expansion00 (fun (Xx:b)=> ((P (Xf x1))->(P (Xg x1))))):(((eq (b->Prop)) (fun (Xx:b)=> ((P (Xf x1))->(P (Xg x1))))) (fun (x:b)=> ((P (Xf x1))->(P (Xg x1)))))
% 74.91/75.16 Found (eta_expansion00 (fun (Xx:b)=> ((P (Xf x1))->(P (Xg x1))))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> ((P (Xf x1))->(P (Xg x1))))) b0)
% 74.91/75.16 Found ((eta_expansion0 Prop) (fun (Xx:b)=> ((P (Xf x1))->(P (Xg x1))))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> ((P (Xf x1))->(P (Xg x1))))) b0)
% 74.91/75.16 Found (((eta_expansion b) Prop) (fun (Xx:b)=> ((P (Xf x1))->(P (Xg x1))))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> ((P (Xf x1))->(P (Xg x1))))) b0)
% 74.91/75.16 Found (((eta_expansion b) Prop) (fun (Xx:b)=> ((P (Xf x1))->(P (Xg x1))))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> ((P (Xf x1))->(P (Xg x1))))) b0)
% 74.91/75.16 Found (((eta_expansion b) Prop) (fun (Xx:b)=> ((P (Xf x1))->(P (Xg x1))))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> ((P (Xf x1))->(P (Xg x1))))) b0)
% 74.91/75.16 Found eq_ref00:=(eq_ref0 (fun (Xx:b)=> ((P (Xf x1))->(P (Xg x1))))):(((eq (b->Prop)) (fun (Xx:b)=> ((P (Xf x1))->(P (Xg x1))))) (fun (Xx:b)=> ((P (Xf x1))->(P (Xg x1)))))
% 74.91/75.16 Found (eq_ref0 (fun (Xx:b)=> ((P (Xf x1))->(P (Xg x1))))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> ((P (Xf x1))->(P (Xg x1))))) b0)
% 74.91/75.16 Found ((eq_ref (b->Prop)) (fun (Xx:b)=> ((P (Xf x1))->(P (Xg x1))))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> ((P (Xf x1))->(P (Xg x1))))) b0)
% 74.91/75.16 Found ((eq_ref (b->Prop)) (fun (Xx:b)=> ((P (Xf x1))->(P (Xg x1))))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> ((P (Xf x1))->(P (Xg x1))))) b0)
% 74.91/75.16 Found ((eq_ref (b->Prop)) (fun (Xx:b)=> ((P (Xf x1))->(P (Xg x1))))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> ((P (Xf x1))->(P (Xg x1))))) b0)
% 74.91/75.16 Found eq_ref00:=(eq_ref0 (f x2)):(((eq Prop) (f x2)) (f x2))
% 74.91/75.16 Found (eq_ref0 (f x2)) as proof of (((eq Prop) (f x2)) (((eq (b->a)) Xg) Xf))
% 74.91/75.16 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) (((eq (b->a)) Xg) Xf))
% 74.91/75.16 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) (((eq (b->a)) Xg) Xf))
% 74.91/75.16 Found (fun (x2:b)=> ((eq_ref Prop) (f x2))) as proof of (((eq Prop) (f x2)) (((eq (b->a)) Xg) Xf))
% 74.91/75.16 Found (fun (x2:b)=> ((eq_ref Prop) (f x2))) as proof of (forall (x:b), (((eq Prop) (f x)) (((eq (b->a)) Xg) Xf)))
% 74.91/75.16 Found eq_ref00:=(eq_ref0 (f x2)):(((eq Prop) (f x2)) (f x2))
% 74.91/75.16 Found (eq_ref0 (f x2)) as proof of (((eq Prop) (f x2)) (((eq (b->a)) Xg) Xf))
% 74.91/75.16 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) (((eq (b->a)) Xg) Xf))
% 74.91/75.16 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) (((eq (b->a)) Xg) Xf))
% 74.91/75.16 Found (fun (x2:b)=> ((eq_ref Prop) (f x2))) as proof of (((eq Prop) (f x2)) (((eq (b->a)) Xg) Xf))
% 80.35/80.58 Found (fun (x2:b)=> ((eq_ref Prop) (f x2))) as proof of (forall (x:b), (((eq Prop) (f x)) (((eq (b->a)) Xg) Xf)))
% 80.35/80.58 Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% 80.35/80.58 Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) (((eq a) (Xf x1)) (Xg x1)))
% 80.35/80.58 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (((eq a) (Xf x1)) (Xg x1)))
% 80.35/80.58 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (((eq a) (Xf x1)) (Xg x1)))
% 80.35/80.58 Found (fun (x3:b)=> ((eq_ref Prop) (f x3))) as proof of (((eq Prop) (f x3)) (((eq a) (Xf x1)) (Xg x1)))
% 80.35/80.58 Found (fun (x3:b)=> ((eq_ref Prop) (f x3))) as proof of (forall (x:b), (((eq Prop) (f x)) (((eq a) (Xf x1)) (Xg x1))))
% 80.35/80.58 Found x00:=(x0 (fun (x2:a)=> (P (Xf x1)))):((P (Xf x1))->(P (Xf x1)))
% 80.35/80.58 Found (x0 (fun (x2:a)=> (P (Xf x1)))) as proof of (P0 (Xf x1))
% 80.35/80.58 Found (x0 (fun (x2:a)=> (P (Xf x1)))) as proof of (P0 (Xf x1))
% 80.35/80.58 Found x00:=(x0 (fun (x2:a)=> (P (Xf x1)))):((P (Xf x1))->(P (Xf x1)))
% 80.35/80.58 Found (x0 (fun (x2:a)=> (P (Xf x1)))) as proof of (P0 (Xf x1))
% 80.35/80.58 Found (x0 (fun (x2:a)=> (P (Xf x1)))) as proof of (P0 (Xf x1))
% 80.35/80.59 Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% 80.35/80.59 Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) (((eq a) (Xf x1)) (Xg x1)))
% 80.35/80.59 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (((eq a) (Xf x1)) (Xg x1)))
% 80.35/80.59 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (((eq a) (Xf x1)) (Xg x1)))
% 80.35/80.59 Found (fun (x3:b)=> ((eq_ref Prop) (f x3))) as proof of (((eq Prop) (f x3)) (((eq a) (Xf x1)) (Xg x1)))
% 80.35/80.59 Found (fun (x3:b)=> ((eq_ref Prop) (f x3))) as proof of (forall (x:b), (((eq Prop) (f x)) (((eq a) (Xf x1)) (Xg x1))))
% 80.35/80.59 Found eq_ref00:=(eq_ref0 (Xf x1)):(((eq a) (Xf x1)) (Xf x1))
% 80.35/80.59 Found (eq_ref0 (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 80.35/80.59 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 80.35/80.59 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 80.35/80.59 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 80.35/80.59 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 80.35/80.59 Found (eq_ref0 b0) as proof of (((eq a) b0) (Xg x1))
% 80.35/80.59 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 80.35/80.59 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 80.35/80.59 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 80.35/80.59 Found eq_ref00:=(eq_ref0 (Xf x1)):(((eq a) (Xf x1)) (Xf x1))
% 80.35/80.59 Found (eq_ref0 (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 80.35/80.59 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 80.35/80.59 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 80.35/80.59 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 80.35/80.59 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 80.35/80.59 Found (eq_ref0 b0) as proof of (((eq a) b0) (Xg x1))
% 80.35/80.59 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 80.35/80.59 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 80.35/80.59 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 80.35/80.59 Found eq_ref00:=(eq_ref0 (Xf x1)):(((eq a) (Xf x1)) (Xf x1))
% 80.35/80.59 Found (eq_ref0 (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 80.35/80.59 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 80.35/80.59 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 80.35/80.59 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 80.35/80.59 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 80.35/80.59 Found (eq_ref0 b0) as proof of (((eq a) b0) (Xg x1))
% 80.35/80.59 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 80.35/80.59 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 80.35/80.59 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 80.35/80.59 Found eq_ref00:=(eq_ref0 (Xf x1)):(((eq a) (Xf x1)) (Xf x1))
% 80.35/80.59 Found (eq_ref0 (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 80.35/80.59 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 80.35/80.59 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 80.35/80.59 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 80.35/80.59 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 80.35/80.59 Found (eq_ref0 b0) as proof of (((eq a) b0) (Xg x1))
% 80.35/80.59 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 80.35/80.59 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 80.35/80.59 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 80.35/80.59 Found eq_ref00:=(eq_ref0 (f x2)):(((eq Prop) (f x2)) (f x2))
% 80.35/80.59 Found (eq_ref0 (f x2)) as proof of (((eq Prop) (f x2)) ((P Xg)->(P Xf)))
% 80.35/80.59 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) ((P Xg)->(P Xf)))
% 81.95/82.20 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) ((P Xg)->(P Xf)))
% 81.95/82.20 Found (fun (x2:b)=> ((eq_ref Prop) (f x2))) as proof of (((eq Prop) (f x2)) ((P Xg)->(P Xf)))
% 81.95/82.20 Found (fun (x2:b)=> ((eq_ref Prop) (f x2))) as proof of (forall (x:b), (((eq Prop) (f x)) ((P Xg)->(P Xf))))
% 81.95/82.20 Found eq_ref00:=(eq_ref0 (f x2)):(((eq Prop) (f x2)) (f x2))
% 81.95/82.20 Found (eq_ref0 (f x2)) as proof of (((eq Prop) (f x2)) ((P Xg)->(P Xf)))
% 81.95/82.20 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) ((P Xg)->(P Xf)))
% 81.95/82.20 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) ((P Xg)->(P Xf)))
% 81.95/82.20 Found (fun (x2:b)=> ((eq_ref Prop) (f x2))) as proof of (((eq Prop) (f x2)) ((P Xg)->(P Xf)))
% 81.95/82.20 Found (fun (x2:b)=> ((eq_ref Prop) (f x2))) as proof of (forall (x:b), (((eq Prop) (f x)) ((P Xg)->(P Xf))))
% 81.95/82.20 Found eq_ref00:=(eq_ref0 (Xf x1)):(((eq a) (Xf x1)) (Xf x1))
% 81.95/82.20 Found (eq_ref0 (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 81.95/82.20 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 81.95/82.20 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 81.95/82.20 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 81.95/82.20 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 81.95/82.20 Found (eq_ref0 b0) as proof of (((eq a) b0) (Xg x1))
% 81.95/82.20 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 81.95/82.20 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 81.95/82.20 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 81.95/82.20 Found eq_ref00:=(eq_ref0 (Xf x1)):(((eq a) (Xf x1)) (Xf x1))
% 81.95/82.20 Found (eq_ref0 (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 81.95/82.20 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 81.95/82.20 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 81.95/82.20 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 81.95/82.20 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 81.95/82.20 Found (eq_ref0 b0) as proof of (((eq a) b0) (Xg x1))
% 81.95/82.20 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 81.95/82.20 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 81.95/82.20 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 81.95/82.20 Found eq_ref00:=(eq_ref0 (Xf x1)):(((eq a) (Xf x1)) (Xf x1))
% 81.95/82.20 Found (eq_ref0 (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 81.95/82.20 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 81.95/82.20 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 81.95/82.20 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 81.95/82.20 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 81.95/82.20 Found (eq_ref0 b0) as proof of (((eq a) b0) (Xg x1))
% 81.95/82.20 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 81.95/82.20 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 81.95/82.20 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 81.95/82.20 Found eq_ref00:=(eq_ref0 (Xf x1)):(((eq a) (Xf x1)) (Xf x1))
% 81.95/82.20 Found (eq_ref0 (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 81.95/82.20 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 81.95/82.20 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 81.95/82.20 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 81.95/82.20 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 81.95/82.20 Found (eq_ref0 b0) as proof of (((eq a) b0) (Xg x1))
% 81.95/82.20 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 81.95/82.20 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 81.95/82.20 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 81.95/82.20 Found eta_expansion000:=(eta_expansion00 (fun (Xx:b)=> (P (Xg x1)))):(((eq (b->Prop)) (fun (Xx:b)=> (P (Xg x1)))) (fun (x:b)=> (P (Xg x1))))
% 81.95/82.20 Found (eta_expansion00 (fun (Xx:b)=> (P (Xg x1)))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (P (Xg x1)))) b0)
% 81.95/82.20 Found ((eta_expansion0 Prop) (fun (Xx:b)=> (P (Xg x1)))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (P (Xg x1)))) b0)
% 81.95/82.20 Found (((eta_expansion b) Prop) (fun (Xx:b)=> (P (Xg x1)))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (P (Xg x1)))) b0)
% 81.95/82.20 Found (((eta_expansion b) Prop) (fun (Xx:b)=> (P (Xg x1)))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (P (Xg x1)))) b0)
% 81.95/82.20 Found (((eta_expansion b) Prop) (fun (Xx:b)=> (P (Xg x1)))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (P (Xg x1)))) b0)
% 81.95/82.20 Found eq_ref00:=(eq_ref0 (fun (Xx:b)=> (P (Xg x1)))):(((eq (b->Prop)) (fun (Xx:b)=> (P (Xg x1)))) (fun (Xx:b)=> (P (Xg x1))))
% 81.95/82.20 Found (eq_ref0 (fun (Xx:b)=> (P (Xg x1)))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (P (Xg x1)))) b0)
% 81.95/82.20 Found ((eq_ref (b->Prop)) (fun (Xx:b)=> (P (Xg x1)))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (P (Xg x1)))) b0)
% 88.55/88.77 Found ((eq_ref (b->Prop)) (fun (Xx:b)=> (P (Xg x1)))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (P (Xg x1)))) b0)
% 88.55/88.77 Found ((eq_ref (b->Prop)) (fun (Xx:b)=> (P (Xg x1)))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (P (Xg x1)))) b0)
% 88.55/88.77 Found eq_ref00:=(eq_ref0 (f x2)):(((eq Prop) (f x2)) (f x2))
% 88.55/88.77 Found (eq_ref0 (f x2)) as proof of (((eq Prop) (f x2)) (forall (x10:b), (((eq a) (Xf x10)) (Xg x10))))
% 88.55/88.77 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) (forall (x10:b), (((eq a) (Xf x10)) (Xg x10))))
% 88.55/88.77 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) (forall (x10:b), (((eq a) (Xf x10)) (Xg x10))))
% 88.55/88.77 Found (fun (x2:b)=> ((eq_ref Prop) (f x2))) as proof of (((eq Prop) (f x2)) (forall (x10:b), (((eq a) (Xf x10)) (Xg x10))))
% 88.55/88.77 Found (fun (x2:b)=> ((eq_ref Prop) (f x2))) as proof of (forall (x:b), (((eq Prop) (f x)) (forall (x10:b), (((eq a) (Xf x10)) (Xg x10)))))
% 88.55/88.77 Found eq_ref00:=(eq_ref0 (f x2)):(((eq Prop) (f x2)) (f x2))
% 88.55/88.77 Found (eq_ref0 (f x2)) as proof of (((eq Prop) (f x2)) (forall (x10:b), (((eq a) (Xf x10)) (Xg x10))))
% 88.55/88.77 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) (forall (x10:b), (((eq a) (Xf x10)) (Xg x10))))
% 88.55/88.77 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) (forall (x10:b), (((eq a) (Xf x10)) (Xg x10))))
% 88.55/88.77 Found (fun (x2:b)=> ((eq_ref Prop) (f x2))) as proof of (((eq Prop) (f x2)) (forall (x10:b), (((eq a) (Xf x10)) (Xg x10))))
% 88.55/88.77 Found (fun (x2:b)=> ((eq_ref Prop) (f x2))) as proof of (forall (x:b), (((eq Prop) (f x)) (forall (x10:b), (((eq a) (Xf x10)) (Xg x10)))))
% 88.55/88.77 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 88.55/88.77 Found (eq_ref0 b0) as proof of (P b0)
% 88.55/88.77 Found ((eq_ref a) b0) as proof of (P b0)
% 88.55/88.77 Found ((eq_ref a) b0) as proof of (P b0)
% 88.55/88.77 Found ((eq_ref a) b0) as proof of (P b0)
% 88.55/88.77 Found eq_ref00:=(eq_ref0 (Xg x1)):(((eq a) (Xg x1)) (Xg x1))
% 88.55/88.77 Found (eq_ref0 (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 88.55/88.77 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 88.55/88.77 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 88.55/88.77 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 88.55/88.77 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 88.55/88.77 Found (eq_ref0 b0) as proof of (P b0)
% 88.55/88.77 Found ((eq_ref a) b0) as proof of (P b0)
% 88.55/88.77 Found ((eq_ref a) b0) as proof of (P b0)
% 88.55/88.77 Found ((eq_ref a) b0) as proof of (P b0)
% 88.55/88.77 Found eq_ref00:=(eq_ref0 (Xg x1)):(((eq a) (Xg x1)) (Xg x1))
% 88.55/88.77 Found (eq_ref0 (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 88.55/88.77 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 88.55/88.77 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 88.55/88.77 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 88.55/88.77 Found eq_ref00:=(eq_ref0 (b0 x1)):(((eq a) (b0 x1)) (b0 x1))
% 88.55/88.77 Found (eq_ref0 (b0 x1)) as proof of (P b0)
% 88.55/88.77 Found ((eq_ref a) (b0 x1)) as proof of (P b0)
% 88.55/88.77 Found ((eq_ref a) (b0 x1)) as proof of (P b0)
% 88.55/88.77 Found ((eq_ref a) (b0 x1)) as proof of (P b0)
% 88.55/88.77 Found eta_expansion_dep000:=(eta_expansion_dep00 Xg):(((eq (b->a)) Xg) (fun (x:b)=> (Xg x)))
% 88.55/88.77 Found (eta_expansion_dep00 Xg) as proof of (((eq (b->a)) Xg) b0)
% 88.55/88.77 Found ((eta_expansion_dep0 (fun (x3:b)=> a)) Xg) as proof of (((eq (b->a)) Xg) b0)
% 88.55/88.77 Found (((eta_expansion_dep b) (fun (x3:b)=> a)) Xg) as proof of (((eq (b->a)) Xg) b0)
% 88.55/88.77 Found (((eta_expansion_dep b) (fun (x3:b)=> a)) Xg) as proof of (((eq (b->a)) Xg) b0)
% 88.55/88.77 Found (((eta_expansion_dep b) (fun (x3:b)=> a)) Xg) as proof of (((eq (b->a)) Xg) b0)
% 88.55/88.77 Found eq_ref00:=(eq_ref0 (b0 x1)):(((eq a) (b0 x1)) (b0 x1))
% 88.55/88.77 Found (eq_ref0 (b0 x1)) as proof of (P b0)
% 88.55/88.77 Found ((eq_ref a) (b0 x1)) as proof of (P b0)
% 88.55/88.77 Found ((eq_ref a) (b0 x1)) as proof of (P b0)
% 88.55/88.77 Found ((eq_ref a) (b0 x1)) as proof of (P b0)
% 88.55/88.77 Found eq_ref00:=(eq_ref0 Xg):(((eq (b->a)) Xg) Xg)
% 88.55/88.77 Found (eq_ref0 Xg) as proof of (((eq (b->a)) Xg) b0)
% 88.55/88.77 Found ((eq_ref (b->a)) Xg) as proof of (((eq (b->a)) Xg) b0)
% 88.55/88.77 Found ((eq_ref (b->a)) Xg) as proof of (((eq (b->a)) Xg) b0)
% 88.55/88.77 Found ((eq_ref (b->a)) Xg) as proof of (((eq (b->a)) Xg) b0)
% 88.55/88.77 Found x00:=(x0 (fun (x1:a)=> (P Xf))):((P Xf)->(P Xf))
% 88.55/88.77 Found (x0 (fun (x1:a)=> (P Xf))) as proof of (P0 Xf)
% 88.55/88.77 Found (x0 (fun (x1:a)=> (P Xf))) as proof of (P0 Xf)
% 88.55/88.77 Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% 88.55/88.77 Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) (P Xf))
% 98.81/99.05 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (P Xf))
% 98.81/99.05 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (P Xf))
% 98.81/99.05 Found (fun (x3:b)=> ((eq_ref Prop) (f x3))) as proof of (((eq Prop) (f x3)) (P Xf))
% 98.81/99.05 Found (fun (x3:b)=> ((eq_ref Prop) (f x3))) as proof of (forall (x:b), (((eq Prop) (f x)) (P Xf)))
% 98.81/99.05 Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% 98.81/99.05 Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) (P Xf))
% 98.81/99.05 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (P Xf))
% 98.81/99.05 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (P Xf))
% 98.81/99.05 Found (fun (x3:b)=> ((eq_ref Prop) (f x3))) as proof of (((eq Prop) (f x3)) (P Xf))
% 98.81/99.05 Found (fun (x3:b)=> ((eq_ref Prop) (f x3))) as proof of (forall (x:b), (((eq Prop) (f x)) (P Xf)))
% 98.81/99.05 Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% 98.81/99.05 Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) (((eq a) (Xf x1)) (Xg x1)))
% 98.81/99.05 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (((eq a) (Xf x1)) (Xg x1)))
% 98.81/99.05 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (((eq a) (Xf x1)) (Xg x1)))
% 98.81/99.05 Found (fun (x3:b)=> ((eq_ref Prop) (f x3))) as proof of (((eq Prop) (f x3)) (((eq a) (Xf x1)) (Xg x1)))
% 98.81/99.05 Found (fun (x3:b)=> ((eq_ref Prop) (f x3))) as proof of (forall (x:b), (((eq Prop) (f x)) (((eq a) (Xf x1)) (Xg x1))))
% 98.81/99.05 Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% 98.81/99.05 Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) (((eq a) (Xf x1)) (Xg x1)))
% 98.81/99.05 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (((eq a) (Xf x1)) (Xg x1)))
% 98.81/99.05 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (((eq a) (Xf x1)) (Xg x1)))
% 98.81/99.05 Found (fun (x3:b)=> ((eq_ref Prop) (f x3))) as proof of (((eq Prop) (f x3)) (((eq a) (Xf x1)) (Xg x1)))
% 98.81/99.05 Found (fun (x3:b)=> ((eq_ref Prop) (f x3))) as proof of (forall (x:b), (((eq Prop) (f x)) (((eq a) (Xf x1)) (Xg x1))))
% 98.81/99.05 Found x2:(P (Xg x1))
% 98.81/99.05 Instantiate: b0:=(Xg x1):a
% 98.81/99.05 Found x2 as proof of (P0 b0)
% 98.81/99.05 Found eq_ref00:=(eq_ref0 (Xf x1)):(((eq a) (Xf x1)) (Xf x1))
% 98.81/99.05 Found (eq_ref0 (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 98.81/99.05 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 98.81/99.05 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 98.81/99.05 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 98.81/99.05 Found x2:(P (Xg x1))
% 98.81/99.05 Instantiate: b0:=(Xg x1):a
% 98.81/99.05 Found x2 as proof of (P0 b0)
% 98.81/99.05 Found eq_ref00:=(eq_ref0 (Xf x1)):(((eq a) (Xf x1)) (Xf x1))
% 98.81/99.05 Found (eq_ref0 (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 98.81/99.05 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 98.81/99.05 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 98.81/99.05 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 98.81/99.05 Found x00:=(x0 (fun (x1:a)=> (P Xf))):((P Xf)->(P Xf))
% 98.81/99.05 Found (x0 (fun (x1:a)=> (P Xf))) as proof of (P0 Xf)
% 98.81/99.05 Found (x0 (fun (x1:a)=> (P Xf))) as proof of (P0 Xf)
% 98.81/99.05 Found x00:=(x0 (fun (x1:a)=> (P Xf))):((P Xf)->(P Xf))
% 98.81/99.05 Found (x0 (fun (x1:a)=> (P Xf))) as proof of (P0 Xf)
% 98.81/99.05 Found (x0 (fun (x1:a)=> (P Xf))) as proof of (P0 Xf)
% 98.81/99.05 Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% 98.81/99.05 Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) ((P (Xf x1))->(P (Xg x1))))
% 98.81/99.05 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) ((P (Xf x1))->(P (Xg x1))))
% 98.81/99.05 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) ((P (Xf x1))->(P (Xg x1))))
% 98.81/99.05 Found (fun (x3:b)=> ((eq_ref Prop) (f x3))) as proof of (((eq Prop) (f x3)) ((P (Xf x1))->(P (Xg x1))))
% 98.81/99.05 Found (fun (x3:b)=> ((eq_ref Prop) (f x3))) as proof of (forall (x:b), (((eq Prop) (f x)) ((P (Xf x1))->(P (Xg x1)))))
% 98.81/99.05 Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% 98.81/99.05 Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) ((P (Xf x1))->(P (Xg x1))))
% 98.81/99.05 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) ((P (Xf x1))->(P (Xg x1))))
% 98.81/99.05 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) ((P (Xf x1))->(P (Xg x1))))
% 98.81/99.05 Found (fun (x3:b)=> ((eq_ref Prop) (f x3))) as proof of (((eq Prop) (f x3)) ((P (Xf x1))->(P (Xg x1))))
% 98.81/99.05 Found (fun (x3:b)=> ((eq_ref Prop) (f x3))) as proof of (forall (x:b), (((eq Prop) (f x)) ((P (Xf x1))->(P (Xg x1)))))
% 98.81/99.05 Found x2:(P (Xg x1))
% 98.81/99.05 Instantiate: b0:=(Xg x1):a
% 107.34/107.59 Found x2 as proof of (P0 b0)
% 107.34/107.59 Found eq_ref00:=(eq_ref0 (Xf x1)):(((eq a) (Xf x1)) (Xf x1))
% 107.34/107.59 Found (eq_ref0 (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 107.34/107.59 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 107.34/107.59 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 107.34/107.59 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 107.34/107.59 Found x2:(P (Xg x1))
% 107.34/107.59 Instantiate: b0:=(Xg x1):a
% 107.34/107.59 Found x2 as proof of (P0 b0)
% 107.34/107.59 Found eq_ref00:=(eq_ref0 (Xf x1)):(((eq a) (Xf x1)) (Xf x1))
% 107.34/107.59 Found (eq_ref0 (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 107.34/107.59 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 107.34/107.59 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 107.34/107.59 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 107.34/107.59 Found eq_ref00:=(eq_ref0 Xg):(((eq (b->a)) Xg) Xg)
% 107.34/107.59 Found (eq_ref0 Xg) as proof of (((eq (b->a)) Xg) b0)
% 107.34/107.59 Found ((eq_ref (b->a)) Xg) as proof of (((eq (b->a)) Xg) b0)
% 107.34/107.59 Found ((eq_ref (b->a)) Xg) as proof of (((eq (b->a)) Xg) b0)
% 107.34/107.59 Found ((eq_ref (b->a)) Xg) as proof of (((eq (b->a)) Xg) b0)
% 107.34/107.59 Found eta_expansion000:=(eta_expansion00 Xg):(((eq (b->a)) Xg) (fun (x:b)=> (Xg x)))
% 107.34/107.59 Found (eta_expansion00 Xg) as proof of (((eq (b->a)) Xg) b0)
% 107.34/107.59 Found ((eta_expansion0 a) Xg) as proof of (((eq (b->a)) Xg) b0)
% 107.34/107.59 Found (((eta_expansion b) a) Xg) as proof of (((eq (b->a)) Xg) b0)
% 107.34/107.59 Found (((eta_expansion b) a) Xg) as proof of (((eq (b->a)) Xg) b0)
% 107.34/107.59 Found (((eta_expansion b) a) Xg) as proof of (((eq (b->a)) Xg) b0)
% 107.34/107.59 Found eq_ref00:=(eq_ref0 b00):(((eq (b->a)) b00) b00)
% 107.34/107.59 Found (eq_ref0 b00) as proof of (((eq (b->a)) b00) Xf)
% 107.34/107.59 Found ((eq_ref (b->a)) b00) as proof of (((eq (b->a)) b00) Xf)
% 107.34/107.59 Found ((eq_ref (b->a)) b00) as proof of (((eq (b->a)) b00) Xf)
% 107.34/107.59 Found ((eq_ref (b->a)) b00) as proof of (((eq (b->a)) b00) Xf)
% 107.34/107.59 Found eq_ref00:=(eq_ref0 Xg):(((eq (b->a)) Xg) Xg)
% 107.34/107.59 Found (eq_ref0 Xg) as proof of (((eq (b->a)) Xg) b00)
% 107.34/107.59 Found ((eq_ref (b->a)) Xg) as proof of (((eq (b->a)) Xg) b00)
% 107.34/107.59 Found ((eq_ref (b->a)) Xg) as proof of (((eq (b->a)) Xg) b00)
% 107.34/107.59 Found ((eq_ref (b->a)) Xg) as proof of (((eq (b->a)) Xg) b00)
% 107.34/107.59 Found x00:=(x0 (fun (x1:a)=> (P Xg))):((P Xg)->(P Xg))
% 107.34/107.59 Found (x0 (fun (x1:a)=> (P Xg))) as proof of (P0 Xg)
% 107.34/107.59 Found (x0 (fun (x1:a)=> (P Xg))) as proof of (P0 Xg)
% 107.34/107.59 Found eq_ref00:=(eq_ref0 (f x4)):(((eq Prop) (f x4)) (f x4))
% 107.34/107.59 Found (eq_ref0 (f x4)) as proof of (((eq Prop) (f x4)) (P (Xg x1)))
% 107.34/107.59 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (P (Xg x1)))
% 107.34/107.59 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (P (Xg x1)))
% 107.34/107.59 Found (fun (x4:b)=> ((eq_ref Prop) (f x4))) as proof of (((eq Prop) (f x4)) (P (Xg x1)))
% 107.34/107.59 Found (fun (x4:b)=> ((eq_ref Prop) (f x4))) as proof of (forall (x:b), (((eq Prop) (f x)) (P (Xg x1))))
% 107.34/107.59 Found eq_ref00:=(eq_ref0 (f x4)):(((eq Prop) (f x4)) (f x4))
% 107.34/107.59 Found (eq_ref0 (f x4)) as proof of (((eq Prop) (f x4)) (P (Xg x1)))
% 107.34/107.59 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (P (Xg x1)))
% 107.34/107.59 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (P (Xg x1)))
% 107.34/107.59 Found (fun (x4:b)=> ((eq_ref Prop) (f x4))) as proof of (((eq Prop) (f x4)) (P (Xg x1)))
% 107.34/107.59 Found (fun (x4:b)=> ((eq_ref Prop) (f x4))) as proof of (forall (x:b), (((eq Prop) (f x)) (P (Xg x1))))
% 107.34/107.59 Found eq_ref00:=(eq_ref0 (Xg x1)):(((eq a) (Xg x1)) (Xg x1))
% 107.34/107.59 Found (eq_ref0 (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 107.34/107.59 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 107.34/107.59 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 107.34/107.59 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 107.34/107.59 Found eq_ref00:=(eq_ref0 (Xg x1)):(((eq a) (Xg x1)) (Xg x1))
% 107.34/107.59 Found (eq_ref0 (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 107.34/107.59 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 107.34/107.59 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 107.34/107.59 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 107.34/107.59 Found eta_expansion000:=(eta_expansion00 Xg):(((eq (b->a)) Xg) (fun (x:b)=> (Xg x)))
% 107.34/107.59 Found (eta_expansion00 Xg) as proof of (((eq (b->a)) Xg) b0)
% 107.34/107.59 Found ((eta_expansion0 a) Xg) as proof of (((eq (b->a)) Xg) b0)
% 107.34/107.59 Found (((eta_expansion b) a) Xg) as proof of (((eq (b->a)) Xg) b0)
% 107.34/107.59 Found (((eta_expansion b) a) Xg) as proof of (((eq (b->a)) Xg) b0)
% 107.34/107.59 Found (((eta_expansion b) a) Xg) as proof of (((eq (b->a)) Xg) b0)
% 120.54/120.80 Found eq_ref00:=(eq_ref0 Xg):(((eq (b->a)) Xg) Xg)
% 120.54/120.80 Found (eq_ref0 Xg) as proof of (((eq (b->a)) Xg) b0)
% 120.54/120.80 Found ((eq_ref (b->a)) Xg) as proof of (((eq (b->a)) Xg) b0)
% 120.54/120.80 Found ((eq_ref (b->a)) Xg) as proof of (((eq (b->a)) Xg) b0)
% 120.54/120.80 Found ((eq_ref (b->a)) Xg) as proof of (((eq (b->a)) Xg) b0)
% 120.54/120.80 Found eq_ref00:=(eq_ref0 b0):(((eq (b->a)) b0) b0)
% 120.54/120.80 Found (eq_ref0 b0) as proof of (((eq (b->a)) b0) Xg)
% 120.54/120.80 Found ((eq_ref (b->a)) b0) as proof of (((eq (b->a)) b0) Xg)
% 120.54/120.80 Found ((eq_ref (b->a)) b0) as proof of (((eq (b->a)) b0) Xg)
% 120.54/120.80 Found ((eq_ref (b->a)) b0) as proof of (((eq (b->a)) b0) Xg)
% 120.54/120.80 Found eta_expansion000:=(eta_expansion00 Xf):(((eq (b->a)) Xf) (fun (x:b)=> (Xf x)))
% 120.54/120.80 Found (eta_expansion00 Xf) as proof of (((eq (b->a)) Xf) b0)
% 120.54/120.80 Found ((eta_expansion0 a) Xf) as proof of (((eq (b->a)) Xf) b0)
% 120.54/120.80 Found (((eta_expansion b) a) Xf) as proof of (((eq (b->a)) Xf) b0)
% 120.54/120.80 Found (((eta_expansion b) a) Xf) as proof of (((eq (b->a)) Xf) b0)
% 120.54/120.80 Found (((eta_expansion b) a) Xf) as proof of (((eq (b->a)) Xf) b0)
% 120.54/120.80 Found eq_ref00:=(eq_ref0 (Xf x1)):(((eq a) (Xf x1)) (Xf x1))
% 120.54/120.80 Found (eq_ref0 (Xf x1)) as proof of (((eq a) (Xf x1)) b00)
% 120.54/120.80 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b00)
% 120.54/120.80 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b00)
% 120.54/120.80 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b00)
% 120.54/120.80 Found eq_ref00:=(eq_ref0 b00):(((eq a) b00) b00)
% 120.54/120.80 Found (eq_ref0 b00) as proof of (((eq a) b00) (Xg x1))
% 120.54/120.80 Found ((eq_ref a) b00) as proof of (((eq a) b00) (Xg x1))
% 120.54/120.80 Found ((eq_ref a) b00) as proof of (((eq a) b00) (Xg x1))
% 120.54/120.80 Found ((eq_ref a) b00) as proof of (((eq a) b00) (Xg x1))
% 120.54/120.80 Found eq_ref00:=(eq_ref0 (Xf x1)):(((eq a) (Xf x1)) (Xf x1))
% 120.54/120.80 Found (eq_ref0 (Xf x1)) as proof of (((eq a) (Xf x1)) b00)
% 120.54/120.80 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b00)
% 120.54/120.80 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b00)
% 120.54/120.80 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b00)
% 120.54/120.80 Found eq_ref00:=(eq_ref0 b00):(((eq a) b00) b00)
% 120.54/120.80 Found (eq_ref0 b00) as proof of (((eq a) b00) (Xg x1))
% 120.54/120.80 Found ((eq_ref a) b00) as proof of (((eq a) b00) (Xg x1))
% 120.54/120.80 Found ((eq_ref a) b00) as proof of (((eq a) b00) (Xg x1))
% 120.54/120.80 Found ((eq_ref a) b00) as proof of (((eq a) b00) (Xg x1))
% 120.54/120.80 Found eq_ref00:=(eq_ref0 a0):(((eq b) a0) a0)
% 120.54/120.80 Found (eq_ref0 a0) as proof of (((eq b) a0) x1)
% 120.54/120.80 Found ((eq_ref b) a0) as proof of (((eq b) a0) x1)
% 120.54/120.80 Found ((eq_ref b) a0) as proof of (((eq b) a0) x1)
% 120.54/120.80 Found ((eq_ref b) a0) as proof of (((eq b) a0) x1)
% 120.54/120.80 Found eq_ref00:=(eq_ref0 a0):(((eq b) a0) a0)
% 120.54/120.80 Found (eq_ref0 a0) as proof of (((eq b) a0) x1)
% 120.54/120.80 Found ((eq_ref b) a0) as proof of (((eq b) a0) x1)
% 120.54/120.80 Found ((eq_ref b) a0) as proof of (((eq b) a0) x1)
% 120.54/120.80 Found ((eq_ref b) a0) as proof of (((eq b) a0) x1)
% 120.54/120.80 Found x00:=(x0 (fun (x2:a)=> (P1 (Xg x1)))):((P1 (Xg x1))->(P1 (Xg x1)))
% 120.54/120.80 Found (x0 (fun (x2:a)=> (P1 (Xg x1)))) as proof of (P2 (Xg x1))
% 120.54/120.80 Found (x0 (fun (x2:a)=> (P1 (Xg x1)))) as proof of (P2 (Xg x1))
% 120.54/120.80 Found x00:=(x0 (fun (x2:a)=> (P1 (Xg x1)))):((P1 (Xg x1))->(P1 (Xg x1)))
% 120.54/120.80 Found (x0 (fun (x2:a)=> (P1 (Xg x1)))) as proof of (P2 (Xg x1))
% 120.54/120.80 Found (x0 (fun (x2:a)=> (P1 (Xg x1)))) as proof of (P2 (Xg x1))
% 120.54/120.80 Found x00:=(x0 (fun (x2:a)=> (P1 (Xg x1)))):((P1 (Xg x1))->(P1 (Xg x1)))
% 120.54/120.80 Found (x0 (fun (x2:a)=> (P1 (Xg x1)))) as proof of (P2 (Xg x1))
% 120.54/120.80 Found (x0 (fun (x2:a)=> (P1 (Xg x1)))) as proof of (P2 (Xg x1))
% 120.54/120.80 Found x00:=(x0 (fun (x2:a)=> (P1 (Xg x1)))):((P1 (Xg x1))->(P1 (Xg x1)))
% 120.54/120.80 Found (x0 (fun (x2:a)=> (P1 (Xg x1)))) as proof of (P2 (Xg x1))
% 120.54/120.80 Found (x0 (fun (x2:a)=> (P1 (Xg x1)))) as proof of (P2 (Xg x1))
% 120.54/120.80 Found x00:=(x0 (fun (x2:a)=> (P1 (Xg x1)))):((P1 (Xg x1))->(P1 (Xg x1)))
% 120.54/120.80 Found (x0 (fun (x2:a)=> (P1 (Xg x1)))) as proof of (P2 (Xg x1))
% 120.54/120.80 Found (x0 (fun (x2:a)=> (P1 (Xg x1)))) as proof of (P2 (Xg x1))
% 120.54/120.80 Found x00:=(x0 (fun (x2:a)=> (P1 (Xg x1)))):((P1 (Xg x1))->(P1 (Xg x1)))
% 120.54/120.80 Found (x0 (fun (x2:a)=> (P1 (Xg x1)))) as proof of (P2 (Xg x1))
% 120.54/120.80 Found (x0 (fun (x2:a)=> (P1 (Xg x1)))) as proof of (P2 (Xg x1))
% 120.54/120.80 Found x00:=(x0 (fun (x2:a)=> (P1 (Xg x1)))):((P1 (Xg x1))->(P1 (Xg x1)))
% 120.54/120.80 Found (x0 (fun (x2:a)=> (P1 (Xg x1)))) as proof of (P2 (Xg x1))
% 120.54/120.80 Found (x0 (fun (x2:a)=> (P1 (Xg x1)))) as proof of (P2 (Xg x1))
% 133.80/134.08 Found x00:=(x0 (fun (x2:a)=> (P1 (Xg x1)))):((P1 (Xg x1))->(P1 (Xg x1)))
% 133.80/134.08 Found (x0 (fun (x2:a)=> (P1 (Xg x1)))) as proof of (P2 (Xg x1))
% 133.80/134.08 Found (x0 (fun (x2:a)=> (P1 (Xg x1)))) as proof of (P2 (Xg x1))
% 133.80/134.08 Found eta_expansion000:=(eta_expansion00 (fun (Xx:b)=> (forall (x10:b), (((eq a) (Xg x10)) (Xf x10))))):(((eq (b->Prop)) (fun (Xx:b)=> (forall (x10:b), (((eq a) (Xg x10)) (Xf x10))))) (fun (x:b)=> (forall (x10:b), (((eq a) (Xg x10)) (Xf x10)))))
% 133.80/134.08 Found (eta_expansion00 (fun (Xx:b)=> (forall (x10:b), (((eq a) (Xg x10)) (Xf x10))))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (forall (x10:b), (((eq a) (Xg x10)) (Xf x10))))) b0)
% 133.80/134.08 Found ((eta_expansion0 Prop) (fun (Xx:b)=> (forall (x10:b), (((eq a) (Xg x10)) (Xf x10))))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (forall (x10:b), (((eq a) (Xg x10)) (Xf x10))))) b0)
% 133.80/134.08 Found (((eta_expansion b) Prop) (fun (Xx:b)=> (forall (x10:b), (((eq a) (Xg x10)) (Xf x10))))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (forall (x10:b), (((eq a) (Xg x10)) (Xf x10))))) b0)
% 133.80/134.08 Found (((eta_expansion b) Prop) (fun (Xx:b)=> (forall (x10:b), (((eq a) (Xg x10)) (Xf x10))))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (forall (x10:b), (((eq a) (Xg x10)) (Xf x10))))) b0)
% 133.80/134.08 Found (((eta_expansion b) Prop) (fun (Xx:b)=> (forall (x10:b), (((eq a) (Xg x10)) (Xf x10))))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (forall (x10:b), (((eq a) (Xg x10)) (Xf x10))))) b0)
% 133.80/134.08 Found eta_expansion000:=(eta_expansion00 (fun (Xx:b)=> (forall (x10:b), (((eq a) (Xg x10)) (Xf x10))))):(((eq (b->Prop)) (fun (Xx:b)=> (forall (x10:b), (((eq a) (Xg x10)) (Xf x10))))) (fun (x:b)=> (forall (x10:b), (((eq a) (Xg x10)) (Xf x10)))))
% 133.80/134.08 Found (eta_expansion00 (fun (Xx:b)=> (forall (x10:b), (((eq a) (Xg x10)) (Xf x10))))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (forall (x10:b), (((eq a) (Xg x10)) (Xf x10))))) b0)
% 133.80/134.08 Found ((eta_expansion0 Prop) (fun (Xx:b)=> (forall (x10:b), (((eq a) (Xg x10)) (Xf x10))))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (forall (x10:b), (((eq a) (Xg x10)) (Xf x10))))) b0)
% 133.80/134.08 Found (((eta_expansion b) Prop) (fun (Xx:b)=> (forall (x10:b), (((eq a) (Xg x10)) (Xf x10))))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (forall (x10:b), (((eq a) (Xg x10)) (Xf x10))))) b0)
% 133.80/134.08 Found (((eta_expansion b) Prop) (fun (Xx:b)=> (forall (x10:b), (((eq a) (Xg x10)) (Xf x10))))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (forall (x10:b), (((eq a) (Xg x10)) (Xf x10))))) b0)
% 133.80/134.08 Found (((eta_expansion b) Prop) (fun (Xx:b)=> (forall (x10:b), (((eq a) (Xg x10)) (Xf x10))))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (forall (x10:b), (((eq a) (Xg x10)) (Xf x10))))) b0)
% 133.80/134.08 Found x00:=(x0 (fun (x1:a)=> (P Xg))):((P Xg)->(P Xg))
% 133.80/134.08 Found (x0 (fun (x1:a)=> (P Xg))) as proof of (P0 Xg)
% 133.80/134.08 Found (x0 (fun (x1:a)=> (P Xg))) as proof of (P0 Xg)
% 133.80/134.08 Found x00:=(x0 (fun (x1:a)=> (P b0))):((P b0)->(P b0))
% 133.80/134.08 Found (x0 (fun (x1:a)=> (P b0))) as proof of (P0 b0)
% 133.80/134.08 Found (x0 (fun (x1:a)=> (P b0))) as proof of (P0 b0)
% 133.80/134.08 Found x00:=(x0 (fun (x1:a)=> (P Xg))):((P Xg)->(P Xg))
% 133.80/134.08 Found (x0 (fun (x1:a)=> (P Xg))) as proof of (P0 Xg)
% 133.80/134.08 Found (x0 (fun (x1:a)=> (P Xg))) as proof of (P0 Xg)
% 133.80/134.08 Found x00:=(x0 (fun (x1:a)=> (P b0))):((P b0)->(P b0))
% 133.80/134.08 Found (x0 (fun (x1:a)=> (P b0))) as proof of (P0 b0)
% 133.80/134.08 Found (x0 (fun (x1:a)=> (P b0))) as proof of (P0 b0)
% 133.80/134.08 Found x00:=(x0 (fun (x2:a)=> (P b0))):((P b0)->(P b0))
% 133.80/134.08 Found (x0 (fun (x2:a)=> (P b0))) as proof of (P0 b0)
% 133.80/134.08 Found (x0 (fun (x2:a)=> (P b0))) as proof of (P0 b0)
% 133.80/134.08 Found x00:=(x0 (fun (x2:a)=> (P b0))):((P b0)->(P b0))
% 133.80/134.08 Found (x0 (fun (x2:a)=> (P b0))) as proof of (P0 b0)
% 133.80/134.08 Found (x0 (fun (x2:a)=> (P b0))) as proof of (P0 b0)
% 133.80/134.08 Found x00:=(x0 (fun (x2:a)=> (P (Xf x1)))):((P (Xf x1))->(P (Xf x1)))
% 133.80/134.08 Found (x0 (fun (x2:a)=> (P (Xf x1)))) as proof of (P0 (Xf x1))
% 133.80/134.08 Found (x0 (fun (x2:a)=> (P (Xf x1)))) as proof of (P0 (Xf x1))
% 133.80/134.08 Found x00:=(x0 (fun (x2:a)=> (P (Xf x1)))):((P (Xf x1))->(P (Xf x1)))
% 133.80/134.08 Found (x0 (fun (x2:a)=> (P (Xf x1)))) as proof of (P0 (Xf x1))
% 133.80/134.08 Found (x0 (fun (x2:a)=> (P (Xf x1)))) as proof of (P0 (Xf x1))
% 133.80/134.08 Found eq_ref00:=(eq_ref0 b00):(((eq (b->a)) b00) b00)
% 133.80/134.08 Found (eq_ref0 b00) as proof of (((eq (b->a)) b00) Xf)
% 133.80/134.08 Found ((eq_ref (b->a)) b00) as proof of (((eq (b->a)) b00) Xf)
% 135.49/135.79 Found ((eq_ref (b->a)) b00) as proof of (((eq (b->a)) b00) Xf)
% 135.49/135.79 Found ((eq_ref (b->a)) b00) as proof of (((eq (b->a)) b00) Xf)
% 135.49/135.79 Found eta_expansion_dep000:=(eta_expansion_dep00 b0):(((eq (b->a)) b0) (fun (x:b)=> (b0 x)))
% 135.49/135.79 Found (eta_expansion_dep00 b0) as proof of (((eq (b->a)) b0) b00)
% 135.49/135.79 Found ((eta_expansion_dep0 (fun (x2:b)=> a)) b0) as proof of (((eq (b->a)) b0) b00)
% 135.49/135.79 Found (((eta_expansion_dep b) (fun (x2:b)=> a)) b0) as proof of (((eq (b->a)) b0) b00)
% 135.49/135.79 Found (((eta_expansion_dep b) (fun (x2:b)=> a)) b0) as proof of (((eq (b->a)) b0) b00)
% 135.49/135.79 Found (((eta_expansion_dep b) (fun (x2:b)=> a)) b0) as proof of (((eq (b->a)) b0) b00)
% 135.49/135.79 Found eta_expansion000:=(eta_expansion00 (fun (Xx:b)=> (((eq a) (Xg x1)) (Xf x1)))):(((eq (b->Prop)) (fun (Xx:b)=> (((eq a) (Xg x1)) (Xf x1)))) (fun (x:b)=> (((eq a) (Xg x1)) (Xf x1))))
% 135.49/135.79 Found (eta_expansion00 (fun (Xx:b)=> (((eq a) (Xg x1)) (Xf x1)))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (((eq a) (Xg x1)) (Xf x1)))) b0)
% 135.49/135.79 Found ((eta_expansion0 Prop) (fun (Xx:b)=> (((eq a) (Xg x1)) (Xf x1)))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (((eq a) (Xg x1)) (Xf x1)))) b0)
% 135.49/135.79 Found (((eta_expansion b) Prop) (fun (Xx:b)=> (((eq a) (Xg x1)) (Xf x1)))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (((eq a) (Xg x1)) (Xf x1)))) b0)
% 135.49/135.79 Found (((eta_expansion b) Prop) (fun (Xx:b)=> (((eq a) (Xg x1)) (Xf x1)))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (((eq a) (Xg x1)) (Xf x1)))) b0)
% 135.49/135.79 Found (((eta_expansion b) Prop) (fun (Xx:b)=> (((eq a) (Xg x1)) (Xf x1)))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (((eq a) (Xg x1)) (Xf x1)))) b0)
% 135.49/135.79 Found eq_ref00:=(eq_ref0 (fun (Xx:b)=> (((eq a) (Xg x1)) (Xf x1)))):(((eq (b->Prop)) (fun (Xx:b)=> (((eq a) (Xg x1)) (Xf x1)))) (fun (Xx:b)=> (((eq a) (Xg x1)) (Xf x1))))
% 135.49/135.79 Found (eq_ref0 (fun (Xx:b)=> (((eq a) (Xg x1)) (Xf x1)))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (((eq a) (Xg x1)) (Xf x1)))) b0)
% 135.49/135.79 Found ((eq_ref (b->Prop)) (fun (Xx:b)=> (((eq a) (Xg x1)) (Xf x1)))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (((eq a) (Xg x1)) (Xf x1)))) b0)
% 135.49/135.79 Found ((eq_ref (b->Prop)) (fun (Xx:b)=> (((eq a) (Xg x1)) (Xf x1)))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (((eq a) (Xg x1)) (Xf x1)))) b0)
% 135.49/135.79 Found ((eq_ref (b->Prop)) (fun (Xx:b)=> (((eq a) (Xg x1)) (Xf x1)))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (((eq a) (Xg x1)) (Xf x1)))) b0)
% 135.49/135.79 Found eta_expansion000:=(eta_expansion00 (fun (Xx:b)=> (((eq a) (Xg x1)) (Xf x1)))):(((eq (b->Prop)) (fun (Xx:b)=> (((eq a) (Xg x1)) (Xf x1)))) (fun (x:b)=> (((eq a) (Xg x1)) (Xf x1))))
% 135.49/135.79 Found (eta_expansion00 (fun (Xx:b)=> (((eq a) (Xg x1)) (Xf x1)))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (((eq a) (Xg x1)) (Xf x1)))) b0)
% 135.49/135.79 Found ((eta_expansion0 Prop) (fun (Xx:b)=> (((eq a) (Xg x1)) (Xf x1)))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (((eq a) (Xg x1)) (Xf x1)))) b0)
% 135.49/135.79 Found (((eta_expansion b) Prop) (fun (Xx:b)=> (((eq a) (Xg x1)) (Xf x1)))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (((eq a) (Xg x1)) (Xf x1)))) b0)
% 135.49/135.79 Found (((eta_expansion b) Prop) (fun (Xx:b)=> (((eq a) (Xg x1)) (Xf x1)))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (((eq a) (Xg x1)) (Xf x1)))) b0)
% 135.49/135.79 Found (((eta_expansion b) Prop) (fun (Xx:b)=> (((eq a) (Xg x1)) (Xf x1)))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (((eq a) (Xg x1)) (Xf x1)))) b0)
% 135.49/135.79 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xx:b)=> (((eq a) (Xg x1)) (Xf x1)))):(((eq (b->Prop)) (fun (Xx:b)=> (((eq a) (Xg x1)) (Xf x1)))) (fun (x:b)=> (((eq a) (Xg x1)) (Xf x1))))
% 135.49/135.79 Found (eta_expansion_dep00 (fun (Xx:b)=> (((eq a) (Xg x1)) (Xf x1)))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (((eq a) (Xg x1)) (Xf x1)))) b0)
% 135.49/135.79 Found ((eta_expansion_dep0 (fun (x4:b)=> Prop)) (fun (Xx:b)=> (((eq a) (Xg x1)) (Xf x1)))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (((eq a) (Xg x1)) (Xf x1)))) b0)
% 135.49/135.79 Found (((eta_expansion_dep b) (fun (x4:b)=> Prop)) (fun (Xx:b)=> (((eq a) (Xg x1)) (Xf x1)))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (((eq a) (Xg x1)) (Xf x1)))) b0)
% 135.49/135.79 Found (((eta_expansion_dep b) (fun (x4:b)=> Prop)) (fun (Xx:b)=> (((eq a) (Xg x1)) (Xf x1)))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (((eq a) (Xg x1)) (Xf x1)))) b0)
% 135.49/135.79 Found (((eta_expansion_dep b) (fun (x4:b)=> Prop)) (fun (Xx:b)=> (((eq a) (Xg x1)) (Xf x1)))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (((eq a) (Xg x1)) (Xf x1)))) b0)
% 145.78/146.11 Found eq_ref00:=(eq_ref0 (f x2)):(((eq Prop) (f x2)) (f x2))
% 145.78/146.11 Found (eq_ref0 (f x2)) as proof of (((eq Prop) (f x2)) (forall (x10:b), (((eq a) (Xg x10)) (Xf x10))))
% 145.78/146.11 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) (forall (x10:b), (((eq a) (Xg x10)) (Xf x10))))
% 145.78/146.11 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) (forall (x10:b), (((eq a) (Xg x10)) (Xf x10))))
% 145.78/146.11 Found (fun (x2:b)=> ((eq_ref Prop) (f x2))) as proof of (((eq Prop) (f x2)) (forall (x10:b), (((eq a) (Xg x10)) (Xf x10))))
% 145.78/146.11 Found (fun (x2:b)=> ((eq_ref Prop) (f x2))) as proof of (forall (x:b), (((eq Prop) (f x)) (forall (x10:b), (((eq a) (Xg x10)) (Xf x10)))))
% 145.78/146.11 Found eq_ref00:=(eq_ref0 (f x2)):(((eq Prop) (f x2)) (f x2))
% 145.78/146.11 Found (eq_ref0 (f x2)) as proof of (((eq Prop) (f x2)) (forall (x10:b), (((eq a) (Xg x10)) (Xf x10))))
% 145.78/146.11 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) (forall (x10:b), (((eq a) (Xg x10)) (Xf x10))))
% 145.78/146.11 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) (forall (x10:b), (((eq a) (Xg x10)) (Xf x10))))
% 145.78/146.11 Found (fun (x2:b)=> ((eq_ref Prop) (f x2))) as proof of (((eq Prop) (f x2)) (forall (x10:b), (((eq a) (Xg x10)) (Xf x10))))
% 145.78/146.11 Found (fun (x2:b)=> ((eq_ref Prop) (f x2))) as proof of (forall (x:b), (((eq Prop) (f x)) (forall (x10:b), (((eq a) (Xg x10)) (Xf x10)))))
% 145.78/146.11 Found b_DUMMY:b
% 145.78/146.11 Found b_DUMMY as proof of b
% 145.78/146.11 Found b_DUMMY:b
% 145.78/146.11 Found b_DUMMY as proof of b
% 145.78/146.11 Found eq_ref00:=(eq_ref0 (fun (Xx:b)=> ((P (Xg x1))->(P (Xf x1))))):(((eq (b->Prop)) (fun (Xx:b)=> ((P (Xg x1))->(P (Xf x1))))) (fun (Xx:b)=> ((P (Xg x1))->(P (Xf x1)))))
% 145.78/146.11 Found (eq_ref0 (fun (Xx:b)=> ((P (Xg x1))->(P (Xf x1))))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> ((P (Xg x1))->(P (Xf x1))))) b0)
% 145.78/146.11 Found ((eq_ref (b->Prop)) (fun (Xx:b)=> ((P (Xg x1))->(P (Xf x1))))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> ((P (Xg x1))->(P (Xf x1))))) b0)
% 145.78/146.11 Found ((eq_ref (b->Prop)) (fun (Xx:b)=> ((P (Xg x1))->(P (Xf x1))))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> ((P (Xg x1))->(P (Xf x1))))) b0)
% 145.78/146.11 Found ((eq_ref (b->Prop)) (fun (Xx:b)=> ((P (Xg x1))->(P (Xf x1))))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> ((P (Xg x1))->(P (Xf x1))))) b0)
% 145.78/146.11 Found eq_ref00:=(eq_ref0 (fun (Xx:b)=> ((P (Xg x1))->(P (Xf x1))))):(((eq (b->Prop)) (fun (Xx:b)=> ((P (Xg x1))->(P (Xf x1))))) (fun (Xx:b)=> ((P (Xg x1))->(P (Xf x1)))))
% 145.78/146.11 Found (eq_ref0 (fun (Xx:b)=> ((P (Xg x1))->(P (Xf x1))))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> ((P (Xg x1))->(P (Xf x1))))) b0)
% 145.78/146.11 Found ((eq_ref (b->Prop)) (fun (Xx:b)=> ((P (Xg x1))->(P (Xf x1))))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> ((P (Xg x1))->(P (Xf x1))))) b0)
% 145.78/146.11 Found ((eq_ref (b->Prop)) (fun (Xx:b)=> ((P (Xg x1))->(P (Xf x1))))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> ((P (Xg x1))->(P (Xf x1))))) b0)
% 145.78/146.11 Found ((eq_ref (b->Prop)) (fun (Xx:b)=> ((P (Xg x1))->(P (Xf x1))))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> ((P (Xg x1))->(P (Xf x1))))) b0)
% 145.78/146.11 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xx:b)=> ((P (Xg x1))->(P (Xf x1))))):(((eq (b->Prop)) (fun (Xx:b)=> ((P (Xg x1))->(P (Xf x1))))) (fun (x:b)=> ((P (Xg x1))->(P (Xf x1)))))
% 145.78/146.11 Found (eta_expansion_dep00 (fun (Xx:b)=> ((P (Xg x1))->(P (Xf x1))))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> ((P (Xg x1))->(P (Xf x1))))) b0)
% 145.78/146.11 Found ((eta_expansion_dep0 (fun (x4:b)=> Prop)) (fun (Xx:b)=> ((P (Xg x1))->(P (Xf x1))))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> ((P (Xg x1))->(P (Xf x1))))) b0)
% 145.78/146.11 Found (((eta_expansion_dep b) (fun (x4:b)=> Prop)) (fun (Xx:b)=> ((P (Xg x1))->(P (Xf x1))))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> ((P (Xg x1))->(P (Xf x1))))) b0)
% 145.78/146.11 Found (((eta_expansion_dep b) (fun (x4:b)=> Prop)) (fun (Xx:b)=> ((P (Xg x1))->(P (Xf x1))))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> ((P (Xg x1))->(P (Xf x1))))) b0)
% 145.78/146.11 Found (((eta_expansion_dep b) (fun (x4:b)=> Prop)) (fun (Xx:b)=> ((P (Xg x1))->(P (Xf x1))))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> ((P (Xg x1))->(P (Xf x1))))) b0)
% 145.78/146.11 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xx:b)=> ((P (Xg x1))->(P (Xf x1))))):(((eq (b->Prop)) (fun (Xx:b)=> ((P (Xg x1))->(P (Xf x1))))) (fun (x:b)=> ((P (Xg x1))->(P (Xf x1)))))
% 150.49/150.79 Found (eta_expansion_dep00 (fun (Xx:b)=> ((P (Xg x1))->(P (Xf x1))))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> ((P (Xg x1))->(P (Xf x1))))) b0)
% 150.49/150.79 Found ((eta_expansion_dep0 (fun (x4:b)=> Prop)) (fun (Xx:b)=> ((P (Xg x1))->(P (Xf x1))))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> ((P (Xg x1))->(P (Xf x1))))) b0)
% 150.49/150.79 Found (((eta_expansion_dep b) (fun (x4:b)=> Prop)) (fun (Xx:b)=> ((P (Xg x1))->(P (Xf x1))))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> ((P (Xg x1))->(P (Xf x1))))) b0)
% 150.49/150.79 Found (((eta_expansion_dep b) (fun (x4:b)=> Prop)) (fun (Xx:b)=> ((P (Xg x1))->(P (Xf x1))))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> ((P (Xg x1))->(P (Xf x1))))) b0)
% 150.49/150.79 Found (((eta_expansion_dep b) (fun (x4:b)=> Prop)) (fun (Xx:b)=> ((P (Xg x1))->(P (Xf x1))))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> ((P (Xg x1))->(P (Xf x1))))) b0)
% 150.49/150.79 Found x00:=(x0 (fun (x2:a)=> (P (Xg x1)))):((P (Xg x1))->(P (Xg x1)))
% 150.49/150.79 Found (x0 (fun (x2:a)=> (P (Xg x1)))) as proof of (P0 (Xg x1))
% 150.49/150.79 Found (x0 (fun (x2:a)=> (P (Xg x1)))) as proof of (P0 (Xg x1))
% 150.49/150.79 Found eq_ref000:=(eq_ref00 P):((P (Xg x1))->(P (Xg x1)))
% 150.49/150.79 Found (eq_ref00 P) as proof of (P0 (Xg x1))
% 150.49/150.79 Found ((eq_ref0 (Xg x1)) P) as proof of (P0 (Xg x1))
% 150.49/150.79 Found (((eq_ref a) (Xg x1)) P) as proof of (P0 (Xg x1))
% 150.49/150.79 Found (((eq_ref a) (Xg x1)) P) as proof of (P0 (Xg x1))
% 150.49/150.79 Found eq_ref00:=(eq_ref0 (b0 x10)):(((eq a) (b0 x10)) (b0 x10))
% 150.49/150.79 Found (eq_ref0 (b0 x10)) as proof of (((eq a) (b0 x10)) (Xf x10))
% 150.49/150.79 Found ((eq_ref a) (b0 x10)) as proof of (((eq a) (b0 x10)) (Xf x10))
% 150.49/150.79 Found ((eq_ref a) (b0 x10)) as proof of (((eq a) (b0 x10)) (Xf x10))
% 150.49/150.79 Found (fun (x10:b)=> ((eq_ref a) (b0 x10))) as proof of (((eq a) (b0 x10)) (Xf x10))
% 150.49/150.79 Found (fun (x10:b)=> ((eq_ref a) (b0 x10))) as proof of (forall (x10:b), (((eq a) (b0 x10)) (Xf x10)))
% 150.49/150.79 Found ((ex_intro00 b_DUMMY) (fun (x10:b)=> ((eq_ref a) (b0 x10)))) as proof of (P b0)
% 150.49/150.79 Found (((ex_intro0 (fun (Xx:b)=> (forall (x10:b), (((eq a) (b0 x10)) (Xf x10))))) b_DUMMY) (fun (x10:b)=> ((eq_ref a) (b0 x10)))) as proof of (P b0)
% 150.49/150.79 Found ((((ex_intro b) (fun (Xx:b)=> (forall (x10:b), (((eq a) (b0 x10)) (Xf x10))))) b_DUMMY) (fun (x10:b)=> ((eq_ref a) (b0 x10)))) as proof of (P b0)
% 150.49/150.79 Found ((((ex_intro b) (fun (Xx:b)=> (forall (x10:b), (((eq a) (b0 x10)) (Xf x10))))) b_DUMMY) (fun (x10:b)=> ((eq_ref a) (b0 x10)))) as proof of (P b0)
% 150.49/150.79 Found eq_ref00:=(eq_ref0 (b0 x10)):(((eq a) (b0 x10)) (b0 x10))
% 150.49/150.79 Found (eq_ref0 (b0 x10)) as proof of (((eq a) (b0 x10)) (Xf x10))
% 150.49/150.79 Found ((eq_ref a) (b0 x10)) as proof of (((eq a) (b0 x10)) (Xf x10))
% 150.49/150.79 Found ((eq_ref a) (b0 x10)) as proof of (((eq a) (b0 x10)) (Xf x10))
% 150.49/150.79 Found (fun (x10:b)=> ((eq_ref a) (b0 x10))) as proof of (((eq a) (b0 x10)) (Xf x10))
% 150.49/150.79 Found (fun (x10:b)=> ((eq_ref a) (b0 x10))) as proof of (forall (x10:b), (((eq a) (b0 x10)) (Xf x10)))
% 150.49/150.79 Found ((ex_intro00 b_DUMMY) (fun (x10:b)=> ((eq_ref a) (b0 x10)))) as proof of (P b0)
% 150.49/150.79 Found (((ex_intro0 (fun (Xx:b)=> (forall (x10:b), (((eq a) (b0 x10)) (Xf x10))))) b_DUMMY) (fun (x10:b)=> ((eq_ref a) (b0 x10)))) as proof of (P b0)
% 150.49/150.79 Found ((((ex_intro b) (fun (Xx:b)=> (forall (x10:b), (((eq a) (b0 x10)) (Xf x10))))) b_DUMMY) (fun (x10:b)=> ((eq_ref a) (b0 x10)))) as proof of (P b0)
% 150.49/150.79 Found ((((ex_intro b) (fun (Xx:b)=> (forall (x10:b), (((eq a) (b0 x10)) (Xf x10))))) b_DUMMY) (fun (x10:b)=> ((eq_ref a) (b0 x10)))) as proof of (P b0)
% 150.49/150.79 Found x00:=(x0 (fun (x2:a)=> (P (Xg x1)))):((P (Xg x1))->(P (Xg x1)))
% 150.49/150.79 Found (x0 (fun (x2:a)=> (P (Xg x1)))) as proof of (P0 (Xg x1))
% 150.49/150.79 Found (x0 (fun (x2:a)=> (P (Xg x1)))) as proof of (P0 (Xg x1))
% 150.49/150.79 Found eq_ref000:=(eq_ref00 P):((P (Xg x1))->(P (Xg x1)))
% 150.49/150.79 Found (eq_ref00 P) as proof of (P0 (Xg x1))
% 150.49/150.79 Found ((eq_ref0 (Xg x1)) P) as proof of (P0 (Xg x1))
% 150.49/150.79 Found (((eq_ref a) (Xg x1)) P) as proof of (P0 (Xg x1))
% 150.49/150.79 Found (((eq_ref a) (Xg x1)) P) as proof of (P0 (Xg x1))
% 150.49/150.79 Found b_DUMMY:b
% 150.49/150.79 Found b_DUMMY as proof of b
% 150.49/150.79 Found b_DUMMY:b
% 150.49/150.79 Found b_DUMMY as proof of b
% 150.49/150.79 Found eq_ref00:=(eq_ref0 (Xg x1)):(((eq a) (Xg x1)) (Xg x1))
% 150.49/150.79 Found (eq_ref0 (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 150.49/150.79 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 152.73/153.04 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 152.73/153.04 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 152.73/153.04 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 152.73/153.04 Found (eq_ref0 b0) as proof of (((eq a) b0) (Xf x1))
% 152.73/153.04 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 152.73/153.04 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 152.73/153.04 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 152.73/153.04 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 152.73/153.04 Found (eq_ref0 b0) as proof of (((eq a) b0) (Xf x1))
% 152.73/153.04 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 152.73/153.04 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 152.73/153.04 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 152.73/153.04 Found eq_ref00:=(eq_ref0 (Xg x1)):(((eq a) (Xg x1)) (Xg x1))
% 152.73/153.04 Found (eq_ref0 (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 152.73/153.04 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 152.73/153.04 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 152.73/153.04 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 152.73/153.04 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 152.73/153.04 Found (eq_ref0 b0) as proof of (((eq a) b0) (Xf x1))
% 152.73/153.04 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 152.73/153.04 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 152.73/153.04 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 152.73/153.04 Found eq_ref00:=(eq_ref0 (Xg x1)):(((eq a) (Xg x1)) (Xg x1))
% 152.73/153.04 Found (eq_ref0 (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 152.73/153.04 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 152.73/153.04 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 152.73/153.04 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 152.73/153.04 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 152.73/153.04 Found (eq_ref0 b0) as proof of (((eq a) b0) (Xf x1))
% 152.73/153.04 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 152.73/153.04 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 152.73/153.04 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 152.73/153.04 Found eq_ref00:=(eq_ref0 (Xg x1)):(((eq a) (Xg x1)) (Xg x1))
% 152.73/153.04 Found (eq_ref0 (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 152.73/153.04 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 152.73/153.04 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 152.73/153.04 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 152.73/153.04 Found eq_ref00:=(eq_ref0 (Xg x1)):(((eq a) (Xg x1)) (Xg x1))
% 152.73/153.04 Found (eq_ref0 (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 152.73/153.04 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 152.73/153.04 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 152.73/153.04 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 152.73/153.04 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 152.73/153.04 Found (eq_ref0 b0) as proof of (((eq a) b0) (Xf x1))
% 152.73/153.04 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 152.73/153.04 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 152.73/153.04 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 152.73/153.04 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 152.73/153.04 Found (eq_ref0 b0) as proof of (((eq a) b0) (Xf x1))
% 152.73/153.04 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 152.73/153.04 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 152.73/153.04 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 152.73/153.04 Found eq_ref00:=(eq_ref0 (Xg x1)):(((eq a) (Xg x1)) (Xg x1))
% 152.73/153.04 Found (eq_ref0 (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 152.73/153.04 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 152.73/153.04 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 152.73/153.04 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 152.73/153.04 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 152.73/153.04 Found (eq_ref0 b0) as proof of (((eq a) b0) (Xf x1))
% 152.73/153.04 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 152.73/153.04 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 152.73/153.04 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 152.73/153.04 Found eq_ref00:=(eq_ref0 (Xg x1)):(((eq a) (Xg x1)) (Xg x1))
% 152.73/153.04 Found (eq_ref0 (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 152.73/153.04 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 152.73/153.04 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 152.73/153.04 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 152.73/153.04 Found eq_ref00:=(eq_ref0 (Xg x1)):(((eq a) (Xg x1)) (Xg x1))
% 152.73/153.04 Found (eq_ref0 (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 152.73/153.04 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 152.73/153.04 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 152.73/153.04 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 155.97/156.25 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 155.97/156.25 Found (eq_ref0 b0) as proof of (((eq a) b0) (Xf x1))
% 155.97/156.25 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 155.97/156.25 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 155.97/156.25 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 155.97/156.25 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 155.97/156.25 Found (eq_ref0 b0) as proof of (((eq a) b0) (Xf x1))
% 155.97/156.25 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 155.97/156.25 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 155.97/156.25 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 155.97/156.25 Found eq_ref00:=(eq_ref0 (Xg x1)):(((eq a) (Xg x1)) (Xg x1))
% 155.97/156.25 Found (eq_ref0 (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 155.97/156.25 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 155.97/156.25 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 155.97/156.25 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 155.97/156.25 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 155.97/156.25 Found (eq_ref0 b0) as proof of (((eq a) b0) (Xf x1))
% 155.97/156.25 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 155.97/156.25 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 155.97/156.25 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 155.97/156.25 Found eq_ref00:=(eq_ref0 (Xg x1)):(((eq a) (Xg x1)) (Xg x1))
% 155.97/156.25 Found (eq_ref0 (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 155.97/156.25 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 155.97/156.25 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 155.97/156.25 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 155.97/156.25 Found eq_ref00:=(eq_ref0 (Xg x1)):(((eq a) (Xg x1)) (Xg x1))
% 155.97/156.25 Found (eq_ref0 (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 155.97/156.25 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 155.97/156.25 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 155.97/156.25 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 155.97/156.25 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 155.97/156.25 Found (eq_ref0 b0) as proof of (((eq a) b0) (Xf x1))
% 155.97/156.25 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 155.97/156.25 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 155.97/156.25 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 155.97/156.25 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 155.97/156.25 Found (eq_ref0 b0) as proof of (((eq a) b0) (Xf x1))
% 155.97/156.25 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 155.97/156.25 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 155.97/156.25 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 155.97/156.25 Found eq_ref00:=(eq_ref0 (Xg x1)):(((eq a) (Xg x1)) (Xg x1))
% 155.97/156.25 Found (eq_ref0 (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 155.97/156.25 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 155.97/156.25 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 155.97/156.25 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 155.97/156.25 Found eq_ref00:=(eq_ref0 (Xg x1)):(((eq a) (Xg x1)) (Xg x1))
% 155.97/156.25 Found (eq_ref0 (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 155.97/156.25 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 155.97/156.25 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 155.97/156.25 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 155.97/156.25 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 155.97/156.25 Found (eq_ref0 b0) as proof of (((eq a) b0) (Xf x1))
% 155.97/156.25 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 155.97/156.25 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 155.97/156.25 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 155.97/156.25 Found eq_ref00:=(eq_ref0 (Xg x1)):(((eq a) (Xg x1)) (Xg x1))
% 155.97/156.25 Found (eq_ref0 (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 155.97/156.25 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 155.97/156.25 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 155.97/156.25 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 155.97/156.25 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 155.97/156.25 Found (eq_ref0 b0) as proof of (((eq a) b0) (Xf x1))
% 155.97/156.25 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 155.97/156.25 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 155.97/156.25 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 155.97/156.25 Found eq_ref00:=(eq_ref0 (Xg x1)):(((eq a) (Xg x1)) (Xg x1))
% 155.97/156.25 Found (eq_ref0 (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 155.97/156.25 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 155.97/156.25 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 155.97/156.25 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 155.97/156.25 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 155.97/156.25 Found (eq_ref0 b0) as proof of (((eq a) b0) (Xf x1))
% 159.04/159.36 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 159.04/159.36 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 159.04/159.36 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 159.04/159.36 Found eq_ref00:=(eq_ref0 (Xg x1)):(((eq a) (Xg x1)) (Xg x1))
% 159.04/159.36 Found (eq_ref0 (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 159.04/159.36 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 159.04/159.36 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 159.04/159.36 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 159.04/159.36 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 159.04/159.36 Found (eq_ref0 b0) as proof of (((eq a) b0) (Xf x1))
% 159.04/159.36 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 159.04/159.36 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 159.04/159.36 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 159.04/159.36 Found eq_ref00:=(eq_ref0 (Xg x1)):(((eq a) (Xg x1)) (Xg x1))
% 159.04/159.36 Found (eq_ref0 (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 159.04/159.36 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 159.04/159.36 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 159.04/159.36 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 159.04/159.36 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 159.04/159.36 Found (eq_ref0 b0) as proof of (((eq a) b0) (Xf x1))
% 159.04/159.36 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 159.04/159.36 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 159.04/159.36 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 159.04/159.36 Found eq_ref00:=(eq_ref0 (Xg x1)):(((eq a) (Xg x1)) (Xg x1))
% 159.04/159.36 Found (eq_ref0 (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 159.04/159.36 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 159.04/159.36 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 159.04/159.36 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 159.04/159.36 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 159.04/159.36 Found (eq_ref0 b0) as proof of (((eq a) b0) (Xf x1))
% 159.04/159.36 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 159.04/159.36 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 159.04/159.36 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 159.04/159.36 Found eq_ref00:=(eq_ref0 (Xg x1)):(((eq a) (Xg x1)) (Xg x1))
% 159.04/159.36 Found (eq_ref0 (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 159.04/159.36 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 159.04/159.36 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 159.04/159.36 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 159.04/159.36 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 159.04/159.36 Found (eq_ref0 b0) as proof of (((eq a) b0) (Xf x1))
% 159.04/159.36 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 159.04/159.36 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 159.04/159.36 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 159.04/159.36 Found eq_ref00:=(eq_ref0 (Xg x1)):(((eq a) (Xg x1)) (Xg x1))
% 159.04/159.36 Found (eq_ref0 (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 159.04/159.36 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 159.04/159.36 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 159.04/159.36 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 159.04/159.36 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 159.04/159.36 Found (eq_ref0 b0) as proof of (((eq a) b0) (Xf x1))
% 159.04/159.36 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 159.04/159.36 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 159.04/159.36 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 159.04/159.36 Found eq_ref00:=(eq_ref0 (Xg x1)):(((eq a) (Xg x1)) (Xg x1))
% 159.04/159.36 Found (eq_ref0 (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 159.04/159.36 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 159.04/159.36 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 159.04/159.36 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 159.04/159.36 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 159.04/159.36 Found (eq_ref0 b0) as proof of (((eq a) b0) (Xf x1))
% 159.04/159.36 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 159.04/159.36 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 159.04/159.36 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 159.04/159.36 Found eq_ref00:=(eq_ref0 (Xg x1)):(((eq a) (Xg x1)) (Xg x1))
% 159.04/159.36 Found (eq_ref0 (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 159.04/159.36 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 159.04/159.36 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 159.04/159.36 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 159.04/159.36 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 159.04/159.36 Found (eq_ref0 b0) as proof of (((eq a) b0) (Xf x1))
% 159.04/159.36 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 159.04/159.36 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 164.30/164.60 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 164.30/164.60 Found eq_ref00:=(eq_ref0 (Xg x1)):(((eq a) (Xg x1)) (Xg x1))
% 164.30/164.60 Found (eq_ref0 (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 164.30/164.60 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 164.30/164.60 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 164.30/164.60 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 164.30/164.60 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 164.30/164.60 Found (eq_ref0 b0) as proof of (((eq a) b0) (Xf x1))
% 164.30/164.60 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 164.30/164.60 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 164.30/164.60 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 164.30/164.60 Found eq_ref00:=(eq_ref0 (Xg x1)):(((eq a) (Xg x1)) (Xg x1))
% 164.30/164.60 Found (eq_ref0 (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 164.30/164.60 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 164.30/164.60 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 164.30/164.60 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 164.30/164.60 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 164.30/164.60 Found (eq_ref0 b0) as proof of (((eq a) b0) (Xf x1))
% 164.30/164.60 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 164.30/164.60 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 164.30/164.60 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 164.30/164.60 Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% 164.30/164.60 Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) (((eq a) (Xg x1)) (Xf x1)))
% 164.30/164.60 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (((eq a) (Xg x1)) (Xf x1)))
% 164.30/164.60 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (((eq a) (Xg x1)) (Xf x1)))
% 164.30/164.60 Found (fun (x3:b)=> ((eq_ref Prop) (f x3))) as proof of (((eq Prop) (f x3)) (((eq a) (Xg x1)) (Xf x1)))
% 164.30/164.60 Found (fun (x3:b)=> ((eq_ref Prop) (f x3))) as proof of (forall (x:b), (((eq Prop) (f x)) (((eq a) (Xg x1)) (Xf x1))))
% 164.30/164.60 Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% 164.30/164.60 Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) (((eq a) (Xg x1)) (Xf x1)))
% 164.30/164.60 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (((eq a) (Xg x1)) (Xf x1)))
% 164.30/164.60 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (((eq a) (Xg x1)) (Xf x1)))
% 164.30/164.60 Found (fun (x3:b)=> ((eq_ref Prop) (f x3))) as proof of (((eq Prop) (f x3)) (((eq a) (Xg x1)) (Xf x1)))
% 164.30/164.60 Found (fun (x3:b)=> ((eq_ref Prop) (f x3))) as proof of (forall (x:b), (((eq Prop) (f x)) (((eq a) (Xg x1)) (Xf x1))))
% 164.30/164.60 Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% 164.30/164.60 Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) (((eq a) (Xg x1)) (Xf x1)))
% 164.30/164.60 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (((eq a) (Xg x1)) (Xf x1)))
% 164.30/164.60 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (((eq a) (Xg x1)) (Xf x1)))
% 164.30/164.60 Found (fun (x3:b)=> ((eq_ref Prop) (f x3))) as proof of (((eq Prop) (f x3)) (((eq a) (Xg x1)) (Xf x1)))
% 164.30/164.60 Found (fun (x3:b)=> ((eq_ref Prop) (f x3))) as proof of (forall (x:b), (((eq Prop) (f x)) (((eq a) (Xg x1)) (Xf x1))))
% 164.30/164.60 Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% 164.30/164.60 Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) (((eq a) (Xg x1)) (Xf x1)))
% 164.30/164.60 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (((eq a) (Xg x1)) (Xf x1)))
% 164.30/164.60 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (((eq a) (Xg x1)) (Xf x1)))
% 164.30/164.60 Found (fun (x3:b)=> ((eq_ref Prop) (f x3))) as proof of (((eq Prop) (f x3)) (((eq a) (Xg x1)) (Xf x1)))
% 164.30/164.60 Found (fun (x3:b)=> ((eq_ref Prop) (f x3))) as proof of (forall (x:b), (((eq Prop) (f x)) (((eq a) (Xg x1)) (Xf x1))))
% 164.30/164.60 Found x00:=(x0 (fun (x1:a)=> (P Xg))):((P Xg)->(P Xg))
% 164.30/164.60 Found (x0 (fun (x1:a)=> (P Xg))) as proof of (P0 Xg)
% 164.30/164.60 Found (x0 (fun (x1:a)=> (P Xg))) as proof of (P0 Xg)
% 164.30/164.60 Found b_DUMMY:b
% 164.30/164.60 Found b_DUMMY as proof of b
% 164.30/164.60 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 164.30/164.60 Found (eq_ref0 b0) as proof of (((eq a) b0) (Xf x1))
% 164.30/164.60 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 164.30/164.60 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 164.30/164.60 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 164.30/164.60 Found ((ex_intro00 b_DUMMY) ((eq_ref a) b0)) as proof of (P b0)
% 164.30/164.60 Found (((ex_intro0 (fun (Xx:b)=> (((eq a) b0) (Xf x1)))) b_DUMMY) ((eq_ref a) b0)) as proof of (P b0)
% 164.30/164.60 Found ((((ex_intro b) (fun (Xx:b)=> (((eq a) b0) (Xf x1)))) b_DUMMY) ((eq_ref a) b0)) as proof of (P b0)
% 165.99/166.28 Found ((((ex_intro b) (fun (Xx:b)=> (((eq a) b0) (Xf x1)))) b_DUMMY) ((eq_ref a) b0)) as proof of (P b0)
% 165.99/166.28 Found b_DUMMY:b
% 165.99/166.28 Found b_DUMMY as proof of b
% 165.99/166.28 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 165.99/166.28 Found (eq_ref0 b0) as proof of (((eq a) b0) (Xf x1))
% 165.99/166.28 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 165.99/166.28 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 165.99/166.28 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xf x1))
% 165.99/166.28 Found ((ex_intro00 b_DUMMY) ((eq_ref a) b0)) as proof of (P b0)
% 165.99/166.28 Found (((ex_intro0 (fun (Xx:b)=> (((eq a) b0) (Xf x1)))) b_DUMMY) ((eq_ref a) b0)) as proof of (P b0)
% 165.99/166.28 Found ((((ex_intro b) (fun (Xx:b)=> (((eq a) b0) (Xf x1)))) b_DUMMY) ((eq_ref a) b0)) as proof of (P b0)
% 165.99/166.28 Found ((((ex_intro b) (fun (Xx:b)=> (((eq a) b0) (Xf x1)))) b_DUMMY) ((eq_ref a) b0)) as proof of (P b0)
% 165.99/166.28 Found x00:=(x0 (fun (x1:a)=> (P Xg))):((P Xg)->(P Xg))
% 165.99/166.28 Found (x0 (fun (x1:a)=> (P Xg))) as proof of (P0 Xg)
% 165.99/166.28 Found (x0 (fun (x1:a)=> (P Xg))) as proof of (P0 Xg)
% 165.99/166.28 Found x00:=(x0 (fun (x1:a)=> (P Xg))):((P Xg)->(P Xg))
% 165.99/166.28 Found (x0 (fun (x1:a)=> (P Xg))) as proof of (P0 Xg)
% 165.99/166.28 Found (x0 (fun (x1:a)=> (P Xg))) as proof of (P0 Xg)
% 165.99/166.28 Found x00:=(x0 (fun (x1:a)=> (P Xg))):((P Xg)->(P Xg))
% 165.99/166.28 Found (x0 (fun (x1:a)=> (P Xg))) as proof of (P0 Xg)
% 165.99/166.28 Found (x0 (fun (x1:a)=> (P Xg))) as proof of (P0 Xg)
% 165.99/166.28 Found b_DUMMY:b
% 165.99/166.28 Found b_DUMMY as proof of b
% 165.99/166.28 Found eq_ref00:=(eq_ref0 (b0 x1)):(((eq a) (b0 x1)) (b0 x1))
% 165.99/166.28 Found (eq_ref0 (b0 x1)) as proof of (((eq a) (b0 x1)) (Xf x1))
% 165.99/166.28 Found ((eq_ref a) (b0 x1)) as proof of (((eq a) (b0 x1)) (Xf x1))
% 165.99/166.28 Found ((eq_ref a) (b0 x1)) as proof of (((eq a) (b0 x1)) (Xf x1))
% 165.99/166.28 Found ((eq_ref a) (b0 x1)) as proof of (((eq a) (b0 x1)) (Xf x1))
% 165.99/166.28 Found ((ex_intro00 b_DUMMY) ((eq_ref a) (b0 x1))) as proof of (P b0)
% 165.99/166.28 Found (((ex_intro0 (fun (Xx:b)=> (((eq a) (b0 x1)) (Xf x1)))) b_DUMMY) ((eq_ref a) (b0 x1))) as proof of (P b0)
% 165.99/166.28 Found ((((ex_intro b) (fun (Xx:b)=> (((eq a) (b0 x1)) (Xf x1)))) b_DUMMY) ((eq_ref a) (b0 x1))) as proof of (P b0)
% 165.99/166.28 Found ((((ex_intro b) (fun (Xx:b)=> (((eq a) (b0 x1)) (Xf x1)))) b_DUMMY) ((eq_ref a) (b0 x1))) as proof of (P b0)
% 165.99/166.28 Found eq_ref00:=(eq_ref0 (f x2)):(((eq Prop) (f x2)) (f x2))
% 165.99/166.28 Found (eq_ref0 (f x2)) as proof of (((eq Prop) (f x2)) (forall (x10:b), (((eq a) (Xg x10)) (Xf x10))))
% 165.99/166.28 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) (forall (x10:b), (((eq a) (Xg x10)) (Xf x10))))
% 165.99/166.28 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) (forall (x10:b), (((eq a) (Xg x10)) (Xf x10))))
% 165.99/166.28 Found (fun (x2:b)=> ((eq_ref Prop) (f x2))) as proof of (((eq Prop) (f x2)) (forall (x10:b), (((eq a) (Xg x10)) (Xf x10))))
% 165.99/166.28 Found (fun (x2:b)=> ((eq_ref Prop) (f x2))) as proof of (forall (x:b), (((eq Prop) (f x)) (forall (x10:b), (((eq a) (Xg x10)) (Xf x10)))))
% 165.99/166.28 Found b_DUMMY:b
% 165.99/166.28 Found b_DUMMY as proof of b
% 165.99/166.28 Found eq_ref00:=(eq_ref0 (b0 x1)):(((eq a) (b0 x1)) (b0 x1))
% 165.99/166.28 Found (eq_ref0 (b0 x1)) as proof of (((eq a) (b0 x1)) (Xf x1))
% 165.99/166.28 Found ((eq_ref a) (b0 x1)) as proof of (((eq a) (b0 x1)) (Xf x1))
% 165.99/166.28 Found ((eq_ref a) (b0 x1)) as proof of (((eq a) (b0 x1)) (Xf x1))
% 165.99/166.28 Found ((eq_ref a) (b0 x1)) as proof of (((eq a) (b0 x1)) (Xf x1))
% 165.99/166.28 Found ((ex_intro00 b_DUMMY) ((eq_ref a) (b0 x1))) as proof of (P b0)
% 165.99/166.28 Found (((ex_intro0 (fun (Xx:b)=> (((eq a) (b0 x1)) (Xf x1)))) b_DUMMY) ((eq_ref a) (b0 x1))) as proof of (P b0)
% 165.99/166.28 Found ((((ex_intro b) (fun (Xx:b)=> (((eq a) (b0 x1)) (Xf x1)))) b_DUMMY) ((eq_ref a) (b0 x1))) as proof of (P b0)
% 165.99/166.28 Found ((((ex_intro b) (fun (Xx:b)=> (((eq a) (b0 x1)) (Xf x1)))) b_DUMMY) ((eq_ref a) (b0 x1))) as proof of (P b0)
% 165.99/166.28 Found eq_ref00:=(eq_ref0 (f x2)):(((eq Prop) (f x2)) (f x2))
% 165.99/166.28 Found (eq_ref0 (f x2)) as proof of (((eq Prop) (f x2)) (forall (x10:b), (((eq a) (Xg x10)) (Xf x10))))
% 165.99/166.28 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) (forall (x10:b), (((eq a) (Xg x10)) (Xf x10))))
% 165.99/166.28 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) (forall (x10:b), (((eq a) (Xg x10)) (Xf x10))))
% 165.99/166.28 Found (fun (x2:b)=> ((eq_ref Prop) (f x2))) as proof of (((eq Prop) (f x2)) (forall (x10:b), (((eq a) (Xg x10)) (Xf x10))))
% 165.99/166.28 Found (fun (x2:b)=> ((eq_ref Prop) (f x2))) as proof of (forall (x:b), (((eq Prop) (f x)) (forall (x10:b), (((eq a) (Xg x10)) (Xf x10)))))
% 171.36/171.68 Found eta_expansion000:=(eta_expansion00 (fun (Xx:b)=> (P (Xf x1)))):(((eq (b->Prop)) (fun (Xx:b)=> (P (Xf x1)))) (fun (x:b)=> (P (Xf x1))))
% 171.36/171.68 Found (eta_expansion00 (fun (Xx:b)=> (P (Xf x1)))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (P (Xf x1)))) b0)
% 171.36/171.68 Found ((eta_expansion0 Prop) (fun (Xx:b)=> (P (Xf x1)))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (P (Xf x1)))) b0)
% 171.36/171.68 Found (((eta_expansion b) Prop) (fun (Xx:b)=> (P (Xf x1)))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (P (Xf x1)))) b0)
% 171.36/171.68 Found (((eta_expansion b) Prop) (fun (Xx:b)=> (P (Xf x1)))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (P (Xf x1)))) b0)
% 171.36/171.68 Found (((eta_expansion b) Prop) (fun (Xx:b)=> (P (Xf x1)))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (P (Xf x1)))) b0)
% 171.36/171.68 Found eta_expansion000:=(eta_expansion00 (fun (Xx:b)=> (P (Xf x1)))):(((eq (b->Prop)) (fun (Xx:b)=> (P (Xf x1)))) (fun (x:b)=> (P (Xf x1))))
% 171.36/171.68 Found (eta_expansion00 (fun (Xx:b)=> (P (Xf x1)))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (P (Xf x1)))) b0)
% 171.36/171.68 Found ((eta_expansion0 Prop) (fun (Xx:b)=> (P (Xf x1)))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (P (Xf x1)))) b0)
% 171.36/171.68 Found (((eta_expansion b) Prop) (fun (Xx:b)=> (P (Xf x1)))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (P (Xf x1)))) b0)
% 171.36/171.68 Found (((eta_expansion b) Prop) (fun (Xx:b)=> (P (Xf x1)))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (P (Xf x1)))) b0)
% 171.36/171.68 Found (((eta_expansion b) Prop) (fun (Xx:b)=> (P (Xf x1)))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (P (Xf x1)))) b0)
% 171.36/171.68 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 171.36/171.68 Found (eq_ref0 b0) as proof of (P b0)
% 171.36/171.68 Found ((eq_ref a) b0) as proof of (P b0)
% 171.36/171.68 Found ((eq_ref a) b0) as proof of (P b0)
% 171.36/171.68 Found ((eq_ref a) b0) as proof of (P b0)
% 171.36/171.68 Found eq_ref00:=(eq_ref0 (Xf x1)):(((eq a) (Xf x1)) (Xf x1))
% 171.36/171.68 Found (eq_ref0 (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 171.36/171.68 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 171.36/171.68 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 171.36/171.68 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 171.36/171.68 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 171.36/171.68 Found (eq_ref0 b0) as proof of (P b0)
% 171.36/171.68 Found ((eq_ref a) b0) as proof of (P b0)
% 171.36/171.68 Found ((eq_ref a) b0) as proof of (P b0)
% 171.36/171.68 Found ((eq_ref a) b0) as proof of (P b0)
% 171.36/171.68 Found eq_ref00:=(eq_ref0 (Xf x1)):(((eq a) (Xf x1)) (Xf x1))
% 171.36/171.68 Found (eq_ref0 (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 171.36/171.68 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 171.36/171.68 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 171.36/171.68 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 171.36/171.68 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xx:b)=> (P (Xf x1)))):(((eq (b->Prop)) (fun (Xx:b)=> (P (Xf x1)))) (fun (x:b)=> (P (Xf x1))))
% 171.36/171.68 Found (eta_expansion_dep00 (fun (Xx:b)=> (P (Xf x1)))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (P (Xf x1)))) b0)
% 171.36/171.68 Found ((eta_expansion_dep0 (fun (x5:b)=> Prop)) (fun (Xx:b)=> (P (Xf x1)))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (P (Xf x1)))) b0)
% 171.36/171.68 Found (((eta_expansion_dep b) (fun (x5:b)=> Prop)) (fun (Xx:b)=> (P (Xf x1)))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (P (Xf x1)))) b0)
% 171.36/171.68 Found (((eta_expansion_dep b) (fun (x5:b)=> Prop)) (fun (Xx:b)=> (P (Xf x1)))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (P (Xf x1)))) b0)
% 171.36/171.68 Found (((eta_expansion_dep b) (fun (x5:b)=> Prop)) (fun (Xx:b)=> (P (Xf x1)))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (P (Xf x1)))) b0)
% 171.36/171.68 Found eq_ref00:=(eq_ref0 (fun (Xx:b)=> (P (Xf x1)))):(((eq (b->Prop)) (fun (Xx:b)=> (P (Xf x1)))) (fun (Xx:b)=> (P (Xf x1))))
% 171.36/171.68 Found (eq_ref0 (fun (Xx:b)=> (P (Xf x1)))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (P (Xf x1)))) b0)
% 171.36/171.68 Found ((eq_ref (b->Prop)) (fun (Xx:b)=> (P (Xf x1)))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (P (Xf x1)))) b0)
% 171.36/171.68 Found ((eq_ref (b->Prop)) (fun (Xx:b)=> (P (Xf x1)))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (P (Xf x1)))) b0)
% 171.36/171.68 Found ((eq_ref (b->Prop)) (fun (Xx:b)=> (P (Xf x1)))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (P (Xf x1)))) b0)
% 171.36/171.68 Found x00:=(x0 (fun (x2:a)=> (P (Xf x1)))):((P (Xf x1))->(P (Xf x1)))
% 171.36/171.68 Found (x0 (fun (x2:a)=> (P (Xf x1)))) as proof of (P0 (Xf x1))
% 184.05/184.41 Found (x0 (fun (x2:a)=> (P (Xf x1)))) as proof of (P0 (Xf x1))
% 184.05/184.41 Found x00:=(x0 (fun (x2:a)=> (P (Xf x1)))):((P (Xf x1))->(P (Xf x1)))
% 184.05/184.41 Found (x0 (fun (x2:a)=> (P (Xf x1)))) as proof of (P0 (Xf x1))
% 184.05/184.41 Found (x0 (fun (x2:a)=> (P (Xf x1)))) as proof of (P0 (Xf x1))
% 184.05/184.41 Found b_DUMMY:b
% 184.05/184.41 Found b_DUMMY as proof of b
% 184.05/184.41 Found b_DUMMY:b
% 184.05/184.41 Found b_DUMMY as proof of b
% 184.05/184.41 Found x00:=(x0 (fun (x2:a)=> (P (Xf x1)))):((P (Xf x1))->(P (Xf x1)))
% 184.05/184.41 Found (x0 (fun (x2:a)=> (P (Xf x1)))) as proof of (P0 (Xf x1))
% 184.05/184.41 Found (x0 (fun (x2:a)=> (P (Xf x1)))) as proof of (P0 (Xf x1))
% 184.05/184.41 Found x00:=(x0 (fun (x2:a)=> (P (Xf x1)))):((P (Xf x1))->(P (Xf x1)))
% 184.05/184.41 Found (x0 (fun (x2:a)=> (P (Xf x1)))) as proof of (P0 (Xf x1))
% 184.05/184.41 Found (x0 (fun (x2:a)=> (P (Xf x1)))) as proof of (P0 (Xf x1))
% 184.05/184.41 Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% 184.05/184.41 Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) ((P (Xf x1))->(P (Xg x1))))
% 184.05/184.41 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) ((P (Xf x1))->(P (Xg x1))))
% 184.05/184.41 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) ((P (Xf x1))->(P (Xg x1))))
% 184.05/184.41 Found (fun (x3:b)=> ((eq_ref Prop) (f x3))) as proof of (((eq Prop) (f x3)) ((P (Xf x1))->(P (Xg x1))))
% 184.05/184.41 Found (fun (x3:b)=> ((eq_ref Prop) (f x3))) as proof of (forall (x:b), (((eq Prop) (f x)) ((P (Xf x1))->(P (Xg x1)))))
% 184.05/184.41 Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% 184.05/184.41 Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) ((P (Xf x1))->(P (Xg x1))))
% 184.05/184.41 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) ((P (Xf x1))->(P (Xg x1))))
% 184.05/184.41 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) ((P (Xf x1))->(P (Xg x1))))
% 184.05/184.41 Found (fun (x3:b)=> ((eq_ref Prop) (f x3))) as proof of (((eq Prop) (f x3)) ((P (Xf x1))->(P (Xg x1))))
% 184.05/184.41 Found (fun (x3:b)=> ((eq_ref Prop) (f x3))) as proof of (forall (x:b), (((eq Prop) (f x)) ((P (Xf x1))->(P (Xg x1)))))
% 184.05/184.41 Found b_DUMMY:b
% 184.05/184.41 Found b_DUMMY as proof of b
% 184.05/184.41 Found b_DUMMY:b
% 184.05/184.41 Found b_DUMMY as proof of b
% 184.05/184.41 Found eq_ref00:=(eq_ref0 (Xf x1)):(((eq a) (Xf x1)) (Xf x1))
% 184.05/184.41 Found (eq_ref0 (Xf x1)) as proof of (((eq a) (Xf x1)) b1)
% 184.05/184.41 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b1)
% 184.05/184.41 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b1)
% 184.05/184.41 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b1)
% 184.05/184.41 Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% 184.05/184.41 Found (eq_ref0 b1) as proof of (((eq a) b1) (b0 x1))
% 184.05/184.41 Found ((eq_ref a) b1) as proof of (((eq a) b1) (b0 x1))
% 184.05/184.41 Found ((eq_ref a) b1) as proof of (((eq a) b1) (b0 x1))
% 184.05/184.41 Found ((eq_ref a) b1) as proof of (((eq a) b1) (b0 x1))
% 184.05/184.41 Found eq_ref00:=(eq_ref0 (Xf x1)):(((eq a) (Xf x1)) (Xf x1))
% 184.05/184.41 Found (eq_ref0 (Xf x1)) as proof of (((eq a) (Xf x1)) b1)
% 184.05/184.41 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b1)
% 184.05/184.41 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b1)
% 184.05/184.41 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b1)
% 184.05/184.41 Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% 184.05/184.41 Found (eq_ref0 b1) as proof of (((eq a) b1) (b0 x1))
% 184.05/184.41 Found ((eq_ref a) b1) as proof of (((eq a) b1) (b0 x1))
% 184.05/184.41 Found ((eq_ref a) b1) as proof of (((eq a) b1) (b0 x1))
% 184.05/184.41 Found ((eq_ref a) b1) as proof of (((eq a) b1) (b0 x1))
% 184.05/184.41 Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% 184.05/184.41 Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) (((eq a) (Xg x1)) (Xf x1)))
% 184.05/184.41 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (((eq a) (Xg x1)) (Xf x1)))
% 184.05/184.41 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (((eq a) (Xg x1)) (Xf x1)))
% 184.05/184.41 Found (fun (x3:b)=> ((eq_ref Prop) (f x3))) as proof of (((eq Prop) (f x3)) (((eq a) (Xg x1)) (Xf x1)))
% 184.05/184.41 Found (fun (x3:b)=> ((eq_ref Prop) (f x3))) as proof of (forall (x:b), (((eq Prop) (f x)) (((eq a) (Xg x1)) (Xf x1))))
% 184.05/184.41 Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% 184.05/184.41 Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) (((eq a) (Xg x1)) (Xf x1)))
% 184.05/184.41 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (((eq a) (Xg x1)) (Xf x1)))
% 184.05/184.41 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (((eq a) (Xg x1)) (Xf x1)))
% 184.05/184.41 Found (fun (x3:b)=> ((eq_ref Prop) (f x3))) as proof of (((eq Prop) (f x3)) (((eq a) (Xg x1)) (Xf x1)))
% 184.05/184.41 Found (fun (x3:b)=> ((eq_ref Prop) (f x3))) as proof of (forall (x:b), (((eq Prop) (f x)) (((eq a) (Xg x1)) (Xf x1))))
% 198.80/199.10 Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% 198.80/199.10 Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) (((eq a) (Xg x1)) (Xf x1)))
% 198.80/199.10 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (((eq a) (Xg x1)) (Xf x1)))
% 198.80/199.10 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (((eq a) (Xg x1)) (Xf x1)))
% 198.80/199.10 Found (fun (x3:b)=> ((eq_ref Prop) (f x3))) as proof of (((eq Prop) (f x3)) (((eq a) (Xg x1)) (Xf x1)))
% 198.80/199.10 Found (fun (x3:b)=> ((eq_ref Prop) (f x3))) as proof of (forall (x:b), (((eq Prop) (f x)) (((eq a) (Xg x1)) (Xf x1))))
% 198.80/199.10 Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% 198.80/199.10 Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) (((eq a) (Xg x1)) (Xf x1)))
% 198.80/199.10 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (((eq a) (Xg x1)) (Xf x1)))
% 198.80/199.10 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (((eq a) (Xg x1)) (Xf x1)))
% 198.80/199.10 Found (fun (x3:b)=> ((eq_ref Prop) (f x3))) as proof of (((eq Prop) (f x3)) (((eq a) (Xg x1)) (Xf x1)))
% 198.80/199.10 Found (fun (x3:b)=> ((eq_ref Prop) (f x3))) as proof of (forall (x:b), (((eq Prop) (f x)) (((eq a) (Xg x1)) (Xf x1))))
% 198.80/199.10 Found x2:(P (Xf x1))
% 198.80/199.10 Instantiate: b0:=(Xf x1):a
% 198.80/199.10 Found x2 as proof of (P0 b0)
% 198.80/199.10 Found eq_ref00:=(eq_ref0 (Xg x1)):(((eq a) (Xg x1)) (Xg x1))
% 198.80/199.10 Found (eq_ref0 (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 198.80/199.10 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 198.80/199.10 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 198.80/199.10 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 198.80/199.10 Found x2:(P (Xf x1))
% 198.80/199.10 Instantiate: b0:=(Xf x1):a
% 198.80/199.10 Found x2 as proof of (P0 b0)
% 198.80/199.10 Found eq_ref00:=(eq_ref0 (Xg x1)):(((eq a) (Xg x1)) (Xg x1))
% 198.80/199.10 Found (eq_ref0 (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 198.80/199.10 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 198.80/199.10 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 198.80/199.10 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b0)
% 198.80/199.10 Found eq_ref00:=(eq_ref0 (f x4)):(((eq Prop) (f x4)) (f x4))
% 198.80/199.10 Found (eq_ref0 (f x4)) as proof of (((eq Prop) (f x4)) (P (Xg x1)))
% 198.80/199.10 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (P (Xg x1)))
% 198.80/199.10 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (P (Xg x1)))
% 198.80/199.10 Found (fun (x4:b)=> ((eq_ref Prop) (f x4))) as proof of (((eq Prop) (f x4)) (P (Xg x1)))
% 198.80/199.10 Found (fun (x4:b)=> ((eq_ref Prop) (f x4))) as proof of (forall (x:b), (((eq Prop) (f x)) (P (Xg x1))))
% 198.80/199.10 Found eq_ref00:=(eq_ref0 (f x4)):(((eq Prop) (f x4)) (f x4))
% 198.80/199.10 Found (eq_ref0 (f x4)) as proof of (((eq Prop) (f x4)) (P (Xg x1)))
% 198.80/199.10 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (P (Xg x1)))
% 198.80/199.10 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (P (Xg x1)))
% 198.80/199.10 Found (fun (x4:b)=> ((eq_ref Prop) (f x4))) as proof of (((eq Prop) (f x4)) (P (Xg x1)))
% 198.80/199.10 Found (fun (x4:b)=> ((eq_ref Prop) (f x4))) as proof of (forall (x:b), (((eq Prop) (f x)) (P (Xg x1))))
% 198.80/199.10 Found x2:(P (Xf x1))
% 198.80/199.10 Instantiate: b0:=Xf:(b->a)
% 198.80/199.10 Found x2 as proof of (P0 b0)
% 198.80/199.10 Found eta_expansion000:=(eta_expansion00 Xg):(((eq (b->a)) Xg) (fun (x:b)=> (Xg x)))
% 198.80/199.10 Found (eta_expansion00 Xg) as proof of (((eq (b->a)) Xg) b0)
% 198.80/199.10 Found ((eta_expansion0 a) Xg) as proof of (((eq (b->a)) Xg) b0)
% 198.80/199.10 Found (((eta_expansion b) a) Xg) as proof of (((eq (b->a)) Xg) b0)
% 198.80/199.10 Found (((eta_expansion b) a) Xg) as proof of (((eq (b->a)) Xg) b0)
% 198.80/199.10 Found (((eta_expansion b) a) Xg) as proof of (((eq (b->a)) Xg) b0)
% 198.80/199.10 Found x2:(P (Xf x1))
% 198.80/199.10 Instantiate: b0:=Xf:(b->a)
% 198.80/199.10 Found x2 as proof of (P0 b0)
% 198.80/199.10 Found eta_expansion000:=(eta_expansion00 Xg):(((eq (b->a)) Xg) (fun (x:b)=> (Xg x)))
% 198.80/199.10 Found (eta_expansion00 Xg) as proof of (((eq (b->a)) Xg) b0)
% 198.80/199.10 Found ((eta_expansion0 a) Xg) as proof of (((eq (b->a)) Xg) b0)
% 198.80/199.10 Found (((eta_expansion b) a) Xg) as proof of (((eq (b->a)) Xg) b0)
% 198.80/199.10 Found (((eta_expansion b) a) Xg) as proof of (((eq (b->a)) Xg) b0)
% 198.80/199.10 Found (((eta_expansion b) a) Xg) as proof of (((eq (b->a)) Xg) b0)
% 198.80/199.10 Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% 198.80/199.10 Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) ((P (Xg x1))->(P (Xf x1))))
% 198.80/199.10 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) ((P (Xg x1))->(P (Xf x1))))
% 198.80/199.10 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) ((P (Xg x1))->(P (Xf x1))))
% 201.84/202.16 Found (fun (x3:b)=> ((eq_ref Prop) (f x3))) as proof of (((eq Prop) (f x3)) ((P (Xg x1))->(P (Xf x1))))
% 201.84/202.16 Found (fun (x3:b)=> ((eq_ref Prop) (f x3))) as proof of (forall (x:b), (((eq Prop) (f x)) ((P (Xg x1))->(P (Xf x1)))))
% 201.84/202.16 Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% 201.84/202.16 Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) ((P (Xg x1))->(P (Xf x1))))
% 201.84/202.16 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) ((P (Xg x1))->(P (Xf x1))))
% 201.84/202.16 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) ((P (Xg x1))->(P (Xf x1))))
% 201.84/202.16 Found (fun (x3:b)=> ((eq_ref Prop) (f x3))) as proof of (((eq Prop) (f x3)) ((P (Xg x1))->(P (Xf x1))))
% 201.84/202.16 Found (fun (x3:b)=> ((eq_ref Prop) (f x3))) as proof of (forall (x:b), (((eq Prop) (f x)) ((P (Xg x1))->(P (Xf x1)))))
% 201.84/202.16 Found eq_ref00:=(eq_ref0 b0):(((eq (b->a)) b0) b0)
% 201.84/202.16 Found (eq_ref0 b0) as proof of (((eq (b->a)) b0) Xf)
% 201.84/202.16 Found ((eq_ref (b->a)) b0) as proof of (((eq (b->a)) b0) Xf)
% 201.84/202.16 Found ((eq_ref (b->a)) b0) as proof of (((eq (b->a)) b0) Xf)
% 201.84/202.16 Found ((eq_ref (b->a)) b0) as proof of (((eq (b->a)) b0) Xf)
% 201.84/202.16 Found eta_expansion000:=(eta_expansion00 Xg):(((eq (b->a)) Xg) (fun (x:b)=> (Xg x)))
% 201.84/202.16 Found (eta_expansion00 Xg) as proof of (((eq (b->a)) Xg) b0)
% 201.84/202.16 Found ((eta_expansion0 a) Xg) as proof of (((eq (b->a)) Xg) b0)
% 201.84/202.16 Found (((eta_expansion b) a) Xg) as proof of (((eq (b->a)) Xg) b0)
% 201.84/202.16 Found (((eta_expansion b) a) Xg) as proof of (((eq (b->a)) Xg) b0)
% 201.84/202.16 Found (((eta_expansion b) a) Xg) as proof of (((eq (b->a)) Xg) b0)
% 201.84/202.16 Found eq_ref00:=(eq_ref0 b0):(((eq (b->a)) b0) b0)
% 201.84/202.16 Found (eq_ref0 b0) as proof of (((eq (b->a)) b0) Xf)
% 201.84/202.16 Found ((eq_ref (b->a)) b0) as proof of (((eq (b->a)) b0) Xf)
% 201.84/202.16 Found ((eq_ref (b->a)) b0) as proof of (((eq (b->a)) b0) Xf)
% 201.84/202.16 Found ((eq_ref (b->a)) b0) as proof of (((eq (b->a)) b0) Xf)
% 201.84/202.16 Found eta_expansion000:=(eta_expansion00 Xg):(((eq (b->a)) Xg) (fun (x:b)=> (Xg x)))
% 201.84/202.16 Found (eta_expansion00 Xg) as proof of (((eq (b->a)) Xg) b0)
% 201.84/202.16 Found ((eta_expansion0 a) Xg) as proof of (((eq (b->a)) Xg) b0)
% 201.84/202.16 Found (((eta_expansion b) a) Xg) as proof of (((eq (b->a)) Xg) b0)
% 201.84/202.16 Found (((eta_expansion b) a) Xg) as proof of (((eq (b->a)) Xg) b0)
% 201.84/202.16 Found (((eta_expansion b) a) Xg) as proof of (((eq (b->a)) Xg) b0)
% 201.84/202.16 Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% 201.84/202.16 Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) ((P (Xg x1))->(P (Xf x1))))
% 201.84/202.16 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) ((P (Xg x1))->(P (Xf x1))))
% 201.84/202.16 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) ((P (Xg x1))->(P (Xf x1))))
% 201.84/202.16 Found (fun (x3:b)=> ((eq_ref Prop) (f x3))) as proof of (((eq Prop) (f x3)) ((P (Xg x1))->(P (Xf x1))))
% 201.84/202.16 Found (fun (x3:b)=> ((eq_ref Prop) (f x3))) as proof of (forall (x:b), (((eq Prop) (f x)) ((P (Xg x1))->(P (Xf x1)))))
% 201.84/202.16 Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% 201.84/202.16 Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) ((P (Xg x1))->(P (Xf x1))))
% 201.84/202.16 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) ((P (Xg x1))->(P (Xf x1))))
% 201.84/202.16 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) ((P (Xg x1))->(P (Xf x1))))
% 201.84/202.16 Found (fun (x3:b)=> ((eq_ref Prop) (f x3))) as proof of (((eq Prop) (f x3)) ((P (Xg x1))->(P (Xf x1))))
% 201.84/202.16 Found (fun (x3:b)=> ((eq_ref Prop) (f x3))) as proof of (forall (x:b), (((eq Prop) (f x)) ((P (Xg x1))->(P (Xf x1)))))
% 201.84/202.16 Found eq_ref00:=(eq_ref0 (Xf x1)):(((eq a) (Xf x1)) (Xf x1))
% 201.84/202.16 Found (eq_ref0 (Xf x1)) as proof of (P b0)
% 201.84/202.16 Found ((eq_ref a) (Xf x1)) as proof of (P b0)
% 201.84/202.16 Found ((eq_ref a) (Xf x1)) as proof of (P b0)
% 201.84/202.16 Found ((eq_ref a) (Xf x1)) as proof of (P b0)
% 201.84/202.16 Found eta_expansion000:=(eta_expansion00 Xg):(((eq (b->a)) Xg) (fun (x:b)=> (Xg x)))
% 201.84/202.16 Found (eta_expansion00 Xg) as proof of (((eq (b->a)) Xg) b0)
% 201.84/202.16 Found ((eta_expansion0 a) Xg) as proof of (((eq (b->a)) Xg) b0)
% 201.84/202.16 Found (((eta_expansion b) a) Xg) as proof of (((eq (b->a)) Xg) b0)
% 201.84/202.16 Found (((eta_expansion b) a) Xg) as proof of (((eq (b->a)) Xg) b0)
% 201.84/202.16 Found (((eta_expansion b) a) Xg) as proof of (((eq (b->a)) Xg) b0)
% 201.84/202.16 Found eq_ref00:=(eq_ref0 (Xf x1)):(((eq a) (Xf x1)) (Xf x1))
% 201.84/202.16 Found (eq_ref0 (Xf x1)) as proof of (P b0)
% 201.84/202.16 Found ((eq_ref a) (Xf x1)) as proof of (P b0)
% 215.46/215.82 Found ((eq_ref a) (Xf x1)) as proof of (P b0)
% 215.46/215.82 Found ((eq_ref a) (Xf x1)) as proof of (P b0)
% 215.46/215.82 Found eta_expansion_dep000:=(eta_expansion_dep00 Xg):(((eq (b->a)) Xg) (fun (x:b)=> (Xg x)))
% 215.46/215.82 Found (eta_expansion_dep00 Xg) as proof of (((eq (b->a)) Xg) b0)
% 215.46/215.82 Found ((eta_expansion_dep0 (fun (x3:b)=> a)) Xg) as proof of (((eq (b->a)) Xg) b0)
% 215.46/215.82 Found (((eta_expansion_dep b) (fun (x3:b)=> a)) Xg) as proof of (((eq (b->a)) Xg) b0)
% 215.46/215.82 Found (((eta_expansion_dep b) (fun (x3:b)=> a)) Xg) as proof of (((eq (b->a)) Xg) b0)
% 215.46/215.82 Found (((eta_expansion_dep b) (fun (x3:b)=> a)) Xg) as proof of (((eq (b->a)) Xg) b0)
% 215.46/215.82 Found eq_ref00:=(eq_ref0 (f x4)):(((eq Prop) (f x4)) (f x4))
% 215.46/215.82 Found (eq_ref0 (f x4)) as proof of (((eq Prop) (f x4)) (P (Xf x1)))
% 215.46/215.82 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (P (Xf x1)))
% 215.46/215.82 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (P (Xf x1)))
% 215.46/215.82 Found (fun (x4:b)=> ((eq_ref Prop) (f x4))) as proof of (((eq Prop) (f x4)) (P (Xf x1)))
% 215.46/215.82 Found (fun (x4:b)=> ((eq_ref Prop) (f x4))) as proof of (forall (x:b), (((eq Prop) (f x)) (P (Xf x1))))
% 215.46/215.82 Found eq_ref00:=(eq_ref0 (f x4)):(((eq Prop) (f x4)) (f x4))
% 215.46/215.82 Found (eq_ref0 (f x4)) as proof of (((eq Prop) (f x4)) (P (Xf x1)))
% 215.46/215.82 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (P (Xf x1)))
% 215.46/215.82 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (P (Xf x1)))
% 215.46/215.82 Found (fun (x4:b)=> ((eq_ref Prop) (f x4))) as proof of (((eq Prop) (f x4)) (P (Xf x1)))
% 215.46/215.82 Found (fun (x4:b)=> ((eq_ref Prop) (f x4))) as proof of (forall (x:b), (((eq Prop) (f x)) (P (Xf x1))))
% 215.46/215.82 Found eq_ref00:=(eq_ref0 (f x4)):(((eq Prop) (f x4)) (f x4))
% 215.46/215.82 Found (eq_ref0 (f x4)) as proof of (((eq Prop) (f x4)) (P (Xf x1)))
% 215.46/215.82 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (P (Xf x1)))
% 215.46/215.82 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (P (Xf x1)))
% 215.46/215.82 Found (fun (x4:b)=> ((eq_ref Prop) (f x4))) as proof of (((eq Prop) (f x4)) (P (Xf x1)))
% 215.46/215.82 Found (fun (x4:b)=> ((eq_ref Prop) (f x4))) as proof of (forall (x:b), (((eq Prop) (f x)) (P (Xf x1))))
% 215.46/215.82 Found eq_ref00:=(eq_ref0 (f x4)):(((eq Prop) (f x4)) (f x4))
% 215.46/215.82 Found (eq_ref0 (f x4)) as proof of (((eq Prop) (f x4)) (P (Xf x1)))
% 215.46/215.82 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (P (Xf x1)))
% 215.46/215.82 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (P (Xf x1)))
% 215.46/215.82 Found (fun (x4:b)=> ((eq_ref Prop) (f x4))) as proof of (((eq Prop) (f x4)) (P (Xf x1)))
% 215.46/215.82 Found (fun (x4:b)=> ((eq_ref Prop) (f x4))) as proof of (forall (x:b), (((eq Prop) (f x)) (P (Xf x1))))
% 215.46/215.82 Found eq_ref00:=(eq_ref0 (Xf x1)):(((eq a) (Xf x1)) (Xf x1))
% 215.46/215.82 Found (eq_ref0 (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 215.46/215.82 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 215.46/215.82 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 215.46/215.82 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 215.46/215.82 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 215.46/215.82 Found (eq_ref0 b0) as proof of (((eq a) b0) (Xg x1))
% 215.46/215.82 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 215.46/215.82 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 215.46/215.82 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 215.46/215.82 Found eq_ref00:=(eq_ref0 (Xf x1)):(((eq a) (Xf x1)) (Xf x1))
% 215.46/215.82 Found (eq_ref0 (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 215.46/215.82 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 215.46/215.82 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 215.46/215.82 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 215.46/215.82 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 215.46/215.82 Found (eq_ref0 b0) as proof of (((eq a) b0) (Xg x1))
% 215.46/215.82 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 215.46/215.82 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 215.46/215.82 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 215.46/215.82 Found eq_ref00:=(eq_ref0 (Xf x1)):(((eq a) (Xf x1)) (Xf x1))
% 215.46/215.82 Found (eq_ref0 (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 215.46/215.82 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 215.46/215.82 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 215.46/215.82 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 215.46/215.82 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 215.46/215.82 Found (eq_ref0 b0) as proof of (((eq a) b0) (Xg x1))
% 215.46/215.82 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 215.46/215.82 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 220.76/221.14 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 220.76/221.14 Found eq_ref00:=(eq_ref0 (Xf x1)):(((eq a) (Xf x1)) (Xf x1))
% 220.76/221.14 Found (eq_ref0 (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 220.76/221.14 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 220.76/221.14 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 220.76/221.14 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 220.76/221.14 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 220.76/221.14 Found (eq_ref0 b0) as proof of (((eq a) b0) (Xg x1))
% 220.76/221.14 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 220.76/221.14 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 220.76/221.14 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 220.76/221.14 Found eq_ref00:=(eq_ref0 (Xf x1)):(((eq a) (Xf x1)) (Xf x1))
% 220.76/221.14 Found (eq_ref0 (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 220.76/221.14 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 220.76/221.14 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 220.76/221.14 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 220.76/221.14 Found eq_ref00:=(eq_ref0 (Xf x1)):(((eq a) (Xf x1)) (Xf x1))
% 220.76/221.14 Found (eq_ref0 (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 220.76/221.14 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 220.76/221.14 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 220.76/221.14 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 220.76/221.14 Found eq_ref00:=(eq_ref0 b00):(((eq a) b00) b00)
% 220.76/221.14 Found (eq_ref0 b00) as proof of (((eq a) b00) (Xf x1))
% 220.76/221.14 Found ((eq_ref a) b00) as proof of (((eq a) b00) (Xf x1))
% 220.76/221.14 Found ((eq_ref a) b00) as proof of (((eq a) b00) (Xf x1))
% 220.76/221.14 Found ((eq_ref a) b00) as proof of (((eq a) b00) (Xf x1))
% 220.76/221.14 Found eq_ref00:=(eq_ref0 (Xg x1)):(((eq a) (Xg x1)) (Xg x1))
% 220.76/221.14 Found (eq_ref0 (Xg x1)) as proof of (((eq a) (Xg x1)) b00)
% 220.76/221.14 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b00)
% 220.76/221.14 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b00)
% 220.76/221.14 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b00)
% 220.76/221.14 Found eq_ref00:=(eq_ref0 b00):(((eq a) b00) b00)
% 220.76/221.14 Found (eq_ref0 b00) as proof of (((eq a) b00) (Xf x1))
% 220.76/221.14 Found ((eq_ref a) b00) as proof of (((eq a) b00) (Xf x1))
% 220.76/221.14 Found ((eq_ref a) b00) as proof of (((eq a) b00) (Xf x1))
% 220.76/221.14 Found ((eq_ref a) b00) as proof of (((eq a) b00) (Xf x1))
% 220.76/221.14 Found eq_ref00:=(eq_ref0 (Xg x1)):(((eq a) (Xg x1)) (Xg x1))
% 220.76/221.14 Found (eq_ref0 (Xg x1)) as proof of (((eq a) (Xg x1)) b00)
% 220.76/221.14 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b00)
% 220.76/221.14 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b00)
% 220.76/221.14 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b00)
% 220.76/221.14 Found x00:=(x0 (fun (x1:a)=> (P b0))):((P b0)->(P b0))
% 220.76/221.14 Found (x0 (fun (x1:a)=> (P b0))) as proof of (P0 b0)
% 220.76/221.14 Found (x0 (fun (x1:a)=> (P b0))) as proof of (P0 b0)
% 220.76/221.14 Found eta_expansion_dep000:=(eta_expansion_dep00 Xg):(((eq (b->a)) Xg) (fun (x:b)=> (Xg x)))
% 220.76/221.14 Found (eta_expansion_dep00 Xg) as proof of (((eq (b->a)) Xg) b0)
% 220.76/221.14 Found ((eta_expansion_dep0 (fun (x4:b)=> a)) Xg) as proof of (((eq (b->a)) Xg) b0)
% 220.76/221.14 Found (((eta_expansion_dep b) (fun (x4:b)=> a)) Xg) as proof of (((eq (b->a)) Xg) b0)
% 220.76/221.14 Found (((eta_expansion_dep b) (fun (x4:b)=> a)) Xg) as proof of (((eq (b->a)) Xg) b0)
% 220.76/221.14 Found (((eta_expansion_dep b) (fun (x4:b)=> a)) Xg) as proof of (((eq (b->a)) Xg) b0)
% 220.76/221.14 Found eta_expansion000:=(eta_expansion00 Xg):(((eq (b->a)) Xg) (fun (x:b)=> (Xg x)))
% 220.76/221.14 Found (eta_expansion00 Xg) as proof of (((eq (b->a)) Xg) b0)
% 220.76/221.14 Found ((eta_expansion0 a) Xg) as proof of (((eq (b->a)) Xg) b0)
% 220.76/221.14 Found (((eta_expansion b) a) Xg) as proof of (((eq (b->a)) Xg) b0)
% 220.76/221.14 Found (((eta_expansion b) a) Xg) as proof of (((eq (b->a)) Xg) b0)
% 220.76/221.14 Found (((eta_expansion b) a) Xg) as proof of (((eq (b->a)) Xg) b0)
% 220.76/221.14 Found x00:=(x0 (fun (x1:a)=> (P b0))):((P b0)->(P b0))
% 220.76/221.14 Found (x0 (fun (x1:a)=> (P b0))) as proof of (P0 b0)
% 220.76/221.14 Found (x0 (fun (x1:a)=> (P b0))) as proof of (P0 b0)
% 220.76/221.14 Found eq_ref00:=(eq_ref0 (Xg x1)):(((eq a) (Xg x1)) (Xg x1))
% 220.76/221.14 Found (eq_ref0 (Xg x1)) as proof of (((eq a) (Xg x1)) b00)
% 220.76/221.14 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b00)
% 220.76/221.14 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b00)
% 220.76/221.14 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b00)
% 220.76/221.14 Found eq_ref00:=(eq_ref0 b00):(((eq a) b00) b00)
% 220.76/221.14 Found (eq_ref0 b00) as proof of (((eq a) b00) (Xf x1))
% 220.76/221.14 Found ((eq_ref a) b00) as proof of (((eq a) b00) (Xf x1))
% 261.40/261.76 Found ((eq_ref a) b00) as proof of (((eq a) b00) (Xf x1))
% 261.40/261.76 Found ((eq_ref a) b00) as proof of (((eq a) b00) (Xf x1))
% 261.40/261.76 Found eq_ref00:=(eq_ref0 (Xg x1)):(((eq a) (Xg x1)) (Xg x1))
% 261.40/261.76 Found (eq_ref0 (Xg x1)) as proof of (((eq a) (Xg x1)) b00)
% 261.40/261.76 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b00)
% 261.40/261.76 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b00)
% 261.40/261.76 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b00)
% 261.40/261.76 Found eq_ref00:=(eq_ref0 b00):(((eq a) b00) b00)
% 261.40/261.76 Found (eq_ref0 b00) as proof of (((eq a) b00) (Xf x1))
% 261.40/261.76 Found ((eq_ref a) b00) as proof of (((eq a) b00) (Xf x1))
% 261.40/261.76 Found ((eq_ref a) b00) as proof of (((eq a) b00) (Xf x1))
% 261.40/261.76 Found ((eq_ref a) b00) as proof of (((eq a) b00) (Xf x1))
% 261.40/261.76 Found eq_ref00:=(eq_ref0 a0):(((eq b) a0) a0)
% 261.40/261.76 Found (eq_ref0 a0) as proof of (((eq b) a0) x1)
% 261.40/261.76 Found ((eq_ref b) a0) as proof of (((eq b) a0) x1)
% 261.40/261.76 Found ((eq_ref b) a0) as proof of (((eq b) a0) x1)
% 261.40/261.76 Found ((eq_ref b) a0) as proof of (((eq b) a0) x1)
% 261.40/261.76 Found eq_ref00:=(eq_ref0 a0):(((eq b) a0) a0)
% 261.40/261.76 Found (eq_ref0 a0) as proof of (((eq b) a0) x1)
% 261.40/261.76 Found ((eq_ref b) a0) as proof of (((eq b) a0) x1)
% 261.40/261.76 Found ((eq_ref b) a0) as proof of (((eq b) a0) x1)
% 261.40/261.76 Found ((eq_ref b) a0) as proof of (((eq b) a0) x1)
% 261.40/261.76 Found eq_ref00:=(eq_ref0 a0):(((eq b) a0) a0)
% 261.40/261.76 Found (eq_ref0 a0) as proof of (((eq b) a0) x1)
% 261.40/261.76 Found ((eq_ref b) a0) as proof of (((eq b) a0) x1)
% 261.40/261.76 Found ((eq_ref b) a0) as proof of (((eq b) a0) x1)
% 261.40/261.76 Found ((eq_ref b) a0) as proof of (((eq b) a0) x1)
% 261.40/261.76 Found eq_ref00:=(eq_ref0 a0):(((eq b) a0) a0)
% 261.40/261.76 Found (eq_ref0 a0) as proof of (((eq b) a0) x1)
% 261.40/261.76 Found ((eq_ref b) a0) as proof of (((eq b) a0) x1)
% 261.40/261.76 Found ((eq_ref b) a0) as proof of (((eq b) a0) x1)
% 261.40/261.76 Found ((eq_ref b) a0) as proof of (((eq b) a0) x1)
% 261.40/261.76 Found eq_ref00:=(eq_ref0 b00):(((eq (b->a)) b00) b00)
% 261.40/261.76 Found (eq_ref0 b00) as proof of (((eq (b->a)) b00) Xg)
% 261.40/261.76 Found ((eq_ref (b->a)) b00) as proof of (((eq (b->a)) b00) Xg)
% 261.40/261.76 Found ((eq_ref (b->a)) b00) as proof of (((eq (b->a)) b00) Xg)
% 261.40/261.76 Found ((eq_ref (b->a)) b00) as proof of (((eq (b->a)) b00) Xg)
% 261.40/261.76 Found eq_ref00:=(eq_ref0 b0):(((eq (b->a)) b0) b0)
% 261.40/261.76 Found (eq_ref0 b0) as proof of (((eq (b->a)) b0) b00)
% 261.40/261.76 Found ((eq_ref (b->a)) b0) as proof of (((eq (b->a)) b0) b00)
% 261.40/261.76 Found ((eq_ref (b->a)) b0) as proof of (((eq (b->a)) b0) b00)
% 261.40/261.76 Found ((eq_ref (b->a)) b0) as proof of (((eq (b->a)) b0) b00)
% 261.40/261.76 Found x00:=(x0 (fun (x2:a)=> (P (Xg x1)))):((P (Xg x1))->(P (Xg x1)))
% 261.40/261.76 Found (x0 (fun (x2:a)=> (P (Xg x1)))) as proof of (P0 (Xg x1))
% 261.40/261.76 Found (x0 (fun (x2:a)=> (P (Xg x1)))) as proof of (P0 (Xg x1))
% 261.40/261.76 Found x00:=(x0 (fun (x2:a)=> (P b0))):((P b0)->(P b0))
% 261.40/261.76 Found (x0 (fun (x2:a)=> (P b0))) as proof of (P0 b0)
% 261.40/261.76 Found (x0 (fun (x2:a)=> (P b0))) as proof of (P0 b0)
% 261.40/261.76 Found x00:=(x0 (fun (x2:a)=> (P b0))):((P b0)->(P b0))
% 261.40/261.76 Found (x0 (fun (x2:a)=> (P b0))) as proof of (P0 b0)
% 261.40/261.76 Found (x0 (fun (x2:a)=> (P b0))) as proof of (P0 b0)
% 261.40/261.76 Found x00:=(x0 (fun (x2:a)=> (P b0))):((P b0)->(P b0))
% 261.40/261.76 Found (x0 (fun (x2:a)=> (P b0))) as proof of (P0 b0)
% 261.40/261.76 Found (x0 (fun (x2:a)=> (P b0))) as proof of (P0 b0)
% 261.40/261.76 Found x00:=(x0 (fun (x2:a)=> (P (Xg x1)))):((P (Xg x1))->(P (Xg x1)))
% 261.40/261.76 Found (x0 (fun (x2:a)=> (P (Xg x1)))) as proof of (P0 (Xg x1))
% 261.40/261.76 Found (x0 (fun (x2:a)=> (P (Xg x1)))) as proof of (P0 (Xg x1))
% 261.40/261.76 Found x00:=(x0 (fun (x2:a)=> (P (Xg x1)))):((P (Xg x1))->(P (Xg x1)))
% 261.40/261.76 Found (x0 (fun (x2:a)=> (P (Xg x1)))) as proof of (P0 (Xg x1))
% 261.40/261.76 Found (x0 (fun (x2:a)=> (P (Xg x1)))) as proof of (P0 (Xg x1))
% 261.40/261.76 Found x00:=(x0 (fun (x2:a)=> (P (b0 x1)))):((P (b0 x1))->(P (b0 x1)))
% 261.40/261.76 Found (x0 (fun (x2:a)=> (P (b0 x1)))) as proof of (P0 (b0 x1))
% 261.40/261.76 Found (x0 (fun (x2:a)=> (P (b0 x1)))) as proof of (P0 (b0 x1))
% 261.40/261.76 Found x00:=(x0 (fun (x2:a)=> (P (b0 x1)))):((P (b0 x1))->(P (b0 x1)))
% 261.40/261.76 Found (x0 (fun (x2:a)=> (P (b0 x1)))) as proof of (P0 (b0 x1))
% 261.40/261.76 Found (x0 (fun (x2:a)=> (P (b0 x1)))) as proof of (P0 (b0 x1))
% 261.40/261.76 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xx:b)=> (((eq a) (Xf x1)) (Xg x1)))):(((eq (b->Prop)) (fun (Xx:b)=> (((eq a) (Xf x1)) (Xg x1)))) (fun (x:b)=> (((eq a) (Xf x1)) (Xg x1))))
% 261.40/261.76 Found (eta_expansion_dep00 (fun (Xx:b)=> (((eq a) (Xf x1)) (Xg x1)))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (((eq a) (Xf x1)) (Xg x1)))) b0)
% 275.38/275.75 Found ((eta_expansion_dep0 (fun (x4:b)=> Prop)) (fun (Xx:b)=> (((eq a) (Xf x1)) (Xg x1)))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (((eq a) (Xf x1)) (Xg x1)))) b0)
% 275.38/275.75 Found (((eta_expansion_dep b) (fun (x4:b)=> Prop)) (fun (Xx:b)=> (((eq a) (Xf x1)) (Xg x1)))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (((eq a) (Xf x1)) (Xg x1)))) b0)
% 275.38/275.75 Found (((eta_expansion_dep b) (fun (x4:b)=> Prop)) (fun (Xx:b)=> (((eq a) (Xf x1)) (Xg x1)))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (((eq a) (Xf x1)) (Xg x1)))) b0)
% 275.38/275.75 Found (((eta_expansion_dep b) (fun (x4:b)=> Prop)) (fun (Xx:b)=> (((eq a) (Xf x1)) (Xg x1)))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (((eq a) (Xf x1)) (Xg x1)))) b0)
% 275.38/275.75 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xx:b)=> (((eq a) (Xf x1)) (Xg x1)))):(((eq (b->Prop)) (fun (Xx:b)=> (((eq a) (Xf x1)) (Xg x1)))) (fun (x:b)=> (((eq a) (Xf x1)) (Xg x1))))
% 275.38/275.75 Found (eta_expansion_dep00 (fun (Xx:b)=> (((eq a) (Xf x1)) (Xg x1)))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (((eq a) (Xf x1)) (Xg x1)))) b0)
% 275.38/275.75 Found ((eta_expansion_dep0 (fun (x4:b)=> Prop)) (fun (Xx:b)=> (((eq a) (Xf x1)) (Xg x1)))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (((eq a) (Xf x1)) (Xg x1)))) b0)
% 275.38/275.75 Found (((eta_expansion_dep b) (fun (x4:b)=> Prop)) (fun (Xx:b)=> (((eq a) (Xf x1)) (Xg x1)))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (((eq a) (Xf x1)) (Xg x1)))) b0)
% 275.38/275.75 Found (((eta_expansion_dep b) (fun (x4:b)=> Prop)) (fun (Xx:b)=> (((eq a) (Xf x1)) (Xg x1)))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (((eq a) (Xf x1)) (Xg x1)))) b0)
% 275.38/275.75 Found (((eta_expansion_dep b) (fun (x4:b)=> Prop)) (fun (Xx:b)=> (((eq a) (Xf x1)) (Xg x1)))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> (((eq a) (Xf x1)) (Xg x1)))) b0)
% 275.38/275.75 Found eq_ref00:=(eq_ref0 (Xg x1)):(((eq a) (Xg x1)) (Xg x1))
% 275.38/275.75 Found (eq_ref0 (Xg x1)) as proof of (((eq a) (Xg x1)) b1)
% 275.38/275.75 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b1)
% 275.38/275.75 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b1)
% 275.38/275.75 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b1)
% 275.38/275.75 Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% 275.38/275.75 Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% 275.38/275.75 Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% 275.38/275.75 Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% 275.38/275.75 Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% 275.38/275.75 Found eq_ref00:=(eq_ref0 (Xg x1)):(((eq a) (Xg x1)) (Xg x1))
% 275.38/275.75 Found (eq_ref0 (Xg x1)) as proof of (((eq a) (Xg x1)) b1)
% 275.38/275.75 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b1)
% 275.38/275.75 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b1)
% 275.38/275.75 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b1)
% 275.38/275.75 Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% 275.38/275.75 Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% 275.38/275.75 Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% 275.38/275.75 Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% 275.38/275.75 Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% 275.38/275.75 Found x00:=(x0 (fun (x2:a)=> (P (Xf x1)))):((P (Xf x1))->(P (Xf x1)))
% 275.38/275.75 Found (x0 (fun (x2:a)=> (P (Xf x1)))) as proof of (P0 (Xf x1))
% 275.38/275.75 Found (x0 (fun (x2:a)=> (P (Xf x1)))) as proof of (P0 (Xf x1))
% 275.38/275.75 Found x00:=(x0 (fun (x2:a)=> (P (Xf x1)))):((P (Xf x1))->(P (Xf x1)))
% 275.38/275.75 Found (x0 (fun (x2:a)=> (P (Xf x1)))) as proof of (P0 (Xf x1))
% 275.38/275.75 Found (x0 (fun (x2:a)=> (P (Xf x1)))) as proof of (P0 (Xf x1))
% 275.38/275.75 Found eq_ref00:=(eq_ref0 (fun (Xx:b)=> ((P (Xf x1))->(P (Xg x1))))):(((eq (b->Prop)) (fun (Xx:b)=> ((P (Xf x1))->(P (Xg x1))))) (fun (Xx:b)=> ((P (Xf x1))->(P (Xg x1)))))
% 275.38/275.75 Found (eq_ref0 (fun (Xx:b)=> ((P (Xf x1))->(P (Xg x1))))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> ((P (Xf x1))->(P (Xg x1))))) b0)
% 275.38/275.75 Found ((eq_ref (b->Prop)) (fun (Xx:b)=> ((P (Xf x1))->(P (Xg x1))))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> ((P (Xf x1))->(P (Xg x1))))) b0)
% 275.38/275.75 Found ((eq_ref (b->Prop)) (fun (Xx:b)=> ((P (Xf x1))->(P (Xg x1))))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> ((P (Xf x1))->(P (Xg x1))))) b0)
% 275.38/275.75 Found ((eq_ref (b->Prop)) (fun (Xx:b)=> ((P (Xf x1))->(P (Xg x1))))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> ((P (Xf x1))->(P (Xg x1))))) b0)
% 275.38/275.75 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xx:b)=> ((P (Xf x1))->(P (Xg x1))))):(((eq (b->Prop)) (fun (Xx:b)=> ((P (Xf x1))->(P (Xg x1))))) (fun (x:b)=> ((P (Xf x1))->(P (Xg x1)))))
% 278.89/279.28 Found (eta_expansion_dep00 (fun (Xx:b)=> ((P (Xf x1))->(P (Xg x1))))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> ((P (Xf x1))->(P (Xg x1))))) b0)
% 278.89/279.28 Found ((eta_expansion_dep0 (fun (x4:b)=> Prop)) (fun (Xx:b)=> ((P (Xf x1))->(P (Xg x1))))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> ((P (Xf x1))->(P (Xg x1))))) b0)
% 278.89/279.28 Found (((eta_expansion_dep b) (fun (x4:b)=> Prop)) (fun (Xx:b)=> ((P (Xf x1))->(P (Xg x1))))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> ((P (Xf x1))->(P (Xg x1))))) b0)
% 278.89/279.28 Found (((eta_expansion_dep b) (fun (x4:b)=> Prop)) (fun (Xx:b)=> ((P (Xf x1))->(P (Xg x1))))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> ((P (Xf x1))->(P (Xg x1))))) b0)
% 278.89/279.28 Found (((eta_expansion_dep b) (fun (x4:b)=> Prop)) (fun (Xx:b)=> ((P (Xf x1))->(P (Xg x1))))) as proof of (((eq (b->Prop)) (fun (Xx:b)=> ((P (Xf x1))->(P (Xg x1))))) b0)
% 278.89/279.28 Found x00:=(x0 (fun (x2:a)=> (P (Xg x1)))):((P (Xg x1))->(P (Xg x1)))
% 278.89/279.28 Found (x0 (fun (x2:a)=> (P (Xg x1)))) as proof of (P0 (Xg x1))
% 278.89/279.28 Found (x0 (fun (x2:a)=> (P (Xg x1)))) as proof of (P0 (Xg x1))
% 278.89/279.28 Found x00:=(x0 (fun (x2:a)=> (P (Xg x1)))):((P (Xg x1))->(P (Xg x1)))
% 278.89/279.28 Found (x0 (fun (x2:a)=> (P (Xg x1)))) as proof of (P0 (Xg x1))
% 278.89/279.28 Found (x0 (fun (x2:a)=> (P (Xg x1)))) as proof of (P0 (Xg x1))
% 278.89/279.28 Found x00:=(x0 (fun (x2:a)=> (P (Xg x1)))):((P (Xg x1))->(P (Xg x1)))
% 278.89/279.28 Found (x0 (fun (x2:a)=> (P (Xg x1)))) as proof of (P0 (Xg x1))
% 278.89/279.28 Found (x0 (fun (x2:a)=> (P (Xg x1)))) as proof of (P0 (Xg x1))
% 278.89/279.28 Found x00:=(x0 (fun (x2:a)=> (P (Xg x1)))):((P (Xg x1))->(P (Xg x1)))
% 278.89/279.28 Found (x0 (fun (x2:a)=> (P (Xg x1)))) as proof of (P0 (Xg x1))
% 278.89/279.28 Found (x0 (fun (x2:a)=> (P (Xg x1)))) as proof of (P0 (Xg x1))
% 278.89/279.28 Found x00:=(x0 (fun (x2:a)=> (P (Xg x1)))):((P (Xg x1))->(P (Xg x1)))
% 278.89/279.28 Found (x0 (fun (x2:a)=> (P (Xg x1)))) as proof of (P0 (Xg x1))
% 278.89/279.28 Found (x0 (fun (x2:a)=> (P (Xg x1)))) as proof of (P0 (Xg x1))
% 278.89/279.28 Found x00:=(x0 (fun (x2:a)=> (P (Xg x1)))):((P (Xg x1))->(P (Xg x1)))
% 278.89/279.28 Found (x0 (fun (x2:a)=> (P (Xg x1)))) as proof of (P0 (Xg x1))
% 278.89/279.28 Found (x0 (fun (x2:a)=> (P (Xg x1)))) as proof of (P0 (Xg x1))
% 278.89/279.28 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 278.89/279.28 Found (eq_ref0 b0) as proof of (((eq a) b0) (Xg x1))
% 278.89/279.28 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 278.89/279.28 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 278.89/279.28 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 278.89/279.28 Found eq_ref00:=(eq_ref0 (Xf x1)):(((eq a) (Xf x1)) (Xf x1))
% 278.89/279.28 Found (eq_ref0 (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 278.89/279.28 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 278.89/279.28 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 278.89/279.28 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 278.89/279.28 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 278.89/279.28 Found (eq_ref0 b0) as proof of (((eq a) b0) (Xg x1))
% 278.89/279.28 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 278.89/279.28 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 278.89/279.28 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 278.89/279.28 Found eq_ref00:=(eq_ref0 (Xf x1)):(((eq a) (Xf x1)) (Xf x1))
% 278.89/279.28 Found (eq_ref0 (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 278.89/279.28 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 278.89/279.28 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 278.89/279.28 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 278.89/279.28 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 278.89/279.28 Found (eq_ref0 b0) as proof of (((eq a) b0) (Xg x1))
% 278.89/279.28 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 278.89/279.28 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 278.89/279.28 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 278.89/279.28 Found eq_ref00:=(eq_ref0 (Xf x1)):(((eq a) (Xf x1)) (Xf x1))
% 278.89/279.28 Found (eq_ref0 (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 278.89/279.28 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 278.89/279.28 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 278.89/279.28 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 278.89/279.28 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 278.89/279.28 Found (eq_ref0 b0) as proof of (((eq a) b0) (Xg x1))
% 278.89/279.28 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 278.89/279.28 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 278.89/279.28 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 278.89/279.28 Found eq_ref00:=(eq_ref0 (Xf x1)):(((eq a) (Xf x1)) (Xf x1))
% 278.89/279.28 Found (eq_ref0 (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 280.81/281.24 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 280.81/281.24 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 280.81/281.24 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 280.81/281.24 Found eq_ref00:=(eq_ref0 (Xf x1)):(((eq a) (Xf x1)) (Xf x1))
% 280.81/281.24 Found (eq_ref0 (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 280.81/281.24 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 280.81/281.24 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 280.81/281.24 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 280.81/281.24 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 280.81/281.24 Found (eq_ref0 b0) as proof of (((eq a) b0) (Xg x1))
% 280.81/281.24 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 280.81/281.24 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 280.81/281.24 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 280.81/281.24 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 280.81/281.24 Found (eq_ref0 b0) as proof of (((eq a) b0) (Xg x1))
% 280.81/281.24 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 280.81/281.24 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 280.81/281.24 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 280.81/281.24 Found eq_ref00:=(eq_ref0 (Xf x1)):(((eq a) (Xf x1)) (Xf x1))
% 280.81/281.24 Found (eq_ref0 (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 280.81/281.24 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 280.81/281.24 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 280.81/281.24 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 280.81/281.24 Found eq_ref00:=(eq_ref0 (Xf x1)):(((eq a) (Xf x1)) (Xf x1))
% 280.81/281.24 Found (eq_ref0 (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 280.81/281.24 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 280.81/281.24 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 280.81/281.24 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 280.81/281.24 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 280.81/281.24 Found (eq_ref0 b0) as proof of (((eq a) b0) (Xg x1))
% 280.81/281.24 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 280.81/281.24 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 280.81/281.24 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 280.81/281.24 Found eq_ref00:=(eq_ref0 (Xf x1)):(((eq a) (Xf x1)) (Xf x1))
% 280.81/281.24 Found (eq_ref0 (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 280.81/281.24 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 280.81/281.24 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 280.81/281.24 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 280.81/281.24 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 280.81/281.24 Found (eq_ref0 b0) as proof of (((eq a) b0) (Xg x1))
% 280.81/281.24 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 280.81/281.24 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 280.81/281.24 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 280.81/281.24 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 280.81/281.24 Found (eq_ref0 b0) as proof of (((eq a) b0) (Xg x1))
% 280.81/281.24 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 280.81/281.24 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 280.81/281.24 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 280.81/281.24 Found eq_ref00:=(eq_ref0 (Xf x1)):(((eq a) (Xf x1)) (Xf x1))
% 280.81/281.24 Found (eq_ref0 (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 280.81/281.24 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 280.81/281.24 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 280.81/281.24 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 280.81/281.24 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 280.81/281.24 Found (eq_ref0 b0) as proof of (((eq a) b0) (Xg x1))
% 280.81/281.24 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 280.81/281.24 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 280.81/281.24 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 280.81/281.24 Found eq_ref00:=(eq_ref0 (Xf x1)):(((eq a) (Xf x1)) (Xf x1))
% 280.81/281.24 Found (eq_ref0 (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 280.81/281.24 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 280.81/281.24 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 280.81/281.24 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 280.81/281.24 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 280.81/281.24 Found (eq_ref0 b0) as proof of (((eq a) b0) (Xg x1))
% 280.81/281.24 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 280.81/281.24 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 280.81/281.24 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 280.81/281.24 Found eq_ref00:=(eq_ref0 (Xf x1)):(((eq a) (Xf x1)) (Xf x1))
% 280.81/281.24 Found (eq_ref0 (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 280.81/281.24 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 280.81/281.24 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 293.61/294.01 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 293.61/294.01 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 293.61/294.01 Found (eq_ref0 b0) as proof of (((eq a) b0) (Xg x1))
% 293.61/294.01 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 293.61/294.01 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 293.61/294.01 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 293.61/294.01 Found eq_ref00:=(eq_ref0 (Xf x1)):(((eq a) (Xf x1)) (Xf x1))
% 293.61/294.01 Found (eq_ref0 (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 293.61/294.01 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 293.61/294.01 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 293.61/294.01 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 293.61/294.01 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 293.61/294.01 Found (eq_ref0 b0) as proof of (((eq a) b0) (Xg x1))
% 293.61/294.01 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 293.61/294.01 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 293.61/294.01 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 293.61/294.01 Found eq_ref00:=(eq_ref0 (Xf x1)):(((eq a) (Xf x1)) (Xf x1))
% 293.61/294.01 Found (eq_ref0 (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 293.61/294.01 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 293.61/294.01 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 293.61/294.01 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 293.61/294.01 Found eq_ref00:=(eq_ref0 (Xf x1)):(((eq a) (Xf x1)) (Xf x1))
% 293.61/294.01 Found (eq_ref0 (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 293.61/294.01 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 293.61/294.01 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 293.61/294.01 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 293.61/294.01 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 293.61/294.01 Found (eq_ref0 b0) as proof of (((eq a) b0) (Xg x1))
% 293.61/294.01 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 293.61/294.01 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 293.61/294.01 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 293.61/294.01 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 293.61/294.01 Found (eq_ref0 b0) as proof of (((eq a) b0) (Xg x1))
% 293.61/294.01 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 293.61/294.01 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 293.61/294.01 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 293.61/294.01 Found eq_ref00:=(eq_ref0 (Xf x1)):(((eq a) (Xf x1)) (Xf x1))
% 293.61/294.01 Found (eq_ref0 (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 293.61/294.01 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 293.61/294.01 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 293.61/294.01 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 293.61/294.01 Found eq_ref00:=(eq_ref0 (Xf x1)):(((eq a) (Xf x1)) (Xf x1))
% 293.61/294.01 Found (eq_ref0 (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 293.61/294.01 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 293.61/294.01 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 293.61/294.01 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) b0)
% 293.61/294.01 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 293.61/294.01 Found (eq_ref0 b0) as proof of (((eq a) b0) (Xg x1))
% 293.61/294.01 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 293.61/294.01 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 293.61/294.01 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 293.61/294.01 Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% 293.61/294.01 Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) ((P (Xg x1))->(P (Xf x1))))
% 293.61/294.01 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) ((P (Xg x1))->(P (Xf x1))))
% 293.61/294.01 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) ((P (Xg x1))->(P (Xf x1))))
% 293.61/294.01 Found (fun (x3:b)=> ((eq_ref Prop) (f x3))) as proof of (((eq Prop) (f x3)) ((P (Xg x1))->(P (Xf x1))))
% 293.61/294.01 Found (fun (x3:b)=> ((eq_ref Prop) (f x3))) as proof of (forall (x:b), (((eq Prop) (f x)) ((P (Xg x1))->(P (Xf x1)))))
% 293.61/294.01 Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% 293.61/294.01 Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) ((P (Xg x1))->(P (Xf x1))))
% 293.61/294.01 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) ((P (Xg x1))->(P (Xf x1))))
% 293.61/294.01 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) ((P (Xg x1))->(P (Xf x1))))
% 293.61/294.01 Found (fun (x3:b)=> ((eq_ref Prop) (f x3))) as proof of (((eq Prop) (f x3)) ((P (Xg x1))->(P (Xf x1))))
% 293.61/294.01 Found (fun (x3:b)=> ((eq_ref Prop) (f x3))) as proof of (forall (x:b), (((eq Prop) (f x)) ((P (Xg x1))->(P (Xf x1)))))
% 293.61/294.01 Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% 296.56/296.93 Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) ((P (Xg x1))->(P (Xf x1))))
% 296.56/296.93 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) ((P (Xg x1))->(P (Xf x1))))
% 296.56/296.93 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) ((P (Xg x1))->(P (Xf x1))))
% 296.56/296.93 Found (fun (x3:b)=> ((eq_ref Prop) (f x3))) as proof of (((eq Prop) (f x3)) ((P (Xg x1))->(P (Xf x1))))
% 296.56/296.93 Found (fun (x3:b)=> ((eq_ref Prop) (f x3))) as proof of (forall (x:b), (((eq Prop) (f x)) ((P (Xg x1))->(P (Xf x1)))))
% 296.56/296.93 Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% 296.56/296.93 Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) ((P (Xg x1))->(P (Xf x1))))
% 296.56/296.93 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) ((P (Xg x1))->(P (Xf x1))))
% 296.56/296.93 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) ((P (Xg x1))->(P (Xf x1))))
% 296.56/296.93 Found (fun (x3:b)=> ((eq_ref Prop) (f x3))) as proof of (((eq Prop) (f x3)) ((P (Xg x1))->(P (Xf x1))))
% 296.56/296.93 Found (fun (x3:b)=> ((eq_ref Prop) (f x3))) as proof of (forall (x:b), (((eq Prop) (f x)) ((P (Xg x1))->(P (Xf x1)))))
% 296.56/296.93 Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% 296.56/296.93 Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) (((eq a) (Xf x1)) (Xg x1)))
% 296.56/296.93 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (((eq a) (Xf x1)) (Xg x1)))
% 296.56/296.93 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (((eq a) (Xf x1)) (Xg x1)))
% 296.56/296.93 Found (fun (x3:b)=> ((eq_ref Prop) (f x3))) as proof of (((eq Prop) (f x3)) (((eq a) (Xf x1)) (Xg x1)))
% 296.56/296.93 Found (fun (x3:b)=> ((eq_ref Prop) (f x3))) as proof of (forall (x:b), (((eq Prop) (f x)) (((eq a) (Xf x1)) (Xg x1))))
% 296.56/296.93 Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% 296.56/296.93 Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) (((eq a) (Xf x1)) (Xg x1)))
% 296.56/296.93 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (((eq a) (Xf x1)) (Xg x1)))
% 296.56/296.93 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (((eq a) (Xf x1)) (Xg x1)))
% 296.56/296.93 Found (fun (x3:b)=> ((eq_ref Prop) (f x3))) as proof of (((eq Prop) (f x3)) (((eq a) (Xf x1)) (Xg x1)))
% 296.56/296.93 Found (fun (x3:b)=> ((eq_ref Prop) (f x3))) as proof of (forall (x:b), (((eq Prop) (f x)) (((eq a) (Xf x1)) (Xg x1))))
% 296.56/296.93 Found x1:b
% 296.56/296.93 Found x1 as proof of b
% 296.56/296.93 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 296.56/296.93 Found (eq_ref0 b0) as proof of (((eq a) b0) (Xg x1))
% 296.56/296.93 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 296.56/296.93 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 296.56/296.93 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 296.56/296.93 Found ((ex_intro00 x1) ((eq_ref a) b0)) as proof of (P b0)
% 296.56/296.93 Found (((ex_intro0 (fun (Xx:b)=> (((eq a) b0) (Xg x1)))) x1) ((eq_ref a) b0)) as proof of (P b0)
% 296.56/296.93 Found ((((ex_intro b) (fun (Xx:b)=> (((eq a) b0) (Xg x1)))) x1) ((eq_ref a) b0)) as proof of (P b0)
% 296.56/296.93 Found ((((ex_intro b) (fun (Xx:b)=> (((eq a) b0) (Xg x1)))) x1) ((eq_ref a) b0)) as proof of (P b0)
% 296.56/296.93 Found x1:b
% 296.56/296.93 Found x1 as proof of b
% 296.56/296.93 Found eq_ref00:=(eq_ref0 (Xf x1)):(((eq a) (Xf x1)) (Xf x1))
% 296.56/296.93 Found (eq_ref0 (Xf x1)) as proof of (((eq a) (Xf x1)) (b0 x1))
% 296.56/296.93 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) (b0 x1))
% 296.56/296.93 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) (b0 x1))
% 296.56/296.93 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) (b0 x1))
% 296.56/296.93 Found ((ex_intro00 x1) ((eq_ref a) (Xf x1))) as proof of (P b0)
% 296.56/296.93 Found (((ex_intro0 (fun (Xx:b)=> (((eq a) (Xf x1)) (b0 x1)))) x1) ((eq_ref a) (Xf x1))) as proof of (P b0)
% 296.56/296.93 Found ((((ex_intro b) (fun (Xx:b)=> (((eq a) (Xf x1)) (b0 x1)))) x1) ((eq_ref a) (Xf x1))) as proof of (P b0)
% 296.56/296.93 Found ((((ex_intro b) (fun (Xx:b)=> (((eq a) (Xf x1)) (b0 x1)))) x1) ((eq_ref a) (Xf x1))) as proof of (P b0)
% 296.56/296.93 Found x1:b
% 296.56/296.93 Found x1 as proof of b
% 296.56/296.93 Found eq_ref00:=(eq_ref0 (Xf x1)):(((eq a) (Xf x1)) (Xf x1))
% 296.56/296.93 Found (eq_ref0 (Xf x1)) as proof of (((eq a) (Xf x1)) (b0 x1))
% 296.56/296.93 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) (b0 x1))
% 296.56/296.93 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) (b0 x1))
% 296.56/296.93 Found ((eq_ref a) (Xf x1)) as proof of (((eq a) (Xf x1)) (b0 x1))
% 296.56/296.93 Found ((ex_intro00 x1) ((eq_ref a) (Xf x1))) as proof of (P b0)
% 296.56/296.93 Found (((ex_intro0 (fun (Xx:b)=> (((eq a) (Xf x1)) (b0 x1)))) x1) ((eq_ref a) (Xf x1))) as proof of (P b0)
% 296.56/296.93 Found ((((ex_intro b) (fun (Xx:b)=> (((eq a) (Xf x1)) (b0 x1)))) x1) ((eq_ref a) (Xf x1))) as proof of (P b0)
% 299.79/300.19 Found ((((ex_intro b) (fun (Xx:b)=> (((eq a) (Xf x1)) (b0 x1)))) x1) ((eq_ref a) (Xf x1))) as proof of (P b0)
% 299.79/300.19 Found x1:b
% 299.79/300.19 Found x1 as proof of b
% 299.79/300.19 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 299.79/300.19 Found (eq_ref0 b0) as proof of (((eq a) b0) (Xg x1))
% 299.79/300.19 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 299.79/300.19 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 299.79/300.19 Found ((eq_ref a) b0) as proof of (((eq a) b0) (Xg x1))
% 299.79/300.19 Found ((ex_intro00 x1) ((eq_ref a) b0)) as proof of (P b0)
% 299.79/300.19 Found (((ex_intro0 (fun (Xx:b)=> (((eq a) b0) (Xg x1)))) x1) ((eq_ref a) b0)) as proof of (P b0)
% 299.79/300.19 Found ((((ex_intro b) (fun (Xx:b)=> (((eq a) b0) (Xg x1)))) x1) ((eq_ref a) b0)) as proof of (P b0)
% 299.79/300.19 Found ((((ex_intro b) (fun (Xx:b)=> (((eq a) b0) (Xg x1)))) x1) ((eq_ref a) b0)) as proof of (P b0)
% 299.79/300.19 Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% 299.79/300.19 Found (eq_ref0 b1) as proof of (((eq a) b1) (Xf x1))
% 299.79/300.19 Found ((eq_ref a) b1) as proof of (((eq a) b1) (Xf x1))
% 299.79/300.19 Found ((eq_ref a) b1) as proof of (((eq a) b1) (Xf x1))
% 299.79/300.19 Found ((eq_ref a) b1) as proof of (((eq a) b1) (Xf x1))
% 299.79/300.19 Found eq_ref00:=(eq_ref0 (b0 x1)):(((eq a) (b0 x1)) (b0 x1))
% 299.79/300.19 Found (eq_ref0 (b0 x1)) as proof of (((eq a) (b0 x1)) b1)
% 299.79/300.19 Found ((eq_ref a) (b0 x1)) as proof of (((eq a) (b0 x1)) b1)
% 299.79/300.19 Found ((eq_ref a) (b0 x1)) as proof of (((eq a) (b0 x1)) b1)
% 299.79/300.19 Found ((eq_ref a) (b0 x1)) as proof of (((eq a) (b0 x1)) b1)
% 299.79/300.19 Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% 299.79/300.19 Found (eq_ref0 b1) as proof of (((eq a) b1) (Xf x1))
% 299.79/300.19 Found ((eq_ref a) b1) as proof of (((eq a) b1) (Xf x1))
% 299.79/300.19 Found ((eq_ref a) b1) as proof of (((eq a) b1) (Xf x1))
% 299.79/300.19 Found ((eq_ref a) b1) as proof of (((eq a) b1) (Xf x1))
% 299.79/300.19 Found eq_ref00:=(eq_ref0 (b0 x1)):(((eq a) (b0 x1)) (b0 x1))
% 299.79/300.19 Found (eq_ref0 (b0 x1)) as proof of (((eq a) (b0 x1)) b1)
% 299.79/300.19 Found ((eq_ref a) (b0 x1)) as proof of (((eq a) (b0 x1)) b1)
% 299.79/300.19 Found ((eq_ref a) (b0 x1)) as proof of (((eq a) (b0 x1)) b1)
% 299.79/300.19 Found ((eq_ref a) (b0 x1)) as proof of (((eq a) (b0 x1)) b1)
% 299.79/300.19 Found eq_ref00:=(eq_ref0 (b0 x1)):(((eq a) (b0 x1)) (b0 x1))
% 299.79/300.19 Found (eq_ref0 (b0 x1)) as proof of (((eq a) (b0 x1)) b1)
% 299.79/300.19 Found ((eq_ref a) (b0 x1)) as proof of (((eq a) (b0 x1)) b1)
% 299.79/300.19 Found ((eq_ref a) (b0 x1)) as proof of (((eq a) (b0 x1)) b1)
% 299.79/300.19 Found ((eq_ref a) (b0 x1)) as proof of (((eq a) (b0 x1)) b1)
% 299.79/300.19 Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% 299.79/300.19 Found (eq_ref0 b1) as proof of (((eq a) b1) (Xf x1))
% 299.79/300.19 Found ((eq_ref a) b1) as proof of (((eq a) b1) (Xf x1))
% 299.79/300.19 Found ((eq_ref a) b1) as proof of (((eq a) b1) (Xf x1))
% 299.79/300.19 Found ((eq_ref a) b1) as proof of (((eq a) b1) (Xf x1))
% 299.79/300.19 Found eq_ref00:=(eq_ref0 (Xg x1)):(((eq a) (Xg x1)) (Xg x1))
% 299.79/300.19 Found (eq_ref0 (Xg x1)) as proof of (((eq a) (Xg x1)) b1)
% 299.79/300.19 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b1)
% 299.79/300.19 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b1)
% 299.79/300.19 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b1)
% 299.79/300.19 Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% 299.79/300.19 Found (eq_ref0 b1) as proof of (((eq a) b1) (b0 x1))
% 299.79/300.19 Found ((eq_ref a) b1) as proof of (((eq a) b1) (b0 x1))
% 299.79/300.19 Found ((eq_ref a) b1) as proof of (((eq a) b1) (b0 x1))
% 299.79/300.19 Found ((eq_ref a) b1) as proof of (((eq a) b1) (b0 x1))
% 299.79/300.19 Found eq_ref00:=(eq_ref0 (Xg x1)):(((eq a) (Xg x1)) (Xg x1))
% 299.79/300.19 Found (eq_ref0 (Xg x1)) as proof of (((eq a) (Xg x1)) b1)
% 299.79/300.19 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b1)
% 299.79/300.19 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b1)
% 299.79/300.19 Found ((eq_ref a) (Xg x1)) as proof of (((eq a) (Xg x1)) b1)
% 299.79/300.19 Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% 299.79/300.19 Found (eq_ref0 b1) as proof of (((eq a) b1) (b0 x1))
% 299.79/300.19 Found ((eq_ref a) b1) as proof of (((eq a) b1) (b0 x1))
% 299.79/300.19 Found ((eq_ref a) b1) as proof of (((eq a) b1) (b0 x1))
% 299.79/300.19 Found ((eq_ref a) b1) as proof of (((eq a) b1) (b0 x1))
% 299.79/300.19 Found eq_ref00:=(eq_ref0 (b0 x1)):(((eq a) (b0 x1)) (b0 x1))
% 299.79/300.19 Found (eq_ref0 (b0 x1)) as proof of (((eq a) (b0 x1)) b1)
% 299.79/300.19 Found ((eq_ref a) (b0 x1)) as proof of (((eq a) (b0 x1)) b1)
% 299.79/300.19 Found ((eq_ref a) (b0 x1)) as proof of (((eq a) (b0 x1)) b1)
% 299.79/300.19 Found ((eq_ref a) (b0 x1)) as proof of (((eq a) (b0 x1)) b1)
% 299.79/300.19 Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% 299.79/300.19 Found (eq_ref0 b1) as proof of (((eq a) b1) (Xf x1))
% 299.79/300.19 Found ((eq_ref a)
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