TSTP Solution File: SYO372^5 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SYO372^5 : TPTP v7.5.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 00:51:16 EDT 2022
% Result : Timeout 290.87s 291.29s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SYO372^5 : TPTP v7.5.0. Released v4.0.0.
% 0.03/0.12 % Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.32 % Computer : n012.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPUModel : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % RAMPerCPU : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % DateTime : Sat Mar 12 09:29:20 EST 2022
% 0.11/0.32 % CPUTime :
% 0.11/0.33 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.11/0.33 Python 2.7.5
% 8.89/9.11 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox2/benchmark/', '/export/starexec/sandbox2/benchmark/']
% 8.89/9.11 FOF formula (<kernel.Constant object at 0x9f7368>, <kernel.Type object at 0x9f7050>) of role type named b_type
% 8.89/9.11 Using role type
% 8.89/9.11 Declaring b:Type
% 8.89/9.11 FOF formula (<kernel.Constant object at 0x9d0908>, <kernel.Type object at 0x9f70e0>) of role type named g_type
% 8.89/9.11 Using role type
% 8.89/9.11 Declaring gtype:Type
% 8.89/9.11 FOF formula (<kernel.Constant object at 0x9f7440>, <kernel.DependentProduct object at 0x9f7128>) of role type named g
% 8.89/9.11 Using role type
% 8.89/9.11 Declaring g:(b->Prop)
% 8.89/9.11 FOF formula (<kernel.Constant object at 0x9f7f38>, <kernel.DependentProduct object at 0x9f2fc8>) of role type named h
% 8.89/9.11 Using role type
% 8.89/9.11 Declaring h:((b->Prop)->gtype)
% 8.89/9.11 FOF formula (<kernel.Constant object at 0x9f7050>, <kernel.DependentProduct object at 0x9f2050>) of role type named f
% 8.89/9.11 Using role type
% 8.89/9.11 Declaring f:(b->Prop)
% 8.89/9.11 FOF formula ((forall (Xx:b), ((iff (f Xx)) (g Xx)))->(((eq gtype) (h f)) (h g))) of role conjecture named cEXT_SET2
% 8.89/9.11 Conjecture to prove = ((forall (Xx:b), ((iff (f Xx)) (g Xx)))->(((eq gtype) (h f)) (h g))):Prop
% 8.89/9.11 Parameter b_DUMMY:b.
% 8.89/9.11 Parameter gtype_DUMMY:gtype.
% 8.89/9.11 We need to prove ['((forall (Xx:b), ((iff (f Xx)) (g Xx)))->(((eq gtype) (h f)) (h g)))']
% 8.89/9.11 Parameter b:Type.
% 8.89/9.11 Parameter gtype:Type.
% 8.89/9.11 Parameter g:(b->Prop).
% 8.89/9.11 Parameter h:((b->Prop)->gtype).
% 8.89/9.11 Parameter f:(b->Prop).
% 8.89/9.11 Trying to prove ((forall (Xx:b), ((iff (f Xx)) (g Xx)))->(((eq gtype) (h f)) (h g)))
% 8.89/9.11 Found x00:(P (h f))
% 8.89/9.11 Found (fun (x00:(P (h f)))=> x00) as proof of (P (h f))
% 8.89/9.11 Found (fun (x00:(P (h f)))=> x00) as proof of (P0 (h f))
% 8.89/9.11 Found x00:(P (h f))
% 8.89/9.11 Found (fun (x00:(P (h f)))=> x00) as proof of (P (h f))
% 8.89/9.11 Found (fun (x00:(P (h f)))=> x00) as proof of (P0 (h f))
% 8.89/9.11 Found x00:(P (h f))
% 8.89/9.11 Found (fun (x00:(P (h f)))=> x00) as proof of (P (h f))
% 8.89/9.11 Found (fun (x00:(P (h f)))=> x00) as proof of (P0 (h f))
% 8.89/9.11 Found eq_ref00:=(eq_ref0 (h f)):(((eq gtype) (h f)) (h f))
% 8.89/9.11 Found (eq_ref0 (h f)) as proof of (((eq gtype) (h f)) b0)
% 8.89/9.11 Found ((eq_ref gtype) (h f)) as proof of (((eq gtype) (h f)) b0)
% 8.89/9.11 Found ((eq_ref gtype) (h f)) as proof of (((eq gtype) (h f)) b0)
% 8.89/9.11 Found ((eq_ref gtype) (h f)) as proof of (((eq gtype) (h f)) b0)
% 8.89/9.11 Found eq_ref00:=(eq_ref0 b0):(((eq gtype) b0) b0)
% 8.89/9.11 Found (eq_ref0 b0) as proof of (((eq gtype) b0) (h g))
% 8.89/9.11 Found ((eq_ref gtype) b0) as proof of (((eq gtype) b0) (h g))
% 8.89/9.11 Found ((eq_ref gtype) b0) as proof of (((eq gtype) b0) (h g))
% 8.89/9.11 Found ((eq_ref gtype) b0) as proof of (((eq gtype) b0) (h g))
% 8.89/9.11 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 8.89/9.11 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) g)
% 8.89/9.11 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) g)
% 8.89/9.11 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) g)
% 8.89/9.11 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) g)
% 8.89/9.11 Found eta_expansion000:=(eta_expansion00 f):(((eq (b->Prop)) f) (fun (x:b)=> (f x)))
% 8.89/9.11 Found (eta_expansion00 f) as proof of (((eq (b->Prop)) f) b0)
% 8.89/9.11 Found ((eta_expansion0 Prop) f) as proof of (((eq (b->Prop)) f) b0)
% 8.89/9.11 Found (((eta_expansion b) Prop) f) as proof of (((eq (b->Prop)) f) b0)
% 8.89/9.11 Found (((eta_expansion b) Prop) f) as proof of (((eq (b->Prop)) f) b0)
% 8.89/9.11 Found (((eta_expansion b) Prop) f) as proof of (((eq (b->Prop)) f) b0)
% 8.89/9.11 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 8.89/9.11 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) g)
% 8.89/9.11 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) g)
% 8.89/9.11 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) g)
% 8.89/9.11 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) g)
% 8.89/9.11 Found eta_expansion000:=(eta_expansion00 f):(((eq (b->Prop)) f) (fun (x:b)=> (f x)))
% 8.89/9.11 Found (eta_expansion00 f) as proof of (((eq (b->Prop)) f) b0)
% 8.89/9.11 Found ((eta_expansion0 Prop) f) as proof of (((eq (b->Prop)) f) b0)
% 8.89/9.11 Found (((eta_expansion b) Prop) f) as proof of (((eq (b->Prop)) f) b0)
% 8.89/9.11 Found (((eta_expansion b) Prop) f) as proof of (((eq (b->Prop)) f) b0)
% 8.89/9.11 Found (((eta_expansion b) Prop) f) as proof of (((eq (b->Prop)) f) b0)
% 8.89/9.11 Found eq_ref00:=(eq_ref0 (h g)):(((eq gtype) (h g)) (h g))
% 8.89/9.11 Found (eq_ref0 (h g)) as proof of (((eq gtype) (h g)) b0)
% 8.89/9.11 Found ((eq_ref gtype) (h g)) as proof of (((eq gtype) (h g)) b0)
% 29.89/30.14 Found ((eq_ref gtype) (h g)) as proof of (((eq gtype) (h g)) b0)
% 29.89/30.14 Found ((eq_ref gtype) (h g)) as proof of (((eq gtype) (h g)) b0)
% 29.89/30.14 Found eq_ref00:=(eq_ref0 b0):(((eq gtype) b0) b0)
% 29.89/30.14 Found (eq_ref0 b0) as proof of (((eq gtype) b0) (h f))
% 29.89/30.14 Found ((eq_ref gtype) b0) as proof of (((eq gtype) b0) (h f))
% 29.89/30.14 Found ((eq_ref gtype) b0) as proof of (((eq gtype) b0) (h f))
% 29.89/30.14 Found ((eq_ref gtype) b0) as proof of (((eq gtype) b0) (h f))
% 29.89/30.14 Found x00:(P (h g))
% 29.89/30.14 Found (fun (x00:(P (h g)))=> x00) as proof of (P (h g))
% 29.89/30.14 Found (fun (x00:(P (h g)))=> x00) as proof of (P0 (h g))
% 29.89/30.14 Found x00:(P f)
% 29.89/30.14 Found (fun (x00:(P f))=> x00) as proof of (P f)
% 29.89/30.14 Found (fun (x00:(P f))=> x00) as proof of (P0 f)
% 29.89/30.14 Found x00:(P (h g))
% 29.89/30.14 Found (fun (x00:(P (h g)))=> x00) as proof of (P (h g))
% 29.89/30.14 Found (fun (x00:(P (h g)))=> x00) as proof of (P0 (h g))
% 29.89/30.14 Found x00:(P f)
% 29.89/30.14 Found (fun (x00:(P f))=> x00) as proof of (P f)
% 29.89/30.14 Found (fun (x00:(P f))=> x00) as proof of (P0 f)
% 29.89/30.14 Found x00:(P f)
% 29.89/30.14 Found (fun (x00:(P f))=> x00) as proof of (P f)
% 29.89/30.14 Found (fun (x00:(P f))=> x00) as proof of (P0 f)
% 29.89/30.14 Found x00:(P f)
% 29.89/30.14 Found (fun (x00:(P f))=> x00) as proof of (P f)
% 29.89/30.14 Found (fun (x00:(P f))=> x00) as proof of (P0 f)
% 29.89/30.14 Found x00:(P f)
% 29.89/30.14 Found (fun (x00:(P f))=> x00) as proof of (P f)
% 29.89/30.14 Found (fun (x00:(P f))=> x00) as proof of (P0 f)
% 29.89/30.14 Found x00:(P f)
% 29.89/30.14 Found (fun (x00:(P f))=> x00) as proof of (P f)
% 29.89/30.14 Found (fun (x00:(P f))=> x00) as proof of (P0 f)
% 29.89/30.14 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 29.89/30.14 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) f)
% 29.89/30.14 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 29.89/30.14 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 29.89/30.14 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 29.89/30.14 Found eq_ref00:=(eq_ref0 g):(((eq (b->Prop)) g) g)
% 29.89/30.14 Found (eq_ref0 g) as proof of (((eq (b->Prop)) g) b0)
% 29.89/30.14 Found ((eq_ref (b->Prop)) g) as proof of (((eq (b->Prop)) g) b0)
% 29.89/30.14 Found ((eq_ref (b->Prop)) g) as proof of (((eq (b->Prop)) g) b0)
% 29.89/30.14 Found ((eq_ref (b->Prop)) g) as proof of (((eq (b->Prop)) g) b0)
% 29.89/30.14 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 29.89/30.14 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) f)
% 29.89/30.14 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 29.89/30.14 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 29.89/30.14 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 29.89/30.14 Found eq_ref00:=(eq_ref0 g):(((eq (b->Prop)) g) g)
% 29.89/30.14 Found (eq_ref0 g) as proof of (((eq (b->Prop)) g) b0)
% 29.89/30.14 Found ((eq_ref (b->Prop)) g) as proof of (((eq (b->Prop)) g) b0)
% 29.89/30.14 Found ((eq_ref (b->Prop)) g) as proof of (((eq (b->Prop)) g) b0)
% 29.89/30.14 Found ((eq_ref (b->Prop)) g) as proof of (((eq (b->Prop)) g) b0)
% 29.89/30.14 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 29.89/30.14 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) f)
% 29.89/30.14 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 29.89/30.14 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 29.89/30.14 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 29.89/30.14 Found eq_ref00:=(eq_ref0 g):(((eq (b->Prop)) g) g)
% 29.89/30.14 Found (eq_ref0 g) as proof of (((eq (b->Prop)) g) b0)
% 29.89/30.14 Found ((eq_ref (b->Prop)) g) as proof of (((eq (b->Prop)) g) b0)
% 29.89/30.14 Found ((eq_ref (b->Prop)) g) as proof of (((eq (b->Prop)) g) b0)
% 29.89/30.14 Found ((eq_ref (b->Prop)) g) as proof of (((eq (b->Prop)) g) b0)
% 29.89/30.14 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 29.89/30.14 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) f)
% 29.89/30.14 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 29.89/30.14 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 29.89/30.14 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 29.89/30.14 Found eq_ref00:=(eq_ref0 g):(((eq (b->Prop)) g) g)
% 29.89/30.14 Found (eq_ref0 g) as proof of (((eq (b->Prop)) g) b0)
% 29.89/30.14 Found ((eq_ref (b->Prop)) g) as proof of (((eq (b->Prop)) g) b0)
% 29.89/30.14 Found ((eq_ref (b->Prop)) g) as proof of (((eq (b->Prop)) g) b0)
% 29.89/30.14 Found ((eq_ref (b->Prop)) g) as proof of (((eq (b->Prop)) g) b0)
% 29.89/30.14 Found x00:(P g)
% 29.89/30.14 Found (fun (x00:(P g))=> x00) as proof of (P g)
% 29.89/30.14 Found (fun (x00:(P g))=> x00) as proof of (P0 g)
% 29.89/30.14 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 29.89/30.14 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 29.89/30.14 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 39.49/39.66 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 39.49/39.66 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 39.49/39.66 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 39.49/39.66 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (g x0))
% 39.49/39.66 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 39.49/39.66 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 39.49/39.66 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 39.49/39.66 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 39.49/39.66 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 39.49/39.66 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 39.49/39.66 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 39.49/39.66 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 39.49/39.66 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 39.49/39.66 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (g x0))
% 39.49/39.66 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 39.49/39.66 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 39.49/39.66 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 39.49/39.66 Found x00:(P g)
% 39.49/39.66 Found (fun (x00:(P g))=> x00) as proof of (P g)
% 39.49/39.66 Found (fun (x00:(P g))=> x00) as proof of (P0 g)
% 39.49/39.66 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 39.49/39.66 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 39.49/39.66 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 39.49/39.66 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 39.49/39.66 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 39.49/39.66 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 39.49/39.66 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (g x0))
% 39.49/39.66 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 39.49/39.66 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 39.49/39.66 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 39.49/39.66 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 39.49/39.66 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 39.49/39.66 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 39.49/39.66 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 39.49/39.66 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 39.49/39.66 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 39.49/39.66 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (g x0))
% 39.49/39.66 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 39.49/39.66 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 39.49/39.66 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 39.49/39.66 Found x00:(P g)
% 39.49/39.66 Found (fun (x00:(P g))=> x00) as proof of (P g)
% 39.49/39.66 Found (fun (x00:(P g))=> x00) as proof of (P0 g)
% 39.49/39.66 Found x00:(P g)
% 39.49/39.66 Found (fun (x00:(P g))=> x00) as proof of (P g)
% 39.49/39.66 Found (fun (x00:(P g))=> x00) as proof of (P0 g)
% 39.49/39.66 Found x00:(P g)
% 39.49/39.66 Found (fun (x00:(P g))=> x00) as proof of (P g)
% 39.49/39.66 Found (fun (x00:(P g))=> x00) as proof of (P0 g)
% 39.49/39.66 Found x00:(P g)
% 39.49/39.66 Found (fun (x00:(P g))=> x00) as proof of (P g)
% 39.49/39.66 Found (fun (x00:(P g))=> x00) as proof of (P0 g)
% 39.49/39.66 Found x00:(P g)
% 39.49/39.66 Found (fun (x00:(P g))=> x00) as proof of (P g)
% 39.49/39.66 Found (fun (x00:(P g))=> x00) as proof of (P0 g)
% 39.49/39.66 Found x00:(P g)
% 39.49/39.66 Found (fun (x00:(P g))=> x00) as proof of (P g)
% 39.49/39.66 Found (fun (x00:(P g))=> x00) as proof of (P0 g)
% 39.49/39.66 Found x00:(P g)
% 39.49/39.66 Found (fun (x00:(P g))=> x00) as proof of (P g)
% 39.49/39.66 Found (fun (x00:(P g))=> x00) as proof of (P0 g)
% 39.49/39.66 Found x00:(P g)
% 39.49/39.66 Found (fun (x00:(P g))=> x00) as proof of (P g)
% 39.49/39.66 Found (fun (x00:(P g))=> x00) as proof of (P0 g)
% 39.49/39.66 Found x10:(P (f x0))
% 39.49/39.66 Found (fun (x10:(P (f x0)))=> x10) as proof of (P (f x0))
% 39.49/39.66 Found (fun (x10:(P (f x0)))=> x10) as proof of (P0 (f x0))
% 39.49/39.66 Found x10:(P (f x0))
% 39.49/39.66 Found (fun (x10:(P (f x0)))=> x10) as proof of (P (f x0))
% 39.49/39.66 Found (fun (x10:(P (f x0)))=> x10) as proof of (P0 (f x0))
% 39.49/39.66 Found x10:(P (f x0))
% 39.49/39.66 Found (fun (x10:(P (f x0)))=> x10) as proof of (P (f x0))
% 39.49/39.66 Found (fun (x10:(P (f x0)))=> x10) as proof of (P0 (f x0))
% 39.49/39.66 Found x10:(P (f x0))
% 39.49/39.66 Found (fun (x10:(P (f x0)))=> x10) as proof of (P (f x0))
% 39.49/39.66 Found (fun (x10:(P (f x0)))=> x10) as proof of (P0 (f x0))
% 39.49/39.66 Found x0:(P (h f))
% 39.49/39.66 Instantiate: b0:=(h f):gtype
% 39.49/39.66 Found x0 as proof of (P0 b0)
% 39.49/39.66 Found eq_ref00:=(eq_ref0 (h g)):(((eq gtype) (h g)) (h g))
% 39.49/39.66 Found (eq_ref0 (h g)) as proof of (((eq gtype) (h g)) b0)
% 39.49/39.66 Found ((eq_ref gtype) (h g)) as proof of (((eq gtype) (h g)) b0)
% 39.49/39.66 Found ((eq_ref gtype) (h g)) as proof of (((eq gtype) (h g)) b0)
% 63.86/64.12 Found ((eq_ref gtype) (h g)) as proof of (((eq gtype) (h g)) b0)
% 63.86/64.12 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 63.86/64.12 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) g)
% 63.86/64.12 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) g)
% 63.86/64.12 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) g)
% 63.86/64.12 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) g)
% 63.86/64.12 Found eq_ref00:=(eq_ref0 f):(((eq (b->Prop)) f) f)
% 63.86/64.12 Found (eq_ref0 f) as proof of (((eq (b->Prop)) f) b0)
% 63.86/64.12 Found ((eq_ref (b->Prop)) f) as proof of (((eq (b->Prop)) f) b0)
% 63.86/64.12 Found ((eq_ref (b->Prop)) f) as proof of (((eq (b->Prop)) f) b0)
% 63.86/64.12 Found ((eq_ref (b->Prop)) f) as proof of (((eq (b->Prop)) f) b0)
% 63.86/64.12 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 63.86/64.12 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) g)
% 63.86/64.12 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) g)
% 63.86/64.12 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) g)
% 63.86/64.12 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) g)
% 63.86/64.12 Found eta_expansion000:=(eta_expansion00 f):(((eq (b->Prop)) f) (fun (x:b)=> (f x)))
% 63.86/64.12 Found (eta_expansion00 f) as proof of (((eq (b->Prop)) f) b0)
% 63.86/64.12 Found ((eta_expansion0 Prop) f) as proof of (((eq (b->Prop)) f) b0)
% 63.86/64.12 Found (((eta_expansion b) Prop) f) as proof of (((eq (b->Prop)) f) b0)
% 63.86/64.12 Found (((eta_expansion b) Prop) f) as proof of (((eq (b->Prop)) f) b0)
% 63.86/64.12 Found (((eta_expansion b) Prop) f) as proof of (((eq (b->Prop)) f) b0)
% 63.86/64.12 Found x0:(P (h f))
% 63.86/64.12 Instantiate: a:=f:(b->Prop)
% 63.86/64.12 Found x0 as proof of (P0 (h a))
% 63.86/64.12 Found eq_ref00:=(eq_ref0 a):(((eq (b->Prop)) a) a)
% 63.86/64.12 Found (eq_ref0 a) as proof of (((eq (b->Prop)) a) g)
% 63.86/64.12 Found ((eq_ref (b->Prop)) a) as proof of (((eq (b->Prop)) a) g)
% 63.86/64.12 Found ((eq_ref (b->Prop)) a) as proof of (((eq (b->Prop)) a) g)
% 63.86/64.12 Found ((eq_ref (b->Prop)) a) as proof of (((eq (b->Prop)) a) g)
% 63.86/64.12 Found eq_ref00:=(eq_ref0 (h f)):(((eq gtype) (h f)) (h f))
% 63.86/64.12 Found (eq_ref0 (h f)) as proof of (((eq gtype) (h f)) b0)
% 63.86/64.12 Found ((eq_ref gtype) (h f)) as proof of (((eq gtype) (h f)) b0)
% 63.86/64.12 Found ((eq_ref gtype) (h f)) as proof of (((eq gtype) (h f)) b0)
% 63.86/64.12 Found ((eq_ref gtype) (h f)) as proof of (((eq gtype) (h f)) b0)
% 63.86/64.12 Found eq_ref00:=(eq_ref0 b0):(((eq gtype) b0) b0)
% 63.86/64.12 Found (eq_ref0 b0) as proof of (((eq gtype) b0) (h g))
% 63.86/64.12 Found ((eq_ref gtype) b0) as proof of (((eq gtype) b0) (h g))
% 63.86/64.12 Found ((eq_ref gtype) b0) as proof of (((eq gtype) b0) (h g))
% 63.86/64.12 Found ((eq_ref gtype) b0) as proof of (((eq gtype) b0) (h g))
% 63.86/64.12 Found eq_ref00:=(eq_ref0 (h g)):(((eq gtype) (h g)) (h g))
% 63.86/64.12 Found (eq_ref0 (h g)) as proof of (((eq gtype) (h g)) b0)
% 63.86/64.12 Found ((eq_ref gtype) (h g)) as proof of (((eq gtype) (h g)) b0)
% 63.86/64.12 Found ((eq_ref gtype) (h g)) as proof of (((eq gtype) (h g)) b0)
% 63.86/64.12 Found ((eq_ref gtype) (h g)) as proof of (((eq gtype) (h g)) b0)
% 63.86/64.12 Found x0:(P0 b0)
% 63.86/64.12 Instantiate: b0:=(h f):gtype
% 63.86/64.12 Found (fun (x0:(P0 b0))=> x0) as proof of (P0 (h f))
% 63.86/64.12 Found (fun (P0:(gtype->Prop)) (x0:(P0 b0))=> x0) as proof of ((P0 b0)->(P0 (h f)))
% 63.86/64.12 Found (fun (P0:(gtype->Prop)) (x0:(P0 b0))=> x0) as proof of (P b0)
% 63.86/64.12 Found eq_ref00:=(eq_ref0 (g x0)):(((eq Prop) (g x0)) (g x0))
% 63.86/64.12 Found (eq_ref0 (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 63.86/64.12 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 63.86/64.12 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 63.86/64.12 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 63.86/64.12 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 63.86/64.12 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f x0))
% 63.86/64.12 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 63.86/64.12 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 63.86/64.12 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 63.86/64.12 Found eq_ref00:=(eq_ref0 (g x0)):(((eq Prop) (g x0)) (g x0))
% 63.86/64.12 Found (eq_ref0 (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 63.86/64.12 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 63.86/64.12 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 63.86/64.12 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 63.86/64.12 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 63.86/64.12 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f x0))
% 63.86/64.12 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 63.86/64.12 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 68.77/69.01 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 68.77/69.01 Found x0:(P (h g))
% 68.77/69.01 Instantiate: b0:=(h g):gtype
% 68.77/69.01 Found x0 as proof of (P0 b0)
% 68.77/69.01 Found eq_ref00:=(eq_ref0 (h f)):(((eq gtype) (h f)) (h f))
% 68.77/69.01 Found (eq_ref0 (h f)) as proof of (((eq gtype) (h f)) b0)
% 68.77/69.01 Found ((eq_ref gtype) (h f)) as proof of (((eq gtype) (h f)) b0)
% 68.77/69.01 Found ((eq_ref gtype) (h f)) as proof of (((eq gtype) (h f)) b0)
% 68.77/69.01 Found ((eq_ref gtype) (h f)) as proof of (((eq gtype) (h f)) b0)
% 68.77/69.01 Found eq_ref00:=(eq_ref0 (g x0)):(((eq Prop) (g x0)) (g x0))
% 68.77/69.01 Found (eq_ref0 (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 68.77/69.01 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 68.77/69.01 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 68.77/69.01 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 68.77/69.01 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 68.77/69.01 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f x0))
% 68.77/69.01 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 68.77/69.01 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 68.77/69.01 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 68.77/69.01 Found eq_ref00:=(eq_ref0 (g x0)):(((eq Prop) (g x0)) (g x0))
% 68.77/69.01 Found (eq_ref0 (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 68.77/69.01 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 68.77/69.01 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 68.77/69.01 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 68.77/69.01 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 68.77/69.01 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f x0))
% 68.77/69.01 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 68.77/69.01 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 68.77/69.01 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 68.77/69.01 Found eq_ref00:=(eq_ref0 (g x0)):(((eq Prop) (g x0)) (g x0))
% 68.77/69.01 Found (eq_ref0 (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 68.77/69.01 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 68.77/69.01 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 68.77/69.01 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 68.77/69.01 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 68.77/69.01 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f x0))
% 68.77/69.01 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 68.77/69.01 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 68.77/69.01 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 68.77/69.01 Found eq_ref00:=(eq_ref0 (g x0)):(((eq Prop) (g x0)) (g x0))
% 68.77/69.01 Found (eq_ref0 (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 68.77/69.01 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 68.77/69.01 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 68.77/69.01 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 68.77/69.01 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 68.77/69.01 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f x0))
% 68.77/69.01 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 68.77/69.01 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 68.77/69.01 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 68.77/69.01 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 68.77/69.01 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f x0))
% 68.77/69.01 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 68.77/69.01 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 68.77/69.01 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 68.77/69.01 Found eq_ref00:=(eq_ref0 (g x0)):(((eq Prop) (g x0)) (g x0))
% 68.77/69.01 Found (eq_ref0 (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 68.77/69.01 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 68.77/69.01 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 68.77/69.01 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 68.77/69.01 Found eq_ref00:=(eq_ref0 (g x0)):(((eq Prop) (g x0)) (g x0))
% 68.77/69.01 Found (eq_ref0 (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 68.77/69.01 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 68.77/69.01 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 68.77/69.01 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 68.77/69.01 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 68.77/69.01 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f x0))
% 68.77/69.01 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 68.77/69.01 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 68.77/69.01 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 68.77/69.01 Found eq_ref00:=(eq_ref0 (g x0)):(((eq Prop) (g x0)) (g x0))
% 80.14/80.43 Found (eq_ref0 (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 80.14/80.43 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 80.14/80.43 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 80.14/80.43 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 80.14/80.43 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 80.14/80.43 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f x0))
% 80.14/80.43 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 80.14/80.43 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 80.14/80.43 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 80.14/80.43 Found eq_ref00:=(eq_ref0 (g x0)):(((eq Prop) (g x0)) (g x0))
% 80.14/80.43 Found (eq_ref0 (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 80.14/80.43 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 80.14/80.43 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 80.14/80.43 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 80.14/80.43 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 80.14/80.43 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f x0))
% 80.14/80.43 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 80.14/80.43 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 80.14/80.43 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 80.14/80.43 Found eq_ref00:=(eq_ref0 (g x0)):(((eq Prop) (g x0)) (g x0))
% 80.14/80.43 Found (eq_ref0 (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 80.14/80.43 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 80.14/80.43 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 80.14/80.43 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 80.14/80.43 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 80.14/80.43 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f x0))
% 80.14/80.43 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 80.14/80.43 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 80.14/80.43 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 80.14/80.43 Found eq_ref00:=(eq_ref0 (g x0)):(((eq Prop) (g x0)) (g x0))
% 80.14/80.43 Found (eq_ref0 (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 80.14/80.43 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 80.14/80.43 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 80.14/80.43 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 80.14/80.44 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 80.14/80.44 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f x0))
% 80.14/80.44 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 80.14/80.44 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 80.14/80.44 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 80.14/80.44 Found x00:(P f)
% 80.14/80.44 Found (fun (x00:(P f))=> x00) as proof of (P f)
% 80.14/80.44 Found (fun (x00:(P f))=> x00) as proof of (P0 f)
% 80.14/80.44 Found x00:(P f)
% 80.14/80.44 Found (fun (x00:(P f))=> x00) as proof of (P f)
% 80.14/80.44 Found (fun (x00:(P f))=> x00) as proof of (P0 f)
% 80.14/80.44 Found x00:(P f)
% 80.14/80.44 Found (fun (x00:(P f))=> x00) as proof of (P f)
% 80.14/80.44 Found (fun (x00:(P f))=> x00) as proof of (P0 f)
% 80.14/80.44 Found x00:(P f)
% 80.14/80.44 Found (fun (x00:(P f))=> x00) as proof of (P f)
% 80.14/80.44 Found (fun (x00:(P f))=> x00) as proof of (P0 f)
% 80.14/80.44 Found x30:(P (h f))
% 80.14/80.44 Found (fun (x30:(P (h f)))=> x30) as proof of (P (h f))
% 80.14/80.44 Found (fun (x30:(P (h f)))=> x30) as proof of (P0 (h f))
% 80.14/80.44 Found x10:(P (g x0))
% 80.14/80.44 Found (fun (x10:(P (g x0)))=> x10) as proof of (P (g x0))
% 80.14/80.44 Found (fun (x10:(P (g x0)))=> x10) as proof of (P0 (g x0))
% 80.14/80.44 Found x10:(P (g x0))
% 80.14/80.44 Found (fun (x10:(P (g x0)))=> x10) as proof of (P (g x0))
% 80.14/80.44 Found (fun (x10:(P (g x0)))=> x10) as proof of (P0 (g x0))
% 80.14/80.44 Found x10:(P (g x0))
% 80.14/80.44 Found (fun (x10:(P (g x0)))=> x10) as proof of (P (g x0))
% 80.14/80.44 Found (fun (x10:(P (g x0)))=> x10) as proof of (P0 (g x0))
% 80.14/80.44 Found x10:(P (g x0))
% 80.14/80.44 Found (fun (x10:(P (g x0)))=> x10) as proof of (P (g x0))
% 80.14/80.44 Found (fun (x10:(P (g x0)))=> x10) as proof of (P0 (g x0))
% 80.14/80.44 Found x10:(P (g x0))
% 80.14/80.44 Found (fun (x10:(P (g x0)))=> x10) as proof of (P (g x0))
% 80.14/80.44 Found (fun (x10:(P (g x0)))=> x10) as proof of (P0 (g x0))
% 80.14/80.44 Found x10:(P (g x0))
% 80.14/80.44 Found (fun (x10:(P (g x0)))=> x10) as proof of (P (g x0))
% 80.14/80.44 Found (fun (x10:(P (g x0)))=> x10) as proof of (P0 (g x0))
% 80.14/80.44 Found x10:(P (g x0))
% 80.14/80.44 Found (fun (x10:(P (g x0)))=> x10) as proof of (P (g x0))
% 80.14/80.44 Found (fun (x10:(P (g x0)))=> x10) as proof of (P0 (g x0))
% 80.14/80.44 Found x10:(P (g x0))
% 80.14/80.44 Found (fun (x10:(P (g x0)))=> x10) as proof of (P (g x0))
% 80.14/80.44 Found (fun (x10:(P (g x0)))=> x10) as proof of (P0 (g x0))
% 80.14/80.44 Found x00:(P (h f))
% 93.83/94.09 Found (fun (x00:(P (h f)))=> x00) as proof of (P (h f))
% 93.83/94.09 Found (fun (x00:(P (h f)))=> x00) as proof of (P0 (h f))
% 93.83/94.09 Found eq_ref00:=(eq_ref0 (h f)):(((eq gtype) (h f)) (h f))
% 93.83/94.09 Found (eq_ref0 (h f)) as proof of (((eq gtype) (h f)) b0)
% 93.83/94.09 Found ((eq_ref gtype) (h f)) as proof of (((eq gtype) (h f)) b0)
% 93.83/94.09 Found ((eq_ref gtype) (h f)) as proof of (((eq gtype) (h f)) b0)
% 93.83/94.09 Found ((eq_ref gtype) (h f)) as proof of (((eq gtype) (h f)) b0)
% 93.83/94.09 Found eq_ref00:=(eq_ref0 b0):(((eq gtype) b0) b0)
% 93.83/94.09 Found (eq_ref0 b0) as proof of (((eq gtype) b0) (h g))
% 93.83/94.09 Found ((eq_ref gtype) b0) as proof of (((eq gtype) b0) (h g))
% 93.83/94.09 Found ((eq_ref gtype) b0) as proof of (((eq gtype) b0) (h g))
% 93.83/94.09 Found ((eq_ref gtype) b0) as proof of (((eq gtype) b0) (h g))
% 93.83/94.09 Found x0:(P f)
% 93.83/94.09 Instantiate: b0:=f:(b->Prop)
% 93.83/94.09 Found x0 as proof of (P0 b0)
% 93.83/94.09 Found eq_ref00:=(eq_ref0 g):(((eq (b->Prop)) g) g)
% 93.83/94.09 Found (eq_ref0 g) as proof of (((eq (b->Prop)) g) b0)
% 93.83/94.09 Found ((eq_ref (b->Prop)) g) as proof of (((eq (b->Prop)) g) b0)
% 93.83/94.09 Found ((eq_ref (b->Prop)) g) as proof of (((eq (b->Prop)) g) b0)
% 93.83/94.09 Found ((eq_ref (b->Prop)) g) as proof of (((eq (b->Prop)) g) b0)
% 93.83/94.09 Found eq_ref00:=(eq_ref0 (h f)):(((eq gtype) (h f)) (h f))
% 93.83/94.09 Found (eq_ref0 (h f)) as proof of (((eq gtype) (h f)) b0)
% 93.83/94.09 Found ((eq_ref gtype) (h f)) as proof of (((eq gtype) (h f)) b0)
% 93.83/94.09 Found ((eq_ref gtype) (h f)) as proof of (((eq gtype) (h f)) b0)
% 93.83/94.09 Found ((eq_ref gtype) (h f)) as proof of (((eq gtype) (h f)) b0)
% 93.83/94.09 Found eq_ref00:=(eq_ref0 b0):(((eq gtype) b0) b0)
% 93.83/94.09 Found (eq_ref0 b0) as proof of (((eq gtype) b0) (h g))
% 93.83/94.09 Found ((eq_ref gtype) b0) as proof of (((eq gtype) b0) (h g))
% 93.83/94.09 Found ((eq_ref gtype) b0) as proof of (((eq gtype) b0) (h g))
% 93.83/94.09 Found ((eq_ref gtype) b0) as proof of (((eq gtype) b0) (h g))
% 93.83/94.09 Found x0:(P f)
% 93.83/94.09 Instantiate: b0:=f:(b->Prop)
% 93.83/94.09 Found x0 as proof of (P0 b0)
% 93.83/94.09 Found eq_ref00:=(eq_ref0 g):(((eq (b->Prop)) g) g)
% 93.83/94.09 Found (eq_ref0 g) as proof of (((eq (b->Prop)) g) b0)
% 93.83/94.09 Found ((eq_ref (b->Prop)) g) as proof of (((eq (b->Prop)) g) b0)
% 93.83/94.09 Found ((eq_ref (b->Prop)) g) as proof of (((eq (b->Prop)) g) b0)
% 93.83/94.09 Found ((eq_ref (b->Prop)) g) as proof of (((eq (b->Prop)) g) b0)
% 93.83/94.09 Found x30:(P (h f))
% 93.83/94.09 Found (fun (x30:(P (h f)))=> x30) as proof of (P (h f))
% 93.83/94.09 Found (fun (x30:(P (h f)))=> x30) as proof of (P0 (h f))
% 93.83/94.09 Found x30:(P (h f))
% 93.83/94.09 Found (fun (x30:(P (h f)))=> x30) as proof of (P (h f))
% 93.83/94.09 Found (fun (x30:(P (h f)))=> x30) as proof of (P0 (h f))
% 93.83/94.09 Found eq_ref00:=(eq_ref0 (h f)):(((eq gtype) (h f)) (h f))
% 93.83/94.09 Found (eq_ref0 (h f)) as proof of (((eq gtype) (h f)) b00)
% 93.83/94.09 Found ((eq_ref gtype) (h f)) as proof of (((eq gtype) (h f)) b00)
% 93.83/94.09 Found ((eq_ref gtype) (h f)) as proof of (((eq gtype) (h f)) b00)
% 93.83/94.09 Found ((eq_ref gtype) (h f)) as proof of (((eq gtype) (h f)) b00)
% 93.83/94.09 Found eq_ref00:=(eq_ref0 b00):(((eq gtype) b00) b00)
% 93.83/94.09 Found (eq_ref0 b00) as proof of (((eq gtype) b00) (h g))
% 93.83/94.09 Found ((eq_ref gtype) b00) as proof of (((eq gtype) b00) (h g))
% 93.83/94.09 Found ((eq_ref gtype) b00) as proof of (((eq gtype) b00) (h g))
% 93.83/94.09 Found ((eq_ref gtype) b00) as proof of (((eq gtype) b00) (h g))
% 93.83/94.09 Found x0:(P f)
% 93.83/94.09 Instantiate: f0:=f:(b->Prop)
% 93.83/94.09 Found x0 as proof of (P0 f0)
% 93.83/94.09 Found eq_ref00:=(eq_ref0 (f0 x1)):(((eq Prop) (f0 x1)) (f0 x1))
% 93.83/94.09 Found (eq_ref0 (f0 x1)) as proof of (((eq Prop) (f0 x1)) (g x1))
% 93.83/94.09 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (g x1))
% 93.83/94.09 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (g x1))
% 93.83/94.09 Found (fun (x1:b)=> ((eq_ref Prop) (f0 x1))) as proof of (((eq Prop) (f0 x1)) (g x1))
% 93.83/94.09 Found (fun (x1:b)=> ((eq_ref Prop) (f0 x1))) as proof of (forall (x:b), (((eq Prop) (f0 x)) (g x)))
% 93.83/94.09 Found x0:(P f)
% 93.83/94.09 Instantiate: f0:=f:(b->Prop)
% 93.83/94.09 Found x0 as proof of (P0 f0)
% 93.83/94.09 Found eq_ref00:=(eq_ref0 (f0 x1)):(((eq Prop) (f0 x1)) (f0 x1))
% 93.83/94.09 Found (eq_ref0 (f0 x1)) as proof of (((eq Prop) (f0 x1)) (g x1))
% 93.83/94.09 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (g x1))
% 93.83/94.09 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (g x1))
% 93.83/94.09 Found (fun (x1:b)=> ((eq_ref Prop) (f0 x1))) as proof of (((eq Prop) (f0 x1)) (g x1))
% 93.83/94.09 Found (fun (x1:b)=> ((eq_ref Prop) (f0 x1))) as proof of (forall (x:b), (((eq Prop) (f0 x)) (g x)))
% 93.83/94.09 Found x0:(P f)
% 93.83/94.09 Instantiate: f0:=f:(b->Prop)
% 93.83/94.09 Found x0 as proof of (P0 f0)
% 93.83/94.09 Found eq_ref00:=(eq_ref0 (f0 x1)):(((eq Prop) (f0 x1)) (f0 x1))
% 101.09/101.34 Found (eq_ref0 (f0 x1)) as proof of (((eq Prop) (f0 x1)) (g x1))
% 101.09/101.34 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (g x1))
% 101.09/101.34 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (g x1))
% 101.09/101.34 Found (fun (x1:b)=> ((eq_ref Prop) (f0 x1))) as proof of (((eq Prop) (f0 x1)) (g x1))
% 101.09/101.34 Found (fun (x1:b)=> ((eq_ref Prop) (f0 x1))) as proof of (forall (x:b), (((eq Prop) (f0 x)) (g x)))
% 101.09/101.34 Found x0:(P f)
% 101.09/101.34 Instantiate: f0:=f:(b->Prop)
% 101.09/101.34 Found x0 as proof of (P0 f0)
% 101.09/101.34 Found eq_ref00:=(eq_ref0 (f0 x1)):(((eq Prop) (f0 x1)) (f0 x1))
% 101.09/101.34 Found (eq_ref0 (f0 x1)) as proof of (((eq Prop) (f0 x1)) (g x1))
% 101.09/101.34 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (g x1))
% 101.09/101.34 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (g x1))
% 101.09/101.34 Found (fun (x1:b)=> ((eq_ref Prop) (f0 x1))) as proof of (((eq Prop) (f0 x1)) (g x1))
% 101.09/101.34 Found (fun (x1:b)=> ((eq_ref Prop) (f0 x1))) as proof of (forall (x:b), (((eq Prop) (f0 x)) (g x)))
% 101.09/101.34 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 101.09/101.34 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) g)
% 101.09/101.34 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) g)
% 101.09/101.34 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) g)
% 101.09/101.34 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) g)
% 101.09/101.34 Found eq_ref00:=(eq_ref0 f):(((eq (b->Prop)) f) f)
% 101.09/101.34 Found (eq_ref0 f) as proof of (((eq (b->Prop)) f) b0)
% 101.09/101.34 Found ((eq_ref (b->Prop)) f) as proof of (((eq (b->Prop)) f) b0)
% 101.09/101.34 Found ((eq_ref (b->Prop)) f) as proof of (((eq (b->Prop)) f) b0)
% 101.09/101.34 Found ((eq_ref (b->Prop)) f) as proof of (((eq (b->Prop)) f) b0)
% 101.09/101.34 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 101.09/101.34 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) g)
% 101.09/101.34 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) g)
% 101.09/101.34 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) g)
% 101.09/101.34 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) g)
% 101.09/101.34 Found eq_ref00:=(eq_ref0 f):(((eq (b->Prop)) f) f)
% 101.09/101.34 Found (eq_ref0 f) as proof of (((eq (b->Prop)) f) b0)
% 101.09/101.34 Found ((eq_ref (b->Prop)) f) as proof of (((eq (b->Prop)) f) b0)
% 101.09/101.34 Found ((eq_ref (b->Prop)) f) as proof of (((eq (b->Prop)) f) b0)
% 101.09/101.34 Found ((eq_ref (b->Prop)) f) as proof of (((eq (b->Prop)) f) b0)
% 101.09/101.34 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 101.09/101.34 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) g)
% 101.09/101.34 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) g)
% 101.09/101.34 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) g)
% 101.09/101.34 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) g)
% 101.09/101.34 Found eta_expansion_dep000:=(eta_expansion_dep00 f):(((eq (b->Prop)) f) (fun (x:b)=> (f x)))
% 101.09/101.34 Found (eta_expansion_dep00 f) as proof of (((eq (b->Prop)) f) b0)
% 101.09/101.34 Found ((eta_expansion_dep0 (fun (x1:b)=> Prop)) f) as proof of (((eq (b->Prop)) f) b0)
% 101.09/101.34 Found (((eta_expansion_dep b) (fun (x1:b)=> Prop)) f) as proof of (((eq (b->Prop)) f) b0)
% 101.09/101.34 Found (((eta_expansion_dep b) (fun (x1:b)=> Prop)) f) as proof of (((eq (b->Prop)) f) b0)
% 101.09/101.34 Found (((eta_expansion_dep b) (fun (x1:b)=> Prop)) f) as proof of (((eq (b->Prop)) f) b0)
% 101.09/101.34 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 101.09/101.34 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) g)
% 101.09/101.34 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) g)
% 101.09/101.34 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) g)
% 101.09/101.34 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) g)
% 101.09/101.34 Found eq_ref00:=(eq_ref0 f):(((eq (b->Prop)) f) f)
% 101.09/101.34 Found (eq_ref0 f) as proof of (((eq (b->Prop)) f) b0)
% 101.09/101.34 Found ((eq_ref (b->Prop)) f) as proof of (((eq (b->Prop)) f) b0)
% 101.09/101.34 Found ((eq_ref (b->Prop)) f) as proof of (((eq (b->Prop)) f) b0)
% 101.09/101.34 Found ((eq_ref (b->Prop)) f) as proof of (((eq (b->Prop)) f) b0)
% 101.09/101.34 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 101.09/101.34 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) g)
% 101.09/101.34 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) g)
% 101.09/101.34 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) g)
% 101.09/101.34 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) g)
% 101.09/101.34 Found eq_ref00:=(eq_ref0 f):(((eq (b->Prop)) f) f)
% 101.09/101.34 Found (eq_ref0 f) as proof of (((eq (b->Prop)) f) b0)
% 101.09/101.34 Found ((eq_ref (b->Prop)) f) as proof of (((eq (b->Prop)) f) b0)
% 114.27/114.55 Found ((eq_ref (b->Prop)) f) as proof of (((eq (b->Prop)) f) b0)
% 114.27/114.55 Found ((eq_ref (b->Prop)) f) as proof of (((eq (b->Prop)) f) b0)
% 114.27/114.55 Found x0:(P (h g))
% 114.27/114.55 Instantiate: a:=g:(b->Prop)
% 114.27/114.55 Found x0 as proof of (P0 (h a))
% 114.27/114.55 Found eq_ref00:=(eq_ref0 a):(((eq (b->Prop)) a) a)
% 114.27/114.55 Found (eq_ref0 a) as proof of (((eq (b->Prop)) a) f)
% 114.27/114.55 Found ((eq_ref (b->Prop)) a) as proof of (((eq (b->Prop)) a) f)
% 114.27/114.55 Found ((eq_ref (b->Prop)) a) as proof of (((eq (b->Prop)) a) f)
% 114.27/114.55 Found ((eq_ref (b->Prop)) a) as proof of (((eq (b->Prop)) a) f)
% 114.27/114.55 Found eq_ref00:=(eq_ref0 b0):(((eq gtype) b0) b0)
% 114.27/114.55 Found (eq_ref0 b0) as proof of (((eq gtype) b0) (h f))
% 114.27/114.55 Found ((eq_ref gtype) b0) as proof of (((eq gtype) b0) (h f))
% 114.27/114.55 Found ((eq_ref gtype) b0) as proof of (((eq gtype) b0) (h f))
% 114.27/114.55 Found ((eq_ref gtype) b0) as proof of (((eq gtype) b0) (h f))
% 114.27/114.55 Found eq_ref00:=(eq_ref0 (h g)):(((eq gtype) (h g)) (h g))
% 114.27/114.55 Found (eq_ref0 (h g)) as proof of (((eq gtype) (h g)) b0)
% 114.27/114.55 Found ((eq_ref gtype) (h g)) as proof of (((eq gtype) (h g)) b0)
% 114.27/114.55 Found ((eq_ref gtype) (h g)) as proof of (((eq gtype) (h g)) b0)
% 114.27/114.55 Found ((eq_ref gtype) (h g)) as proof of (((eq gtype) (h g)) b0)
% 114.27/114.55 Found eq_ref00:=(eq_ref0 (h g)):(((eq gtype) (h g)) (h g))
% 114.27/114.55 Found (eq_ref0 (h g)) as proof of (((eq gtype) (h g)) b0)
% 114.27/114.55 Found ((eq_ref gtype) (h g)) as proof of (((eq gtype) (h g)) b0)
% 114.27/114.55 Found ((eq_ref gtype) (h g)) as proof of (((eq gtype) (h g)) b0)
% 114.27/114.55 Found ((eq_ref gtype) (h g)) as proof of (((eq gtype) (h g)) b0)
% 114.27/114.55 Found eq_ref00:=(eq_ref0 b0):(((eq gtype) b0) b0)
% 114.27/114.55 Found (eq_ref0 b0) as proof of (((eq gtype) b0) (h f))
% 114.27/114.55 Found ((eq_ref gtype) b0) as proof of (((eq gtype) b0) (h f))
% 114.27/114.55 Found ((eq_ref gtype) b0) as proof of (((eq gtype) b0) (h f))
% 114.27/114.55 Found ((eq_ref gtype) b0) as proof of (((eq gtype) b0) (h f))
% 114.27/114.55 Found eq_ref00:=(eq_ref0 b0):(((eq gtype) b0) b0)
% 114.27/114.55 Found (eq_ref0 b0) as proof of (((eq gtype) b0) (h f))
% 114.27/114.55 Found ((eq_ref gtype) b0) as proof of (((eq gtype) b0) (h f))
% 114.27/114.55 Found ((eq_ref gtype) b0) as proof of (((eq gtype) b0) (h f))
% 114.27/114.55 Found ((eq_ref gtype) b0) as proof of (((eq gtype) b0) (h f))
% 114.27/114.55 Found eq_ref00:=(eq_ref0 (h g)):(((eq gtype) (h g)) (h g))
% 114.27/114.55 Found (eq_ref0 (h g)) as proof of (((eq gtype) (h g)) b0)
% 114.27/114.55 Found ((eq_ref gtype) (h g)) as proof of (((eq gtype) (h g)) b0)
% 114.27/114.55 Found ((eq_ref gtype) (h g)) as proof of (((eq gtype) (h g)) b0)
% 114.27/114.55 Found ((eq_ref gtype) (h g)) as proof of (((eq gtype) (h g)) b0)
% 114.27/114.55 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 114.27/114.55 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) g)
% 114.27/114.55 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) g)
% 114.27/114.55 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) g)
% 114.27/114.55 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) g)
% 114.27/114.55 Found eta_expansion_dep000:=(eta_expansion_dep00 f):(((eq (b->Prop)) f) (fun (x:b)=> (f x)))
% 114.27/114.55 Found (eta_expansion_dep00 f) as proof of (((eq (b->Prop)) f) b0)
% 114.27/114.55 Found ((eta_expansion_dep0 (fun (x1:b)=> Prop)) f) as proof of (((eq (b->Prop)) f) b0)
% 114.27/114.55 Found (((eta_expansion_dep b) (fun (x1:b)=> Prop)) f) as proof of (((eq (b->Prop)) f) b0)
% 114.27/114.55 Found (((eta_expansion_dep b) (fun (x1:b)=> Prop)) f) as proof of (((eq (b->Prop)) f) b0)
% 114.27/114.55 Found (((eta_expansion_dep b) (fun (x1:b)=> Prop)) f) as proof of (((eq (b->Prop)) f) b0)
% 114.27/114.55 Found x00:(P b0)
% 114.27/114.55 Found (fun (x00:(P b0))=> x00) as proof of (P b0)
% 114.27/114.55 Found (fun (x00:(P b0))=> x00) as proof of (P0 b0)
% 114.27/114.55 Found x00:(P1 (h g))
% 114.27/114.55 Found (fun (x00:(P1 (h g)))=> x00) as proof of (P1 (h g))
% 114.27/114.55 Found (fun (x00:(P1 (h g)))=> x00) as proof of (P2 (h g))
% 114.27/114.55 Found x00:(P1 (h g))
% 114.27/114.55 Found (fun (x00:(P1 (h g)))=> x00) as proof of (P1 (h g))
% 114.27/114.55 Found (fun (x00:(P1 (h g)))=> x00) as proof of (P2 (h g))
% 114.27/114.55 Found x00:(P1 f)
% 114.27/114.55 Found (fun (x00:(P1 f))=> x00) as proof of (P1 f)
% 114.27/114.55 Found (fun (x00:(P1 f))=> x00) as proof of (P2 f)
% 114.27/114.55 Found x00:(P1 f)
% 114.27/114.55 Found (fun (x00:(P1 f))=> x00) as proof of (P1 f)
% 114.27/114.55 Found (fun (x00:(P1 f))=> x00) as proof of (P2 f)
% 114.27/114.55 Found x00:(P1 (h g))
% 114.27/114.55 Found (fun (x00:(P1 (h g)))=> x00) as proof of (P1 (h g))
% 114.27/114.55 Found (fun (x00:(P1 (h g)))=> x00) as proof of (P2 (h g))
% 114.27/114.55 Found x00:(P1 (h g))
% 114.27/114.55 Found (fun (x00:(P1 (h g)))=> x00) as proof of (P1 (h g))
% 114.27/114.55 Found (fun (x00:(P1 (h g)))=> x00) as proof of (P2 (h g))
% 114.27/114.55 Found x00:(P1 f)
% 114.27/114.55 Found (fun (x00:(P1 f))=> x00) as proof of (P1 f)
% 135.21/135.47 Found (fun (x00:(P1 f))=> x00) as proof of (P2 f)
% 135.21/135.47 Found x00:(P1 f)
% 135.21/135.47 Found (fun (x00:(P1 f))=> x00) as proof of (P1 f)
% 135.21/135.47 Found (fun (x00:(P1 f))=> x00) as proof of (P2 f)
% 135.21/135.47 Found x00:(P1 f)
% 135.21/135.47 Found (fun (x00:(P1 f))=> x00) as proof of (P1 f)
% 135.21/135.47 Found (fun (x00:(P1 f))=> x00) as proof of (P2 f)
% 135.21/135.47 Found x00:(P1 f)
% 135.21/135.47 Found (fun (x00:(P1 f))=> x00) as proof of (P1 f)
% 135.21/135.47 Found (fun (x00:(P1 f))=> x00) as proof of (P2 f)
% 135.21/135.47 Found x00:(P1 f)
% 135.21/135.47 Found (fun (x00:(P1 f))=> x00) as proof of (P1 f)
% 135.21/135.47 Found (fun (x00:(P1 f))=> x00) as proof of (P2 f)
% 135.21/135.47 Found x00:(P1 f)
% 135.21/135.47 Found (fun (x00:(P1 f))=> x00) as proof of (P1 f)
% 135.21/135.47 Found (fun (x00:(P1 f))=> x00) as proof of (P2 f)
% 135.21/135.47 Found x00:(P1 f)
% 135.21/135.47 Found (fun (x00:(P1 f))=> x00) as proof of (P1 f)
% 135.21/135.47 Found (fun (x00:(P1 f))=> x00) as proof of (P2 f)
% 135.21/135.47 Found x00:(P1 f)
% 135.21/135.47 Found (fun (x00:(P1 f))=> x00) as proof of (P1 f)
% 135.21/135.47 Found (fun (x00:(P1 f))=> x00) as proof of (P2 f)
% 135.21/135.47 Found x00:(P1 f)
% 135.21/135.47 Found (fun (x00:(P1 f))=> x00) as proof of (P1 f)
% 135.21/135.47 Found (fun (x00:(P1 f))=> x00) as proof of (P2 f)
% 135.21/135.47 Found x00:(P1 f)
% 135.21/135.47 Found (fun (x00:(P1 f))=> x00) as proof of (P1 f)
% 135.21/135.47 Found (fun (x00:(P1 f))=> x00) as proof of (P2 f)
% 135.21/135.47 Found x00:(P f)
% 135.21/135.47 Found (fun (x00:(P f))=> x00) as proof of (P f)
% 135.21/135.47 Found (fun (x00:(P f))=> x00) as proof of (P0 f)
% 135.21/135.47 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 135.21/135.47 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) g)
% 135.21/135.47 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) g)
% 135.21/135.47 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) g)
% 135.21/135.47 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) g)
% 135.21/135.47 Found eta_expansion_dep000:=(eta_expansion_dep00 f):(((eq (b->Prop)) f) (fun (x:b)=> (f x)))
% 135.21/135.47 Found (eta_expansion_dep00 f) as proof of (((eq (b->Prop)) f) b0)
% 135.21/135.47 Found ((eta_expansion_dep0 (fun (x1:b)=> Prop)) f) as proof of (((eq (b->Prop)) f) b0)
% 135.21/135.47 Found (((eta_expansion_dep b) (fun (x1:b)=> Prop)) f) as proof of (((eq (b->Prop)) f) b0)
% 135.21/135.47 Found (((eta_expansion_dep b) (fun (x1:b)=> Prop)) f) as proof of (((eq (b->Prop)) f) b0)
% 135.21/135.47 Found (((eta_expansion_dep b) (fun (x1:b)=> Prop)) f) as proof of (((eq (b->Prop)) f) b0)
% 135.21/135.47 Found eq_ref00:=(eq_ref0 g):(((eq (b->Prop)) g) g)
% 135.21/135.47 Found (eq_ref0 g) as proof of (((eq (b->Prop)) g) b0)
% 135.21/135.47 Found ((eq_ref (b->Prop)) g) as proof of (((eq (b->Prop)) g) b0)
% 135.21/135.47 Found ((eq_ref (b->Prop)) g) as proof of (((eq (b->Prop)) g) b0)
% 135.21/135.47 Found ((eq_ref (b->Prop)) g) as proof of (((eq (b->Prop)) g) b0)
% 135.21/135.47 Found x0:(P0 b0)
% 135.21/135.47 Instantiate: b0:=f:(b->Prop)
% 135.21/135.47 Found (fun (x0:(P0 b0))=> x0) as proof of (P0 f)
% 135.21/135.47 Found (fun (P0:((b->Prop)->Prop)) (x0:(P0 b0))=> x0) as proof of ((P0 b0)->(P0 f))
% 135.21/135.47 Found (fun (P0:((b->Prop)->Prop)) (x0:(P0 b0))=> x0) as proof of (P b0)
% 135.21/135.47 Found x00:(P (h g))
% 135.21/135.47 Found (fun (x00:(P (h g)))=> x00) as proof of (P (h g))
% 135.21/135.47 Found (fun (x00:(P (h g)))=> x00) as proof of (P0 (h g))
% 135.21/135.47 Found eq_ref00:=(eq_ref0 b0):(((eq gtype) b0) b0)
% 135.21/135.47 Found (eq_ref0 b0) as proof of (((eq gtype) b0) (h f))
% 135.21/135.47 Found ((eq_ref gtype) b0) as proof of (((eq gtype) b0) (h f))
% 135.21/135.47 Found ((eq_ref gtype) b0) as proof of (((eq gtype) b0) (h f))
% 135.21/135.47 Found ((eq_ref gtype) b0) as proof of (((eq gtype) b0) (h f))
% 135.21/135.47 Found eq_ref00:=(eq_ref0 (h g)):(((eq gtype) (h g)) (h g))
% 135.21/135.47 Found (eq_ref0 (h g)) as proof of (((eq gtype) (h g)) b0)
% 135.21/135.47 Found ((eq_ref gtype) (h g)) as proof of (((eq gtype) (h g)) b0)
% 135.21/135.47 Found ((eq_ref gtype) (h g)) as proof of (((eq gtype) (h g)) b0)
% 135.21/135.47 Found ((eq_ref gtype) (h g)) as proof of (((eq gtype) (h g)) b0)
% 135.21/135.47 Found x00:(P f)
% 135.21/135.47 Found (fun (x00:(P f))=> x00) as proof of (P f)
% 135.21/135.47 Found (fun (x00:(P f))=> x00) as proof of (P0 f)
% 135.21/135.47 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 135.21/135.47 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) g)
% 135.21/135.47 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) g)
% 135.21/135.47 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) g)
% 135.21/135.47 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) g)
% 135.21/135.47 Found eta_expansion_dep000:=(eta_expansion_dep00 f):(((eq (b->Prop)) f) (fun (x:b)=> (f x)))
% 135.21/135.47 Found (eta_expansion_dep00 f) as proof of (((eq (b->Prop)) f) b0)
% 135.21/135.47 Found ((eta_expansion_dep0 (fun (x1:b)=> Prop)) f) as proof of (((eq (b->Prop)) f) b0)
% 135.21/135.47 Found (((eta_expansion_dep b) (fun (x1:b)=> Prop)) f) as proof of (((eq (b->Prop)) f) b0)
% 135.21/135.47 Found (((eta_expansion_dep b) (fun (x1:b)=> Prop)) f) as proof of (((eq (b->Prop)) f) b0)
% 137.89/138.23 Found (((eta_expansion_dep b) (fun (x1:b)=> Prop)) f) as proof of (((eq (b->Prop)) f) b0)
% 137.89/138.23 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 137.89/138.23 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (g x0))
% 137.89/138.23 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 137.89/138.23 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 137.89/138.23 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 137.89/138.23 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 137.89/138.23 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 137.89/138.23 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 137.89/138.23 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 137.89/138.23 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 137.89/138.23 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 137.89/138.23 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (g x0))
% 137.89/138.23 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 137.89/138.23 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 137.89/138.23 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 137.89/138.23 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 137.89/138.23 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 137.89/138.23 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 137.89/138.23 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 137.89/138.23 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 137.89/138.23 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 137.89/138.23 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 137.89/138.23 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 137.89/138.23 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 137.89/138.23 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 137.89/138.23 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 137.89/138.23 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (g x0))
% 137.89/138.23 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 137.89/138.23 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 137.89/138.23 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 137.89/138.23 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 137.89/138.23 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (g x0))
% 137.89/138.23 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 137.89/138.23 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 137.89/138.23 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 137.89/138.23 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 137.89/138.23 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 137.89/138.23 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 137.89/138.23 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 137.89/138.23 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 137.89/138.23 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 137.89/138.23 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 137.89/138.23 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 137.89/138.23 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 137.89/138.23 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 137.89/138.23 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 137.89/138.23 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (g x0))
% 137.89/138.23 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 137.89/138.23 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 137.89/138.23 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 137.89/138.23 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 137.89/138.23 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 137.89/138.23 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 137.89/138.23 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 137.89/138.23 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 137.89/138.23 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 137.89/138.23 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (g x0))
% 137.89/138.23 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 137.89/138.23 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 137.89/138.23 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 137.89/138.23 Found x0:(P g)
% 137.89/138.23 Instantiate: b0:=g:(b->Prop)
% 137.89/138.23 Found x0 as proof of (P0 b0)
% 137.89/138.23 Found eta_expansion_dep000:=(eta_expansion_dep00 f):(((eq (b->Prop)) f) (fun (x:b)=> (f x)))
% 137.89/138.23 Found (eta_expansion_dep00 f) as proof of (((eq (b->Prop)) f) b0)
% 137.89/138.23 Found ((eta_expansion_dep0 (fun (x2:b)=> Prop)) f) as proof of (((eq (b->Prop)) f) b0)
% 144.48/144.79 Found (((eta_expansion_dep b) (fun (x2:b)=> Prop)) f) as proof of (((eq (b->Prop)) f) b0)
% 144.48/144.79 Found (((eta_expansion_dep b) (fun (x2:b)=> Prop)) f) as proof of (((eq (b->Prop)) f) b0)
% 144.48/144.79 Found (((eta_expansion_dep b) (fun (x2:b)=> Prop)) f) as proof of (((eq (b->Prop)) f) b0)
% 144.48/144.79 Found eq_ref00:=(eq_ref0 g):(((eq (b->Prop)) g) g)
% 144.48/144.79 Found (eq_ref0 g) as proof of (((eq (b->Prop)) g) b0)
% 144.48/144.79 Found ((eq_ref (b->Prop)) g) as proof of (((eq (b->Prop)) g) b0)
% 144.48/144.79 Found ((eq_ref (b->Prop)) g) as proof of (((eq (b->Prop)) g) b0)
% 144.48/144.79 Found ((eq_ref (b->Prop)) g) as proof of (((eq (b->Prop)) g) b0)
% 144.48/144.79 Found x0:(P0 b0)
% 144.48/144.79 Instantiate: b0:=f:(b->Prop)
% 144.48/144.79 Found (fun (x0:(P0 b0))=> x0) as proof of (P0 f)
% 144.48/144.79 Found (fun (P0:((b->Prop)->Prop)) (x0:(P0 b0))=> x0) as proof of ((P0 b0)->(P0 f))
% 144.48/144.79 Found (fun (P0:((b->Prop)->Prop)) (x0:(P0 b0))=> x0) as proof of (P b0)
% 144.48/144.79 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 144.48/144.79 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (g x0))
% 144.48/144.79 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 144.48/144.79 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 144.48/144.79 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 144.48/144.79 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 144.48/144.79 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 144.48/144.79 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 144.48/144.79 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 144.48/144.79 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 144.48/144.79 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 144.48/144.79 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (g x0))
% 144.48/144.79 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 144.48/144.79 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 144.48/144.79 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 144.48/144.79 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 144.48/144.79 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 144.48/144.79 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 144.48/144.79 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 144.48/144.79 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 144.48/144.79 Found eq_ref00:=(eq_ref0 b00):(((eq (b->Prop)) b00) b00)
% 144.48/144.79 Found (eq_ref0 b00) as proof of (((eq (b->Prop)) b00) b0)
% 144.48/144.79 Found ((eq_ref (b->Prop)) b00) as proof of (((eq (b->Prop)) b00) b0)
% 144.48/144.79 Found ((eq_ref (b->Prop)) b00) as proof of (((eq (b->Prop)) b00) b0)
% 144.48/144.79 Found ((eq_ref (b->Prop)) b00) as proof of (((eq (b->Prop)) b00) b0)
% 144.48/144.79 Found eta_expansion_dep000:=(eta_expansion_dep00 f):(((eq (b->Prop)) f) (fun (x:b)=> (f x)))
% 144.48/144.79 Found (eta_expansion_dep00 f) as proof of (((eq (b->Prop)) f) b00)
% 144.48/144.79 Found ((eta_expansion_dep0 (fun (x1:b)=> Prop)) f) as proof of (((eq (b->Prop)) f) b00)
% 144.48/144.79 Found (((eta_expansion_dep b) (fun (x1:b)=> Prop)) f) as proof of (((eq (b->Prop)) f) b00)
% 144.48/144.79 Found (((eta_expansion_dep b) (fun (x1:b)=> Prop)) f) as proof of (((eq (b->Prop)) f) b00)
% 144.48/144.79 Found (((eta_expansion_dep b) (fun (x1:b)=> Prop)) f) as proof of (((eq (b->Prop)) f) b00)
% 144.48/144.79 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 144.48/144.79 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 144.48/144.79 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 144.48/144.79 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 144.48/144.79 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 144.48/144.79 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 144.48/144.79 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (g x0))
% 144.48/144.79 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 144.48/144.79 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 144.48/144.79 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 144.48/144.79 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 144.48/144.79 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (g x0))
% 144.48/144.79 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 144.48/144.79 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 144.48/144.79 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 144.48/144.79 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 144.48/144.79 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 144.48/144.79 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 144.48/144.79 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 144.48/144.79 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 144.48/144.79 Found x0:(P g)
% 153.60/153.92 Instantiate: b0:=g:(b->Prop)
% 153.60/153.92 Found x0 as proof of (P0 b0)
% 153.60/153.92 Found eta_expansion_dep000:=(eta_expansion_dep00 f):(((eq (b->Prop)) f) (fun (x:b)=> (f x)))
% 153.60/153.92 Found (eta_expansion_dep00 f) as proof of (((eq (b->Prop)) f) b0)
% 153.60/153.92 Found ((eta_expansion_dep0 (fun (x2:b)=> Prop)) f) as proof of (((eq (b->Prop)) f) b0)
% 153.60/153.92 Found (((eta_expansion_dep b) (fun (x2:b)=> Prop)) f) as proof of (((eq (b->Prop)) f) b0)
% 153.60/153.92 Found (((eta_expansion_dep b) (fun (x2:b)=> Prop)) f) as proof of (((eq (b->Prop)) f) b0)
% 153.60/153.92 Found (((eta_expansion_dep b) (fun (x2:b)=> Prop)) f) as proof of (((eq (b->Prop)) f) b0)
% 153.60/153.92 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 153.60/153.92 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 153.60/153.92 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 153.60/153.92 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 153.60/153.92 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 153.60/153.92 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 153.60/153.92 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (g x0))
% 153.60/153.92 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 153.60/153.92 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 153.60/153.92 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 153.60/153.92 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 153.60/153.92 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 153.60/153.92 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 153.60/153.92 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 153.60/153.92 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 153.60/153.92 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 153.60/153.92 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (g x0))
% 153.60/153.92 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 153.60/153.92 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 153.60/153.92 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 153.60/153.92 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 153.60/153.92 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) g)
% 153.60/153.92 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) g)
% 153.60/153.92 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) g)
% 153.60/153.92 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) g)
% 153.60/153.92 Found eta_expansion000:=(eta_expansion00 f):(((eq (b->Prop)) f) (fun (x:b)=> (f x)))
% 153.60/153.92 Found (eta_expansion00 f) as proof of (((eq (b->Prop)) f) b0)
% 153.60/153.92 Found ((eta_expansion0 Prop) f) as proof of (((eq (b->Prop)) f) b0)
% 153.60/153.92 Found (((eta_expansion b) Prop) f) as proof of (((eq (b->Prop)) f) b0)
% 153.60/153.92 Found (((eta_expansion b) Prop) f) as proof of (((eq (b->Prop)) f) b0)
% 153.60/153.92 Found (((eta_expansion b) Prop) f) as proof of (((eq (b->Prop)) f) b0)
% 153.60/153.92 Found eq_ref00:=(eq_ref0 b0):(((eq gtype) b0) b0)
% 153.60/153.92 Found (eq_ref0 b0) as proof of (((eq gtype) b0) (h f))
% 153.60/153.92 Found ((eq_ref gtype) b0) as proof of (((eq gtype) b0) (h f))
% 153.60/153.92 Found ((eq_ref gtype) b0) as proof of (((eq gtype) b0) (h f))
% 153.60/153.92 Found ((eq_ref gtype) b0) as proof of (((eq gtype) b0) (h f))
% 153.60/153.92 Found eq_ref00:=(eq_ref0 (h g)):(((eq gtype) (h g)) (h g))
% 153.60/153.92 Found (eq_ref0 (h g)) as proof of (((eq gtype) (h g)) b0)
% 153.60/153.92 Found ((eq_ref gtype) (h g)) as proof of (((eq gtype) (h g)) b0)
% 153.60/153.92 Found ((eq_ref gtype) (h g)) as proof of (((eq gtype) (h g)) b0)
% 153.60/153.92 Found ((eq_ref gtype) (h g)) as proof of (((eq gtype) (h g)) b0)
% 153.60/153.92 Found eq_ref00:=(eq_ref0 b00):(((eq (b->Prop)) b00) b00)
% 153.60/153.92 Found (eq_ref0 b00) as proof of (((eq (b->Prop)) b00) b0)
% 153.60/153.92 Found ((eq_ref (b->Prop)) b00) as proof of (((eq (b->Prop)) b00) b0)
% 153.60/153.92 Found ((eq_ref (b->Prop)) b00) as proof of (((eq (b->Prop)) b00) b0)
% 153.60/153.92 Found ((eq_ref (b->Prop)) b00) as proof of (((eq (b->Prop)) b00) b0)
% 153.60/153.92 Found eta_expansion_dep000:=(eta_expansion_dep00 f):(((eq (b->Prop)) f) (fun (x:b)=> (f x)))
% 153.60/153.92 Found (eta_expansion_dep00 f) as proof of (((eq (b->Prop)) f) b00)
% 153.60/153.92 Found ((eta_expansion_dep0 (fun (x1:b)=> Prop)) f) as proof of (((eq (b->Prop)) f) b00)
% 153.60/153.92 Found (((eta_expansion_dep b) (fun (x1:b)=> Prop)) f) as proof of (((eq (b->Prop)) f) b00)
% 153.60/153.92 Found (((eta_expansion_dep b) (fun (x1:b)=> Prop)) f) as proof of (((eq (b->Prop)) f) b00)
% 153.60/153.92 Found (((eta_expansion_dep b) (fun (x1:b)=> Prop)) f) as proof of (((eq (b->Prop)) f) b00)
% 153.60/153.92 Found x0:(P g)
% 153.60/153.92 Instantiate: b0:=g:(b->Prop)
% 153.60/153.92 Found x0 as proof of (P0 b0)
% 153.60/153.92 Found eta_expansion000:=(eta_expansion00 f):(((eq (b->Prop)) f) (fun (x:b)=> (f x)))
% 174.36/174.68 Found (eta_expansion00 f) as proof of (((eq (b->Prop)) f) b0)
% 174.36/174.68 Found ((eta_expansion0 Prop) f) as proof of (((eq (b->Prop)) f) b0)
% 174.36/174.68 Found (((eta_expansion b) Prop) f) as proof of (((eq (b->Prop)) f) b0)
% 174.36/174.68 Found (((eta_expansion b) Prop) f) as proof of (((eq (b->Prop)) f) b0)
% 174.36/174.68 Found (((eta_expansion b) Prop) f) as proof of (((eq (b->Prop)) f) b0)
% 174.36/174.68 Found eq_ref00:=(eq_ref0 (h g)):(((eq gtype) (h g)) (h g))
% 174.36/174.68 Found (eq_ref0 (h g)) as proof of (((eq gtype) (h g)) b00)
% 174.36/174.68 Found ((eq_ref gtype) (h g)) as proof of (((eq gtype) (h g)) b00)
% 174.36/174.68 Found ((eq_ref gtype) (h g)) as proof of (((eq gtype) (h g)) b00)
% 174.36/174.68 Found ((eq_ref gtype) (h g)) as proof of (((eq gtype) (h g)) b00)
% 174.36/174.68 Found eq_ref00:=(eq_ref0 b00):(((eq gtype) b00) b00)
% 174.36/174.68 Found (eq_ref0 b00) as proof of (((eq gtype) b00) (h f))
% 174.36/174.68 Found ((eq_ref gtype) b00) as proof of (((eq gtype) b00) (h f))
% 174.36/174.68 Found ((eq_ref gtype) b00) as proof of (((eq gtype) b00) (h f))
% 174.36/174.68 Found ((eq_ref gtype) b00) as proof of (((eq gtype) b00) (h f))
% 174.36/174.68 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 174.36/174.68 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) g)
% 174.36/174.68 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) g)
% 174.36/174.68 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) g)
% 174.36/174.68 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) g)
% 174.36/174.68 Found eta_expansion000:=(eta_expansion00 f):(((eq (b->Prop)) f) (fun (x:b)=> (f x)))
% 174.36/174.68 Found (eta_expansion00 f) as proof of (((eq (b->Prop)) f) b0)
% 174.36/174.68 Found ((eta_expansion0 Prop) f) as proof of (((eq (b->Prop)) f) b0)
% 174.36/174.68 Found (((eta_expansion b) Prop) f) as proof of (((eq (b->Prop)) f) b0)
% 174.36/174.68 Found (((eta_expansion b) Prop) f) as proof of (((eq (b->Prop)) f) b0)
% 174.36/174.68 Found (((eta_expansion b) Prop) f) as proof of (((eq (b->Prop)) f) b0)
% 174.36/174.68 Found x00:(P (h f))
% 174.36/174.68 Found (fun (x00:(P (h f)))=> x00) as proof of (P (h f))
% 174.36/174.68 Found (fun (x00:(P (h f)))=> x00) as proof of (P0 (h f))
% 174.36/174.68 Found x0:(P g)
% 174.36/174.68 Instantiate: b0:=g:(b->Prop)
% 174.36/174.68 Found x0 as proof of (P0 b0)
% 174.36/174.68 Found eta_expansion000:=(eta_expansion00 f):(((eq (b->Prop)) f) (fun (x:b)=> (f x)))
% 174.36/174.68 Found (eta_expansion00 f) as proof of (((eq (b->Prop)) f) b0)
% 174.36/174.68 Found ((eta_expansion0 Prop) f) as proof of (((eq (b->Prop)) f) b0)
% 174.36/174.68 Found (((eta_expansion b) Prop) f) as proof of (((eq (b->Prop)) f) b0)
% 174.36/174.68 Found (((eta_expansion b) Prop) f) as proof of (((eq (b->Prop)) f) b0)
% 174.36/174.68 Found (((eta_expansion b) Prop) f) as proof of (((eq (b->Prop)) f) b0)
% 174.36/174.68 Found x30:(P (h g))
% 174.36/174.68 Found (fun (x30:(P (h g)))=> x30) as proof of (P (h g))
% 174.36/174.68 Found (fun (x30:(P (h g)))=> x30) as proof of (P0 (h g))
% 174.36/174.68 Found x10:(P (f x0))
% 174.36/174.68 Found (fun (x10:(P (f x0)))=> x10) as proof of (P (f x0))
% 174.36/174.68 Found (fun (x10:(P (f x0)))=> x10) as proof of (P0 (f x0))
% 174.36/174.68 Found x10:(P (f x0))
% 174.36/174.68 Found (fun (x10:(P (f x0)))=> x10) as proof of (P (f x0))
% 174.36/174.68 Found (fun (x10:(P (f x0)))=> x10) as proof of (P0 (f x0))
% 174.36/174.68 Found x0:(P g)
% 174.36/174.68 Instantiate: f0:=g:(b->Prop)
% 174.36/174.68 Found x0 as proof of (P0 f0)
% 174.36/174.68 Found x0:(P g)
% 174.36/174.68 Instantiate: f0:=g:(b->Prop)
% 174.36/174.68 Found x0 as proof of (P0 f0)
% 174.36/174.68 Found x0:(P g)
% 174.36/174.68 Instantiate: f0:=g:(b->Prop)
% 174.36/174.68 Found x0 as proof of (P0 f0)
% 174.36/174.68 Found x0:(P g)
% 174.36/174.68 Instantiate: f0:=g:(b->Prop)
% 174.36/174.68 Found x0 as proof of (P0 f0)
% 174.36/174.68 Found eq_ref00:=(eq_ref0 (f0 x1)):(((eq Prop) (f0 x1)) (f0 x1))
% 174.36/174.68 Found (eq_ref0 (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% 174.36/174.68 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% 174.36/174.68 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% 174.36/174.68 Found (fun (x1:b)=> ((eq_ref Prop) (f0 x1))) as proof of (((eq Prop) (f0 x1)) (f x1))
% 174.36/174.68 Found (fun (x1:b)=> ((eq_ref Prop) (f0 x1))) as proof of (forall (x:b), (((eq Prop) (f0 x)) (f x)))
% 174.36/174.68 Found eq_ref00:=(eq_ref0 (f0 x1)):(((eq Prop) (f0 x1)) (f0 x1))
% 174.36/174.68 Found (eq_ref0 (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% 174.36/174.68 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% 174.36/174.68 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% 174.36/174.68 Found (fun (x1:b)=> ((eq_ref Prop) (f0 x1))) as proof of (((eq Prop) (f0 x1)) (f x1))
% 174.36/174.68 Found (fun (x1:b)=> ((eq_ref Prop) (f0 x1))) as proof of (forall (x:b), (((eq Prop) (f0 x)) (f x)))
% 174.36/174.68 Found eq_ref00:=(eq_ref0 (f0 x1)):(((eq Prop) (f0 x1)) (f0 x1))
% 174.36/174.68 Found (eq_ref0 (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% 182.31/182.64 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% 182.31/182.64 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% 182.31/182.64 Found (fun (x1:b)=> ((eq_ref Prop) (f0 x1))) as proof of (((eq Prop) (f0 x1)) (f x1))
% 182.31/182.64 Found (fun (x1:b)=> ((eq_ref Prop) (f0 x1))) as proof of (forall (x:b), (((eq Prop) (f0 x)) (f x)))
% 182.31/182.64 Found eq_ref00:=(eq_ref0 (f0 x1)):(((eq Prop) (f0 x1)) (f0 x1))
% 182.31/182.64 Found (eq_ref0 (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% 182.31/182.64 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% 182.31/182.64 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% 182.31/182.64 Found (fun (x1:b)=> ((eq_ref Prop) (f0 x1))) as proof of (((eq Prop) (f0 x1)) (f x1))
% 182.31/182.64 Found (fun (x1:b)=> ((eq_ref Prop) (f0 x1))) as proof of (forall (x:b), (((eq Prop) (f0 x)) (f x)))
% 182.31/182.64 Found x30:(P f)
% 182.31/182.64 Found (fun (x30:(P f))=> x30) as proof of (P f)
% 182.31/182.64 Found (fun (x30:(P f))=> x30) as proof of (P0 f)
% 182.31/182.64 Found x30:(P (h g))
% 182.31/182.64 Found (fun (x30:(P (h g)))=> x30) as proof of (P (h g))
% 182.31/182.64 Found (fun (x30:(P (h g)))=> x30) as proof of (P0 (h g))
% 182.31/182.64 Found eq_ref00:=(eq_ref0 b0):(((eq gtype) b0) b0)
% 182.31/182.64 Found (eq_ref0 b0) as proof of (((eq gtype) b0) (h f))
% 182.31/182.64 Found ((eq_ref gtype) b0) as proof of (((eq gtype) b0) (h f))
% 182.31/182.64 Found ((eq_ref gtype) b0) as proof of (((eq gtype) b0) (h f))
% 182.31/182.64 Found ((eq_ref gtype) b0) as proof of (((eq gtype) b0) (h f))
% 182.31/182.64 Found eq_ref00:=(eq_ref0 (h g)):(((eq gtype) (h g)) (h g))
% 182.31/182.64 Found (eq_ref0 (h g)) as proof of (((eq gtype) (h g)) b0)
% 182.31/182.64 Found ((eq_ref gtype) (h g)) as proof of (((eq gtype) (h g)) b0)
% 182.31/182.64 Found ((eq_ref gtype) (h g)) as proof of (((eq gtype) (h g)) b0)
% 182.31/182.64 Found ((eq_ref gtype) (h g)) as proof of (((eq gtype) (h g)) b0)
% 182.31/182.64 Found x20:=(x2 x10):(f Xx)
% 182.31/182.64 Found (x2 x10) as proof of (f Xx)
% 182.31/182.64 Found (x2 x10) as proof of (f Xx)
% 182.31/182.64 Found x10:=(x1 x20):(g Xx)
% 182.31/182.64 Found (x1 x20) as proof of (g Xx)
% 182.31/182.64 Found (x1 x20) as proof of (g Xx)
% 182.31/182.64 Found x10:(P (f x0))
% 182.31/182.64 Found (fun (x10:(P (f x0)))=> x10) as proof of (P (f x0))
% 182.31/182.64 Found (fun (x10:(P (f x0)))=> x10) as proof of (P0 (f x0))
% 182.31/182.64 Found x10:(P (f x0))
% 182.31/182.64 Found (fun (x10:(P (f x0)))=> x10) as proof of (P (f x0))
% 182.31/182.64 Found (fun (x10:(P (f x0)))=> x10) as proof of (P0 (f x0))
% 182.31/182.64 Found x0:(P g)
% 182.31/182.64 Instantiate: f0:=g:(b->Prop)
% 182.31/182.64 Found x0 as proof of (P0 f0)
% 182.31/182.64 Found x0:(P g)
% 182.31/182.64 Instantiate: f0:=g:(b->Prop)
% 182.31/182.64 Found x0 as proof of (P0 f0)
% 182.31/182.64 Found x0:(P g)
% 182.31/182.64 Instantiate: f0:=g:(b->Prop)
% 182.31/182.64 Found x0 as proof of (P0 f0)
% 182.31/182.64 Found x0:(P g)
% 182.31/182.64 Instantiate: f0:=g:(b->Prop)
% 182.31/182.64 Found x0 as proof of (P0 f0)
% 182.31/182.64 Found eq_ref00:=(eq_ref0 (f0 x1)):(((eq Prop) (f0 x1)) (f0 x1))
% 182.31/182.64 Found (eq_ref0 (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% 182.31/182.64 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% 182.31/182.64 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% 182.31/182.64 Found (fun (x1:b)=> ((eq_ref Prop) (f0 x1))) as proof of (((eq Prop) (f0 x1)) (f x1))
% 182.31/182.64 Found (fun (x1:b)=> ((eq_ref Prop) (f0 x1))) as proof of (forall (x:b), (((eq Prop) (f0 x)) (f x)))
% 182.31/182.64 Found eq_ref00:=(eq_ref0 (f0 x1)):(((eq Prop) (f0 x1)) (f0 x1))
% 182.31/182.64 Found (eq_ref0 (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% 182.31/182.64 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% 182.31/182.64 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% 182.31/182.64 Found (fun (x1:b)=> ((eq_ref Prop) (f0 x1))) as proof of (((eq Prop) (f0 x1)) (f x1))
% 182.31/182.64 Found (fun (x1:b)=> ((eq_ref Prop) (f0 x1))) as proof of (forall (x:b), (((eq Prop) (f0 x)) (f x)))
% 182.31/182.64 Found eq_ref00:=(eq_ref0 (f0 x1)):(((eq Prop) (f0 x1)) (f0 x1))
% 182.31/182.64 Found (eq_ref0 (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% 182.31/182.64 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% 182.31/182.64 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% 182.31/182.64 Found (fun (x1:b)=> ((eq_ref Prop) (f0 x1))) as proof of (((eq Prop) (f0 x1)) (f x1))
% 182.31/182.64 Found (fun (x1:b)=> ((eq_ref Prop) (f0 x1))) as proof of (forall (x:b), (((eq Prop) (f0 x)) (f x)))
% 182.31/182.64 Found eq_ref00:=(eq_ref0 (f0 x1)):(((eq Prop) (f0 x1)) (f0 x1))
% 182.31/182.64 Found (eq_ref0 (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% 182.31/182.64 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% 182.31/182.64 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% 182.31/182.64 Found (fun (x1:b)=> ((eq_ref Prop) (f0 x1))) as proof of (((eq Prop) (f0 x1)) (f x1))
% 196.58/196.91 Found (fun (x1:b)=> ((eq_ref Prop) (f0 x1))) as proof of (forall (x:b), (((eq Prop) (f0 x)) (f x)))
% 196.58/196.91 Found x30:(P f)
% 196.58/196.91 Found (fun (x30:(P f))=> x30) as proof of (P f)
% 196.58/196.91 Found (fun (x30:(P f))=> x30) as proof of (P0 f)
% 196.58/196.91 Found x1:(P (f x0))
% 196.58/196.91 Instantiate: b0:=(f x0):Prop
% 196.58/196.91 Found x1 as proof of (P0 b0)
% 196.58/196.91 Found eq_ref00:=(eq_ref0 (g x0)):(((eq Prop) (g x0)) (g x0))
% 196.58/196.91 Found (eq_ref0 (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 196.58/196.91 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 196.58/196.91 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 196.58/196.91 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 196.58/196.91 Found x1:(P (f x0))
% 196.58/196.91 Instantiate: b0:=(f x0):Prop
% 196.58/196.91 Found x1 as proof of (P0 b0)
% 196.58/196.91 Found eq_ref00:=(eq_ref0 (g x0)):(((eq Prop) (g x0)) (g x0))
% 196.58/196.91 Found (eq_ref0 (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 196.58/196.91 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 196.58/196.91 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 196.58/196.91 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 196.58/196.91 Found x00:(P b0)
% 196.58/196.91 Found (fun (x00:(P b0))=> x00) as proof of (P b0)
% 196.58/196.91 Found (fun (x00:(P b0))=> x00) as proof of (P0 b0)
% 196.58/196.91 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 196.58/196.91 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) g)
% 196.58/196.91 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) g)
% 196.58/196.91 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) g)
% 196.58/196.91 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) g)
% 196.58/196.91 Found eta_expansion000:=(eta_expansion00 f):(((eq (b->Prop)) f) (fun (x:b)=> (f x)))
% 196.58/196.91 Found (eta_expansion00 f) as proof of (((eq (b->Prop)) f) b0)
% 196.58/196.91 Found ((eta_expansion0 Prop) f) as proof of (((eq (b->Prop)) f) b0)
% 196.58/196.91 Found (((eta_expansion b) Prop) f) as proof of (((eq (b->Prop)) f) b0)
% 196.58/196.91 Found (((eta_expansion b) Prop) f) as proof of (((eq (b->Prop)) f) b0)
% 196.58/196.91 Found (((eta_expansion b) Prop) f) as proof of (((eq (b->Prop)) f) b0)
% 196.58/196.91 Found x00:(P (h f))
% 196.58/196.91 Found (fun (x00:(P (h f)))=> x00) as proof of (P (h f))
% 196.58/196.91 Found (fun (x00:(P (h f)))=> x00) as proof of (P0 (h f))
% 196.58/196.91 Found eq_ref00:=(eq_ref0 (h f)):(((eq gtype) (h f)) (h f))
% 196.58/196.91 Found (eq_ref0 (h f)) as proof of (((eq gtype) (h f)) b0)
% 196.58/196.91 Found ((eq_ref gtype) (h f)) as proof of (((eq gtype) (h f)) b0)
% 196.58/196.91 Found ((eq_ref gtype) (h f)) as proof of (((eq gtype) (h f)) b0)
% 196.58/196.91 Found ((eq_ref gtype) (h f)) as proof of (((eq gtype) (h f)) b0)
% 196.58/196.91 Found eq_ref00:=(eq_ref0 b0):(((eq gtype) b0) b0)
% 196.58/196.91 Found (eq_ref0 b0) as proof of (((eq gtype) b0) (h g))
% 196.58/196.91 Found ((eq_ref gtype) b0) as proof of (((eq gtype) b0) (h g))
% 196.58/196.91 Found ((eq_ref gtype) b0) as proof of (((eq gtype) b0) (h g))
% 196.58/196.91 Found ((eq_ref gtype) b0) as proof of (((eq gtype) b0) (h g))
% 196.58/196.91 Found x20:=(x2 x10):(f Xx)
% 196.58/196.91 Found (x2 x10) as proof of (f Xx)
% 196.58/196.91 Found (x2 x10) as proof of (f Xx)
% 196.58/196.91 Found x10:=(x1 x20):(g Xx)
% 196.58/196.91 Found (x1 x20) as proof of (g Xx)
% 196.58/196.91 Found (x1 x20) as proof of (g Xx)
% 196.58/196.91 Found x00:(P (h f))
% 196.58/196.91 Found (fun (x00:(P (h f)))=> x00) as proof of (P (h f))
% 196.58/196.91 Found (fun (x00:(P (h f)))=> x00) as proof of (P0 (h f))
% 196.58/196.91 Found x20:=(x2 x10):(f Xx)
% 196.58/196.91 Found (x2 x10) as proof of (f Xx)
% 196.58/196.91 Found (x2 x10) as proof of (f Xx)
% 196.58/196.91 Found x1:(P (f x0))
% 196.58/196.91 Instantiate: b0:=(f x0):Prop
% 196.58/196.91 Found x1 as proof of (P0 b0)
% 196.58/196.91 Found eq_ref00:=(eq_ref0 (g x0)):(((eq Prop) (g x0)) (g x0))
% 196.58/196.91 Found (eq_ref0 (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 196.58/196.91 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 196.58/196.91 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 196.58/196.91 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 196.58/196.91 Found x1:(P (f x0))
% 196.58/196.91 Instantiate: b0:=(f x0):Prop
% 196.58/196.91 Found x1 as proof of (P0 b0)
% 196.58/196.91 Found eq_ref00:=(eq_ref0 (g x0)):(((eq Prop) (g x0)) (g x0))
% 196.58/196.91 Found (eq_ref0 (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 196.58/196.91 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 196.58/196.91 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 196.58/196.91 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 196.58/196.91 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 196.58/196.91 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) f)
% 196.58/196.91 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 196.58/196.91 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 196.58/196.91 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 198.86/199.21 Found eta_expansion000:=(eta_expansion00 g):(((eq (b->Prop)) g) (fun (x:b)=> (g x)))
% 198.86/199.21 Found (eta_expansion00 g) as proof of (((eq (b->Prop)) g) b0)
% 198.86/199.21 Found ((eta_expansion0 Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 198.86/199.21 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 198.86/199.21 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 198.86/199.21 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 198.86/199.21 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 198.86/199.21 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) f)
% 198.86/199.21 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 198.86/199.21 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 198.86/199.21 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 198.86/199.21 Found eta_expansion000:=(eta_expansion00 g):(((eq (b->Prop)) g) (fun (x:b)=> (g x)))
% 198.86/199.21 Found (eta_expansion00 g) as proof of (((eq (b->Prop)) g) b0)
% 198.86/199.21 Found ((eta_expansion0 Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 198.86/199.21 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 198.86/199.21 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 198.86/199.21 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 198.86/199.21 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 198.86/199.21 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) g)
% 198.86/199.21 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) g)
% 198.86/199.21 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) g)
% 198.86/199.21 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) g)
% 198.86/199.21 Found eta_expansion000:=(eta_expansion00 f):(((eq (b->Prop)) f) (fun (x:b)=> (f x)))
% 198.86/199.21 Found (eta_expansion00 f) as proof of (((eq (b->Prop)) f) b0)
% 198.86/199.21 Found ((eta_expansion0 Prop) f) as proof of (((eq (b->Prop)) f) b0)
% 198.86/199.21 Found (((eta_expansion b) Prop) f) as proof of (((eq (b->Prop)) f) b0)
% 198.86/199.21 Found (((eta_expansion b) Prop) f) as proof of (((eq (b->Prop)) f) b0)
% 198.86/199.21 Found (((eta_expansion b) Prop) f) as proof of (((eq (b->Prop)) f) b0)
% 198.86/199.21 Found x30:(P f)
% 198.86/199.21 Found (fun (x30:(P f))=> x30) as proof of (P f)
% 198.86/199.21 Found (fun (x30:(P f))=> x30) as proof of (P0 f)
% 198.86/199.21 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 198.86/199.21 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) f)
% 198.86/199.21 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 198.86/199.21 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 198.86/199.21 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 198.86/199.21 Found eta_expansion000:=(eta_expansion00 g):(((eq (b->Prop)) g) (fun (x:b)=> (g x)))
% 198.86/199.21 Found (eta_expansion00 g) as proof of (((eq (b->Prop)) g) b0)
% 198.86/199.21 Found ((eta_expansion0 Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 198.86/199.21 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 198.86/199.21 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 198.86/199.21 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 198.86/199.21 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 198.86/199.21 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) f)
% 198.86/199.21 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 198.86/199.21 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 198.86/199.21 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 198.86/199.21 Found eta_expansion000:=(eta_expansion00 g):(((eq (b->Prop)) g) (fun (x:b)=> (g x)))
% 198.86/199.21 Found (eta_expansion00 g) as proof of (((eq (b->Prop)) g) b0)
% 198.86/199.21 Found ((eta_expansion0 Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 198.86/199.21 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 198.86/199.21 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 198.86/199.21 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 198.86/199.21 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 198.86/199.21 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) f)
% 198.86/199.21 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 198.86/199.21 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 198.86/199.21 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 198.86/199.21 Found eta_expansion000:=(eta_expansion00 g):(((eq (b->Prop)) g) (fun (x:b)=> (g x)))
% 198.86/199.21 Found (eta_expansion00 g) as proof of (((eq (b->Prop)) g) b0)
% 198.86/199.21 Found ((eta_expansion0 Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 198.86/199.21 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 202.92/203.23 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 202.92/203.23 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 202.92/203.23 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 202.92/203.23 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) f)
% 202.92/203.23 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 202.92/203.23 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 202.92/203.23 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 202.92/203.23 Found eta_expansion000:=(eta_expansion00 g):(((eq (b->Prop)) g) (fun (x:b)=> (g x)))
% 202.92/203.23 Found (eta_expansion00 g) as proof of (((eq (b->Prop)) g) b0)
% 202.92/203.23 Found ((eta_expansion0 Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 202.92/203.23 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 202.92/203.23 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 202.92/203.23 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 202.92/203.23 Found x30:(P f)
% 202.92/203.23 Found (fun (x30:(P f))=> x30) as proof of (P f)
% 202.92/203.23 Found (fun (x30:(P f))=> x30) as proof of (P0 f)
% 202.92/203.23 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 202.92/203.23 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) f)
% 202.92/203.23 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 202.92/203.23 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 202.92/203.23 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 202.92/203.23 Found eta_expansion000:=(eta_expansion00 g):(((eq (b->Prop)) g) (fun (x:b)=> (g x)))
% 202.92/203.23 Found (eta_expansion00 g) as proof of (((eq (b->Prop)) g) b0)
% 202.92/203.23 Found ((eta_expansion0 Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 202.92/203.23 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 202.92/203.23 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 202.92/203.23 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 202.92/203.23 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 202.92/203.23 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) f)
% 202.92/203.23 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 202.92/203.23 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 202.92/203.23 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 202.92/203.23 Found eta_expansion000:=(eta_expansion00 g):(((eq (b->Prop)) g) (fun (x:b)=> (g x)))
% 202.92/203.23 Found (eta_expansion00 g) as proof of (((eq (b->Prop)) g) b0)
% 202.92/203.23 Found ((eta_expansion0 Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 202.92/203.23 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 202.92/203.23 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 202.92/203.23 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 202.92/203.23 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 202.92/203.23 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) f)
% 202.92/203.23 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 202.92/203.23 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 202.92/203.23 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 202.92/203.23 Found eta_expansion000:=(eta_expansion00 g):(((eq (b->Prop)) g) (fun (x:b)=> (g x)))
% 202.92/203.23 Found (eta_expansion00 g) as proof of (((eq (b->Prop)) g) b0)
% 202.92/203.23 Found ((eta_expansion0 Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 202.92/203.23 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 202.92/203.23 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 202.92/203.23 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 202.92/203.23 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 202.92/203.23 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) f)
% 202.92/203.23 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 202.92/203.23 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 202.92/203.23 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 202.92/203.23 Found eta_expansion000:=(eta_expansion00 g):(((eq (b->Prop)) g) (fun (x:b)=> (g x)))
% 202.92/203.23 Found (eta_expansion00 g) as proof of (((eq (b->Prop)) g) b0)
% 202.92/203.23 Found ((eta_expansion0 Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 202.92/203.23 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 202.92/203.23 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 202.92/203.23 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 202.92/203.23 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 202.92/203.23 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) f)
% 202.92/203.23 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 212.05/212.38 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 212.05/212.38 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 212.05/212.38 Found eta_expansion000:=(eta_expansion00 g):(((eq (b->Prop)) g) (fun (x:b)=> (g x)))
% 212.05/212.38 Found (eta_expansion00 g) as proof of (((eq (b->Prop)) g) b0)
% 212.05/212.38 Found ((eta_expansion0 Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 212.05/212.38 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 212.05/212.38 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 212.05/212.38 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 212.05/212.38 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 212.05/212.38 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) f)
% 212.05/212.38 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 212.05/212.38 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 212.05/212.38 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 212.05/212.38 Found eta_expansion000:=(eta_expansion00 g):(((eq (b->Prop)) g) (fun (x:b)=> (g x)))
% 212.05/212.38 Found (eta_expansion00 g) as proof of (((eq (b->Prop)) g) b0)
% 212.05/212.38 Found ((eta_expansion0 Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 212.05/212.38 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 212.05/212.38 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 212.05/212.38 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 212.05/212.38 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 212.05/212.38 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) f)
% 212.05/212.38 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 212.05/212.38 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 212.05/212.38 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 212.05/212.38 Found eta_expansion000:=(eta_expansion00 g):(((eq (b->Prop)) g) (fun (x:b)=> (g x)))
% 212.05/212.38 Found (eta_expansion00 g) as proof of (((eq (b->Prop)) g) b0)
% 212.05/212.38 Found ((eta_expansion0 Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 212.05/212.38 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 212.05/212.38 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 212.05/212.38 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 212.05/212.38 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 212.05/212.38 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) f)
% 212.05/212.38 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 212.05/212.38 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 212.05/212.38 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 212.05/212.38 Found eta_expansion000:=(eta_expansion00 g):(((eq (b->Prop)) g) (fun (x:b)=> (g x)))
% 212.05/212.38 Found (eta_expansion00 g) as proof of (((eq (b->Prop)) g) b0)
% 212.05/212.38 Found ((eta_expansion0 Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 212.05/212.38 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 212.05/212.38 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 212.05/212.38 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 212.05/212.38 Found x30:(P (h g))
% 212.05/212.38 Found (fun (x30:(P (h g)))=> x30) as proof of (P (h g))
% 212.05/212.38 Found (fun (x30:(P (h g)))=> x30) as proof of (P0 (h g))
% 212.05/212.38 Found x10:=(x1 x20):(g Xx)
% 212.05/212.38 Found (x1 x20) as proof of (g Xx)
% 212.05/212.38 Found (x1 x20) as proof of (g Xx)
% 212.05/212.38 Found x20:=(x2 x10):(f Xx)
% 212.05/212.38 Found (x2 x10) as proof of (f Xx)
% 212.05/212.38 Found (x2 x10) as proof of (f Xx)
% 212.05/212.38 Found x30:=(x3 x20):(f Xx)
% 212.05/212.38 Found (x3 x20) as proof of (f Xx)
% 212.05/212.38 Found (x3 x20) as proof of (f Xx)
% 212.05/212.38 Found x20:=(x2 x30):(g Xx)
% 212.05/212.38 Found (x2 x30) as proof of (g Xx)
% 212.05/212.38 Found (x2 x30) as proof of (g Xx)
% 212.05/212.38 Found x30:(P (h g))
% 212.05/212.38 Found (fun (x30:(P (h g)))=> x30) as proof of (P (h g))
% 212.05/212.38 Found (fun (x30:(P (h g)))=> x30) as proof of (P0 (h g))
% 212.05/212.38 Found x00:(P f)
% 212.05/212.38 Found (fun (x00:(P f))=> x00) as proof of (P f)
% 212.05/212.38 Found (fun (x00:(P f))=> x00) as proof of (P0 f)
% 212.05/212.38 Found x30:(P f)
% 212.05/212.38 Found (fun (x30:(P f))=> x30) as proof of (P f)
% 212.05/212.38 Found (fun (x30:(P f))=> x30) as proof of (P0 f)
% 212.05/212.38 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 212.05/212.38 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) f)
% 212.05/212.38 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 212.05/212.38 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 212.05/212.38 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 212.05/212.38 Found eta_expansion000:=(eta_expansion00 g):(((eq (b->Prop)) g) (fun (x:b)=> (g x)))
% 212.05/212.38 Found (eta_expansion00 g) as proof of (((eq (b->Prop)) g) b0)
% 213.94/214.29 Found ((eta_expansion0 Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 213.94/214.29 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 213.94/214.29 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 213.94/214.29 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 213.94/214.29 Found x30:(P f)
% 213.94/214.29 Found (fun (x30:(P f))=> x30) as proof of (P f)
% 213.94/214.29 Found (fun (x30:(P f))=> x30) as proof of (P0 f)
% 213.94/214.29 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 213.94/214.29 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) f)
% 213.94/214.29 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 213.94/214.29 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 213.94/214.29 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 213.94/214.29 Found eta_expansion_dep000:=(eta_expansion_dep00 g):(((eq (b->Prop)) g) (fun (x:b)=> (g x)))
% 213.94/214.29 Found (eta_expansion_dep00 g) as proof of (((eq (b->Prop)) g) b0)
% 213.94/214.29 Found ((eta_expansion_dep0 (fun (x1:b)=> Prop)) g) as proof of (((eq (b->Prop)) g) b0)
% 213.94/214.29 Found (((eta_expansion_dep b) (fun (x1:b)=> Prop)) g) as proof of (((eq (b->Prop)) g) b0)
% 213.94/214.29 Found (((eta_expansion_dep b) (fun (x1:b)=> Prop)) g) as proof of (((eq (b->Prop)) g) b0)
% 213.94/214.29 Found (((eta_expansion_dep b) (fun (x1:b)=> Prop)) g) as proof of (((eq (b->Prop)) g) b0)
% 213.94/214.29 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 213.94/214.29 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) f)
% 213.94/214.29 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 213.94/214.29 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 213.94/214.29 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 213.94/214.29 Found eta_expansion000:=(eta_expansion00 g):(((eq (b->Prop)) g) (fun (x:b)=> (g x)))
% 213.94/214.29 Found (eta_expansion00 g) as proof of (((eq (b->Prop)) g) b0)
% 213.94/214.29 Found ((eta_expansion0 Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 213.94/214.29 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 213.94/214.29 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 213.94/214.29 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 213.94/214.29 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 213.94/214.29 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) f)
% 213.94/214.29 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 213.94/214.29 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 213.94/214.29 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 213.94/214.29 Found eta_expansion000:=(eta_expansion00 g):(((eq (b->Prop)) g) (fun (x:b)=> (g x)))
% 213.94/214.29 Found (eta_expansion00 g) as proof of (((eq (b->Prop)) g) b0)
% 213.94/214.29 Found ((eta_expansion0 Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 213.94/214.29 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 213.94/214.29 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 213.94/214.29 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 213.94/214.29 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 213.94/214.29 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) f)
% 213.94/214.29 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 213.94/214.29 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 213.94/214.29 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 213.94/214.29 Found eta_expansion000:=(eta_expansion00 g):(((eq (b->Prop)) g) (fun (x:b)=> (g x)))
% 213.94/214.29 Found (eta_expansion00 g) as proof of (((eq (b->Prop)) g) b0)
% 213.94/214.29 Found ((eta_expansion0 Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 213.94/214.29 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 213.94/214.29 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 213.94/214.29 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 213.94/214.29 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 213.94/214.29 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) f)
% 213.94/214.29 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 213.94/214.29 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 213.94/214.29 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 213.94/214.29 Found eta_expansion000:=(eta_expansion00 g):(((eq (b->Prop)) g) (fun (x:b)=> (g x)))
% 213.94/214.29 Found (eta_expansion00 g) as proof of (((eq (b->Prop)) g) b0)
% 213.94/214.29 Found ((eta_expansion0 Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 213.94/214.29 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 213.94/214.29 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 238.52/238.84 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 238.52/238.84 Found x20:=(x2 x10):(f Xx)
% 238.52/238.84 Found (x2 x10) as proof of (f Xx)
% 238.52/238.84 Found (x2 x10) as proof of (f Xx)
% 238.52/238.84 Found x10:=(x1 x20):(g Xx)
% 238.52/238.84 Found (x1 x20) as proof of (g Xx)
% 238.52/238.84 Found (x1 x20) as proof of (g Xx)
% 238.52/238.84 Found eq_ref00:=(eq_ref0 (h g)):(((eq gtype) (h g)) (h g))
% 238.52/238.84 Found (eq_ref0 (h g)) as proof of (((eq gtype) (h g)) b1)
% 238.52/238.84 Found ((eq_ref gtype) (h g)) as proof of (((eq gtype) (h g)) b1)
% 238.52/238.84 Found ((eq_ref gtype) (h g)) as proof of (((eq gtype) (h g)) b1)
% 238.52/238.84 Found ((eq_ref gtype) (h g)) as proof of (((eq gtype) (h g)) b1)
% 238.52/238.84 Found eq_ref00:=(eq_ref0 b1):(((eq gtype) b1) b1)
% 238.52/238.84 Found (eq_ref0 b1) as proof of (((eq gtype) b1) b0)
% 238.52/238.84 Found ((eq_ref gtype) b1) as proof of (((eq gtype) b1) b0)
% 238.52/238.84 Found ((eq_ref gtype) b1) as proof of (((eq gtype) b1) b0)
% 238.52/238.84 Found ((eq_ref gtype) b1) as proof of (((eq gtype) b1) b0)
% 238.52/238.84 Found x00:(P f)
% 238.52/238.84 Found (fun (x00:(P f))=> x00) as proof of (P f)
% 238.52/238.84 Found (fun (x00:(P f))=> x00) as proof of (P0 f)
% 238.52/238.84 Found x30:(P f)
% 238.52/238.84 Found (fun (x30:(P f))=> x30) as proof of (P f)
% 238.52/238.84 Found (fun (x30:(P f))=> x30) as proof of (P0 f)
% 238.52/238.84 Found x20:=(x2 x10):(f Xx)
% 238.52/238.84 Found (x2 x10) as proof of (f Xx)
% 238.52/238.84 Found (x2 x10) as proof of (f Xx)
% 238.52/238.84 Found x10:=(x1 x20):(g Xx)
% 238.52/238.84 Found (x1 x20) as proof of (g Xx)
% 238.52/238.84 Found (x1 x20) as proof of (g Xx)
% 238.52/238.84 Found x30:=(x3 x20):(f Xx)
% 238.52/238.84 Found (x3 x20) as proof of (f Xx)
% 238.52/238.84 Found (x3 x20) as proof of (f Xx)
% 238.52/238.84 Found x20:=(x2 x10):(f Xx)
% 238.52/238.84 Found (x2 x10) as proof of (f Xx)
% 238.52/238.84 Found (x2 x10) as proof of (f Xx)
% 238.52/238.84 Found x00:(P1 g)
% 238.52/238.84 Found (fun (x00:(P1 g))=> x00) as proof of (P1 g)
% 238.52/238.84 Found (fun (x00:(P1 g))=> x00) as proof of (P2 g)
% 238.52/238.84 Found x30:(P f)
% 238.52/238.84 Found (fun (x30:(P f))=> x30) as proof of (P f)
% 238.52/238.84 Found (fun (x30:(P f))=> x30) as proof of (P0 f)
% 238.52/238.84 Found x00:(P1 g)
% 238.52/238.84 Found (fun (x00:(P1 g))=> x00) as proof of (P1 g)
% 238.52/238.84 Found (fun (x00:(P1 g))=> x00) as proof of (P2 g)
% 238.52/238.84 Found x00:(P1 g)
% 238.52/238.84 Found (fun (x00:(P1 g))=> x00) as proof of (P1 g)
% 238.52/238.84 Found (fun (x00:(P1 g))=> x00) as proof of (P2 g)
% 238.52/238.84 Found x00:(P1 g)
% 238.52/238.84 Found (fun (x00:(P1 g))=> x00) as proof of (P1 g)
% 238.52/238.84 Found (fun (x00:(P1 g))=> x00) as proof of (P2 g)
% 238.52/238.84 Found x00:(P f)
% 238.52/238.84 Found (fun (x00:(P f))=> x00) as proof of (P f)
% 238.52/238.84 Found (fun (x00:(P f))=> x00) as proof of (P0 f)
% 238.52/238.84 Found x00:(P f)
% 238.52/238.84 Found (fun (x00:(P f))=> x00) as proof of (P f)
% 238.52/238.84 Found (fun (x00:(P f))=> x00) as proof of (P0 f)
% 238.52/238.84 Found x00:(P1 g)
% 238.52/238.84 Found (fun (x00:(P1 g))=> x00) as proof of (P1 g)
% 238.52/238.84 Found (fun (x00:(P1 g))=> x00) as proof of (P2 g)
% 238.52/238.84 Found x00:(P1 g)
% 238.52/238.84 Found (fun (x00:(P1 g))=> x00) as proof of (P1 g)
% 238.52/238.84 Found (fun (x00:(P1 g))=> x00) as proof of (P2 g)
% 238.52/238.84 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 238.52/238.84 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 238.52/238.84 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 238.52/238.84 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 238.52/238.84 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 238.52/238.84 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 238.52/238.84 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (g x0))
% 238.52/238.84 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 238.52/238.84 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 238.52/238.84 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 238.52/238.85 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 238.52/238.85 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 238.52/238.85 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 238.52/238.85 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 238.52/238.85 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 238.52/238.85 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 238.52/238.85 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (g x0))
% 238.52/238.85 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 238.52/238.85 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 238.52/238.85 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 238.52/238.85 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 238.52/238.85 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 238.52/238.85 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 238.52/238.85 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 238.52/238.85 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 238.52/238.85 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 238.52/238.85 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (g x0))
% 241.41/241.81 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 241.41/241.81 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 241.41/241.81 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 241.41/241.81 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 241.41/241.81 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 241.41/241.81 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 241.41/241.81 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 241.41/241.81 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 241.41/241.81 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 241.41/241.81 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (g x0))
% 241.41/241.81 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 241.41/241.81 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 241.41/241.81 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 241.41/241.81 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 241.41/241.81 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 241.41/241.81 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 241.41/241.81 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 241.41/241.81 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 241.41/241.81 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 241.41/241.81 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (g x0))
% 241.41/241.81 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 241.41/241.81 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 241.41/241.81 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 241.41/241.81 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 241.41/241.81 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 241.41/241.81 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 241.41/241.81 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 241.41/241.81 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 241.41/241.81 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 241.41/241.81 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (g x0))
% 241.41/241.81 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 241.41/241.81 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 241.41/241.81 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 241.41/241.81 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 241.41/241.81 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 241.41/241.81 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 241.41/241.81 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 241.41/241.81 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 241.41/241.81 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 241.41/241.81 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (g x0))
% 241.41/241.81 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 241.41/241.81 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 241.41/241.81 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 241.41/241.81 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 241.41/241.81 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 241.41/241.81 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 241.41/241.81 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 241.41/241.81 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 241.41/241.81 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 241.41/241.81 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (g x0))
% 241.41/241.81 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 241.41/241.81 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 241.41/241.81 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 241.41/241.81 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 241.41/241.81 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 241.41/241.81 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 241.41/241.81 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 241.41/241.81 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 241.41/241.81 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 241.41/241.81 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (g x0))
% 241.41/241.81 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 241.41/241.81 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 241.41/241.81 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 241.41/241.81 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 241.41/241.81 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 241.41/241.81 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 241.41/241.81 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 241.41/241.81 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 253.73/254.10 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 253.73/254.10 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (g x0))
% 253.73/254.10 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 253.73/254.10 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 253.73/254.10 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 253.73/254.10 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 253.73/254.10 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 253.73/254.10 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 253.73/254.10 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 253.73/254.10 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 253.73/254.10 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 253.73/254.10 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (g x0))
% 253.73/254.10 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 253.73/254.10 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 253.73/254.10 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 253.73/254.10 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 253.73/254.10 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 253.73/254.10 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 253.73/254.10 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 253.73/254.10 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 253.73/254.10 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 253.73/254.10 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (g x0))
% 253.73/254.10 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 253.73/254.10 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 253.73/254.10 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 253.73/254.10 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 253.73/254.10 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 253.73/254.10 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 253.73/254.10 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 253.73/254.10 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 253.73/254.10 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 253.73/254.10 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (g x0))
% 253.73/254.10 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 253.73/254.10 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 253.73/254.10 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 253.73/254.10 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 253.73/254.10 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 253.73/254.10 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 253.73/254.10 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 253.73/254.10 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 253.73/254.10 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 253.73/254.10 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (g x0))
% 253.73/254.10 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 253.73/254.10 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 253.73/254.10 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 253.73/254.10 Found x00:(P1 g)
% 253.73/254.10 Found (fun (x00:(P1 g))=> x00) as proof of (P1 g)
% 253.73/254.10 Found (fun (x00:(P1 g))=> x00) as proof of (P2 g)
% 253.73/254.10 Found x00:(P1 g)
% 253.73/254.10 Found (fun (x00:(P1 g))=> x00) as proof of (P1 g)
% 253.73/254.10 Found (fun (x00:(P1 g))=> x00) as proof of (P2 g)
% 253.73/254.10 Found x00:(P f)
% 253.73/254.10 Found (fun (x00:(P f))=> x00) as proof of (P f)
% 253.73/254.10 Found (fun (x00:(P f))=> x00) as proof of (P0 f)
% 253.73/254.10 Found x00:(P f)
% 253.73/254.10 Found (fun (x00:(P f))=> x00) as proof of (P f)
% 253.73/254.10 Found (fun (x00:(P f))=> x00) as proof of (P0 f)
% 253.73/254.10 Found x30:(P f)
% 253.73/254.10 Found (fun (x30:(P f))=> x30) as proof of (P f)
% 253.73/254.10 Found (fun (x30:(P f))=> x30) as proof of (P0 f)
% 253.73/254.10 Found x30:(P f)
% 253.73/254.10 Found (fun (x30:(P f))=> x30) as proof of (P f)
% 253.73/254.10 Found (fun (x30:(P f))=> x30) as proof of (P0 f)
% 253.73/254.10 Found x20:=(x2 x10):(f Xx)
% 253.73/254.10 Found (x2 x10) as proof of (f Xx)
% 253.73/254.10 Found (x2 x10) as proof of (f Xx)
% 253.73/254.10 Found x10:=(x1 x20):(g Xx)
% 253.73/254.10 Found (x1 x20) as proof of (g Xx)
% 253.73/254.10 Found (x1 x20) as proof of (g Xx)
% 253.73/254.10 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 253.73/254.10 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 253.73/254.10 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 253.73/254.10 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 253.73/254.10 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 253.73/254.10 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 253.73/254.10 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (g x0))
% 253.73/254.10 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 253.73/254.10 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 266.33/266.72 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 266.33/266.72 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 266.33/266.72 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 266.33/266.72 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 266.33/266.72 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 266.33/266.72 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 266.33/266.72 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 266.33/266.72 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (g x0))
% 266.33/266.72 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 266.33/266.72 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 266.33/266.72 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 266.33/266.72 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 266.33/266.72 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 266.33/266.72 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 266.33/266.72 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 266.33/266.72 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 266.33/266.72 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 266.33/266.72 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (g x0))
% 266.33/266.72 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 266.33/266.72 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 266.33/266.72 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 266.33/266.72 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 266.33/266.72 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 266.33/266.72 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 266.33/266.72 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 266.33/266.72 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 266.33/266.72 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 266.33/266.72 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (g x0))
% 266.33/266.72 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 266.33/266.72 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 266.33/266.72 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 266.33/266.72 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 266.33/266.72 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 266.33/266.72 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 266.33/266.72 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 266.33/266.72 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 266.33/266.72 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 266.33/266.72 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (g x0))
% 266.33/266.72 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 266.33/266.72 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 266.33/266.72 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 266.33/266.72 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 266.33/266.72 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 266.33/266.72 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 266.33/266.72 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 266.33/266.72 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 266.33/266.72 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 266.33/266.72 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (g x0))
% 266.33/266.72 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 266.33/266.72 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 266.33/266.72 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 266.33/266.72 Found x30:(P f)
% 266.33/266.72 Found (fun (x30:(P f))=> x30) as proof of (P f)
% 266.33/266.72 Found (fun (x30:(P f))=> x30) as proof of (P0 f)
% 266.33/266.72 Found x30:(P f)
% 266.33/266.72 Found (fun (x30:(P f))=> x30) as proof of (P f)
% 266.33/266.72 Found (fun (x30:(P f))=> x30) as proof of (P0 f)
% 266.33/266.72 Found x00:(P g)
% 266.33/266.72 Found (fun (x00:(P g))=> x00) as proof of (P g)
% 266.33/266.72 Found (fun (x00:(P g))=> x00) as proof of (P0 g)
% 266.33/266.72 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 266.33/266.72 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) f)
% 266.33/266.72 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 266.33/266.72 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 266.33/266.72 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 266.33/266.72 Found eta_expansion000:=(eta_expansion00 g):(((eq (b->Prop)) g) (fun (x:b)=> (g x)))
% 266.33/266.72 Found (eta_expansion00 g) as proof of (((eq (b->Prop)) g) b0)
% 266.33/266.72 Found ((eta_expansion0 Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 266.33/266.72 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 266.33/266.72 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 279.16/279.54 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 279.16/279.54 Found x00:(P g)
% 279.16/279.54 Found (fun (x00:(P g))=> x00) as proof of (P g)
% 279.16/279.54 Found (fun (x00:(P g))=> x00) as proof of (P0 g)
% 279.16/279.54 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 279.16/279.54 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) f)
% 279.16/279.54 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 279.16/279.54 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 279.16/279.54 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 279.16/279.54 Found eta_expansion000:=(eta_expansion00 g):(((eq (b->Prop)) g) (fun (x:b)=> (g x)))
% 279.16/279.54 Found (eta_expansion00 g) as proof of (((eq (b->Prop)) g) b0)
% 279.16/279.54 Found ((eta_expansion0 Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 279.16/279.54 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 279.16/279.54 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 279.16/279.54 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 279.16/279.54 Found x00:(P1 g)
% 279.16/279.54 Found (fun (x00:(P1 g))=> x00) as proof of (P1 g)
% 279.16/279.54 Found (fun (x00:(P1 g))=> x00) as proof of (P2 g)
% 279.16/279.54 Found x00:(P1 g)
% 279.16/279.54 Found (fun (x00:(P1 g))=> x00) as proof of (P1 g)
% 279.16/279.54 Found (fun (x00:(P1 g))=> x00) as proof of (P2 g)
% 279.16/279.54 Found x00:(P1 g)
% 279.16/279.54 Found (fun (x00:(P1 g))=> x00) as proof of (P1 g)
% 279.16/279.54 Found (fun (x00:(P1 g))=> x00) as proof of (P2 g)
% 279.16/279.54 Found x00:(P1 g)
% 279.16/279.54 Found (fun (x00:(P1 g))=> x00) as proof of (P1 g)
% 279.16/279.54 Found (fun (x00:(P1 g))=> x00) as proof of (P2 g)
% 279.16/279.54 Found x00:(P (h g))
% 279.16/279.54 Found (fun (x00:(P (h g)))=> x00) as proof of (P (h g))
% 279.16/279.54 Found (fun (x00:(P (h g)))=> x00) as proof of (P0 (h g))
% 279.16/279.54 Found x00:(P1 g)
% 279.16/279.54 Found (fun (x00:(P1 g))=> x00) as proof of (P1 g)
% 279.16/279.54 Found (fun (x00:(P1 g))=> x00) as proof of (P2 g)
% 279.16/279.54 Found x00:(P1 g)
% 279.16/279.54 Found (fun (x00:(P1 g))=> x00) as proof of (P1 g)
% 279.16/279.54 Found (fun (x00:(P1 g))=> x00) as proof of (P2 g)
% 279.16/279.54 Found x00:(P1 g)
% 279.16/279.54 Found (fun (x00:(P1 g))=> x00) as proof of (P1 g)
% 279.16/279.54 Found (fun (x00:(P1 g))=> x00) as proof of (P2 g)
% 279.16/279.54 Found x00:(P1 g)
% 279.16/279.54 Found (fun (x00:(P1 g))=> x00) as proof of (P1 g)
% 279.16/279.54 Found (fun (x00:(P1 g))=> x00) as proof of (P2 g)
% 279.16/279.54 Found x00:(P1 g)
% 279.16/279.54 Found (fun (x00:(P1 g))=> x00) as proof of (P1 g)
% 279.16/279.54 Found (fun (x00:(P1 g))=> x00) as proof of (P2 g)
% 279.16/279.54 Found x00:(P1 g)
% 279.16/279.54 Found (fun (x00:(P1 g))=> x00) as proof of (P1 g)
% 279.16/279.54 Found (fun (x00:(P1 g))=> x00) as proof of (P2 g)
% 279.16/279.54 Found x00:(P1 g)
% 279.16/279.54 Found (fun (x00:(P1 g))=> x00) as proof of (P1 g)
% 279.16/279.54 Found (fun (x00:(P1 g))=> x00) as proof of (P2 g)
% 279.16/279.54 Found x00:(P1 g)
% 279.16/279.54 Found (fun (x00:(P1 g))=> x00) as proof of (P1 g)
% 279.16/279.54 Found (fun (x00:(P1 g))=> x00) as proof of (P2 g)
% 279.16/279.54 Found x00:(P1 g)
% 279.16/279.54 Found (fun (x00:(P1 g))=> x00) as proof of (P1 g)
% 279.16/279.54 Found (fun (x00:(P1 g))=> x00) as proof of (P2 g)
% 279.16/279.54 Found x00:(P1 g)
% 279.16/279.54 Found (fun (x00:(P1 g))=> x00) as proof of (P1 g)
% 279.16/279.54 Found (fun (x00:(P1 g))=> x00) as proof of (P2 g)
% 279.16/279.54 Found x00:(P1 g)
% 279.16/279.54 Found (fun (x00:(P1 g))=> x00) as proof of (P1 g)
% 279.16/279.54 Found (fun (x00:(P1 g))=> x00) as proof of (P2 g)
% 279.16/279.54 Found x00:(P1 g)
% 279.16/279.54 Found (fun (x00:(P1 g))=> x00) as proof of (P1 g)
% 279.16/279.54 Found (fun (x00:(P1 g))=> x00) as proof of (P2 g)
% 279.16/279.54 Found x20:=(x2 x10):(f Xx)
% 279.16/279.54 Found (x2 x10) as proof of (f Xx)
% 279.16/279.54 Found (x2 x10) as proof of (f Xx)
% 279.16/279.54 Found x00:(P1 g)
% 279.16/279.54 Found (fun (x00:(P1 g))=> x00) as proof of (P1 g)
% 279.16/279.54 Found (fun (x00:(P1 g))=> x00) as proof of (P2 g)
% 279.16/279.54 Found x00:(P1 g)
% 279.16/279.54 Found (fun (x00:(P1 g))=> x00) as proof of (P1 g)
% 279.16/279.54 Found (fun (x00:(P1 g))=> x00) as proof of (P2 g)
% 279.16/279.54 Found x00:(P1 g)
% 279.16/279.54 Found (fun (x00:(P1 g))=> x00) as proof of (P1 g)
% 279.16/279.54 Found (fun (x00:(P1 g))=> x00) as proof of (P2 g)
% 279.16/279.54 Found x00:(P1 g)
% 279.16/279.54 Found (fun (x00:(P1 g))=> x00) as proof of (P1 g)
% 279.16/279.54 Found (fun (x00:(P1 g))=> x00) as proof of (P2 g)
% 279.16/279.54 Found x00:(P1 g)
% 279.16/279.54 Found (fun (x00:(P1 g))=> x00) as proof of (P1 g)
% 279.16/279.54 Found (fun (x00:(P1 g))=> x00) as proof of (P2 g)
% 279.16/279.54 Found x00:(P1 g)
% 279.16/279.54 Found (fun (x00:(P1 g))=> x00) as proof of (P1 g)
% 279.16/279.54 Found (fun (x00:(P1 g))=> x00) as proof of (P2 g)
% 279.16/279.54 Found x00:(P1 g)
% 279.16/279.54 Found (fun (x00:(P1 g))=> x00) as proof of (P1 g)
% 279.16/279.54 Found (fun (x00:(P1 g))=> x00) as proof of (P2 g)
% 279.16/279.54 Found x00:(P1 g)
% 279.16/279.54 Found (fun (x00:(P1 g))=> x00) as proof of (P1 g)
% 279.16/279.54 Found (fun (x00:(P1 g))=> x00) as proof of (P2 g)
% 279.16/279.54 Found eta_expansion000:=(eta_expansion00 f):(((eq (b->Prop)) f) (fun (x:b)=> (f x)))
% 279.16/279.54 Found (eta_expansion00 f) as proof of (((eq (b->Prop)) f) b0)
% 290.87/291.29 Found ((eta_expansion0 Prop) f) as proof of (((eq (b->Prop)) f) b0)
% 290.87/291.29 Found (((eta_expansion b) Prop) f) as proof of (((eq (b->Prop)) f) b0)
% 290.87/291.29 Found (((eta_expansion b) Prop) f) as proof of (((eq (b->Prop)) f) b0)
% 290.87/291.29 Found (((eta_expansion b) Prop) f) as proof of (((eq (b->Prop)) f) b0)
% 290.87/291.29 Found x0:(P0 b0)
% 290.87/291.29 Instantiate: b0:=g:(b->Prop)
% 290.87/291.29 Found (fun (x0:(P0 b0))=> x0) as proof of (P0 g)
% 290.87/291.29 Found (fun (P0:((b->Prop)->Prop)) (x0:(P0 b0))=> x0) as proof of ((P0 b0)->(P0 g))
% 290.87/291.29 Found (fun (P0:((b->Prop)->Prop)) (x0:(P0 b0))=> x0) as proof of (P b0)
% 290.87/291.29 Found x00:(P g)
% 290.87/291.29 Found (fun (x00:(P g))=> x00) as proof of (P g)
% 290.87/291.29 Found (fun (x00:(P g))=> x00) as proof of (P0 g)
% 290.87/291.29 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 290.87/291.29 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) f)
% 290.87/291.29 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 290.87/291.29 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 290.87/291.29 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 290.87/291.29 Found eta_expansion000:=(eta_expansion00 g):(((eq (b->Prop)) g) (fun (x:b)=> (g x)))
% 290.87/291.29 Found (eta_expansion00 g) as proof of (((eq (b->Prop)) g) b0)
% 290.87/291.29 Found ((eta_expansion0 Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 290.87/291.29 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 290.87/291.29 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 290.87/291.29 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 290.87/291.29 Found x00:(P g)
% 290.87/291.29 Found (fun (x00:(P g))=> x00) as proof of (P g)
% 290.87/291.29 Found (fun (x00:(P g))=> x00) as proof of (P0 g)
% 290.87/291.29 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 290.87/291.29 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) f)
% 290.87/291.29 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 290.87/291.29 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 290.87/291.29 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 290.87/291.29 Found eta_expansion000:=(eta_expansion00 g):(((eq (b->Prop)) g) (fun (x:b)=> (g x)))
% 290.87/291.29 Found (eta_expansion00 g) as proof of (((eq (b->Prop)) g) b0)
% 290.87/291.29 Found ((eta_expansion0 Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 290.87/291.29 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 290.87/291.29 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 290.87/291.29 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 290.87/291.29 Found x00:(P1 g)
% 290.87/291.29 Found (fun (x00:(P1 g))=> x00) as proof of (P1 g)
% 290.87/291.29 Found (fun (x00:(P1 g))=> x00) as proof of (P2 g)
% 290.87/291.29 Found x00:(P1 g)
% 290.87/291.29 Found (fun (x00:(P1 g))=> x00) as proof of (P1 g)
% 290.87/291.29 Found (fun (x00:(P1 g))=> x00) as proof of (P2 g)
% 290.87/291.29 Found x00:(P1 g)
% 290.87/291.29 Found (fun (x00:(P1 g))=> x00) as proof of (P1 g)
% 290.87/291.29 Found (fun (x00:(P1 g))=> x00) as proof of (P2 g)
% 290.87/291.29 Found x00:(P1 g)
% 290.87/291.29 Found (fun (x00:(P1 g))=> x00) as proof of (P1 g)
% 290.87/291.29 Found (fun (x00:(P1 g))=> x00) as proof of (P2 g)
% 290.87/291.29 Found x00:(P1 g)
% 290.87/291.29 Found (fun (x00:(P1 g))=> x00) as proof of (P1 g)
% 290.87/291.29 Found (fun (x00:(P1 g))=> x00) as proof of (P2 g)
% 290.87/291.29 Found x00:(P1 g)
% 290.87/291.29 Found (fun (x00:(P1 g))=> x00) as proof of (P1 g)
% 290.87/291.29 Found (fun (x00:(P1 g))=> x00) as proof of (P2 g)
% 290.87/291.29 Found x00:(P1 g)
% 290.87/291.29 Found (fun (x00:(P1 g))=> x00) as proof of (P1 g)
% 290.87/291.29 Found (fun (x00:(P1 g))=> x00) as proof of (P2 g)
% 290.87/291.29 Found x00:(P1 g)
% 290.87/291.29 Found (fun (x00:(P1 g))=> x00) as proof of (P1 g)
% 290.87/291.29 Found (fun (x00:(P1 g))=> x00) as proof of (P2 g)
% 290.87/291.29 Found x10:(P1 (f x0))
% 290.87/291.29 Found (fun (x10:(P1 (f x0)))=> x10) as proof of (P1 (f x0))
% 290.87/291.29 Found (fun (x10:(P1 (f x0)))=> x10) as proof of (P2 (f x0))
% 290.87/291.29 Found x10:(P1 (f x0))
% 290.87/291.29 Found (fun (x10:(P1 (f x0)))=> x10) as proof of (P1 (f x0))
% 290.87/291.29 Found (fun (x10:(P1 (f x0)))=> x10) as proof of (P2 (f x0))
% 290.87/291.29 Found x10:(P1 (f x0))
% 290.87/291.29 Found (fun (x10:(P1 (f x0)))=> x10) as proof of (P1 (f x0))
% 290.87/291.29 Found (fun (x10:(P1 (f x0)))=> x10) as proof of (P2 (f x0))
% 290.87/291.29 Found x10:(P1 (f x0))
% 290.87/291.29 Found (fun (x10:(P1 (f x0)))=> x10) as proof of (P1 (f x0))
% 290.87/291.29 Found (fun (x10:(P1 (f x0)))=> x10) as proof of (P2 (f x0))
% 290.87/291.29 Found x10:(P1 (f x0))
% 290.87/291.29 Found (fun (x10:(P1 (f x0)))=> x10) as proof of (P1 (f x0))
% 290.87/291.29 Found (fun (x10:(P1 (f x0)))=> x10) as proof of (P2 (f x0))
% 290.87/291.29 Found x10:(P1 (f x0))
% 290.87/291.29 Found (fun (x10:(P1 (f x0)))=> x10) as proof of (P1 (f x0))
% 290.87/291.29 Found (fun (x10:(P1 (f x0)))=> x10) as proof of (P2 (f x0))
% 290.87/291.29 Found x10:(P1 (f x0))
% 290.87/291.29 Found (fun (x10:(
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