%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SEU953^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n093.star.cs.uiowa.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory   : 32286.75MB
% OS       : Linux 2.6.32-431.20.3.el6.x86_64
% CPULimit : 300s
% DateTime : Thu Jul 17 13:33:26 EDT 2014

% Result   : Timeout 300.10s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SEU953^5 : TPTP v6.1.0. Released v4.0.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n093.star.cs.uiowa.edu
% % Model    : x86_64 x86_64
% % CPU      : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% % Memory   : 32286.75MB
% % OS       : Linux 2.6.32-431.20.3.el6.x86_64
% % CPULimit : 300
% % DateTime : Thu Jul 17 11:45:31 CDT 2014
% % CPUTime  : 300.10 
% Python 2.7.5
% Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% FOF formula (<kernel.Constant object at 0x20c77e8>, <kernel.DependentProduct object at 0x20c7998>) of role type named g
% Using role type
% Declaring g:(fofType->fofType)
% FOF formula ((forall (Xx:fofType) (Xy:fofType), ((((eq fofType) (g Xx)) (g Xy))->(((eq fofType) Xx) Xy)))->((ex (fofType->fofType)) (fun (Xh:(fofType->fofType))=> (((eq (fofType->fofType)) (fun (Xx:fofType)=> (Xh (g Xx)))) (fun (Xx:fofType)=> Xx))))) of role conjecture named cTHM591_pme
% Conjecture to prove = ((forall (Xx:fofType) (Xy:fofType), ((((eq fofType) (g Xx)) (g Xy))->(((eq fofType) Xx) Xy)))->((ex (fofType->fofType)) (fun (Xh:(fofType->fofType))=> (((eq (fofType->fofType)) (fun (Xx:fofType)=> (Xh (g Xx)))) (fun (Xx:fofType)=> Xx))))):Prop
% Parameter fofType_DUMMY:fofType.
% We need to prove ['((forall (Xx:fofType) (Xy:fofType), ((((eq fofType) (g Xx)) (g Xy))->(((eq fofType) Xx) Xy)))->((ex (fofType->fofType)) (fun (Xh:(fofType->fofType))=> (((eq (fofType->fofType)) (fun (Xx:fofType)=> (Xh (g Xx)))) (fun (Xx:fofType)=> Xx)))))']
% Parameter fofType:Type.
% Parameter g:(fofType->fofType).
% Trying to prove ((forall (Xx:fofType) (Xy:fofType), ((((eq fofType) (g Xx)) (g Xy))->(((eq fofType) Xx) Xy)))->((ex (fofType->fofType)) (fun (Xh:(fofType->fofType))=> (((eq (fofType->fofType)) (fun (Xx:fofType)=> (Xh (g Xx)))) (fun (Xx:fofType)=> Xx)))))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found eq_ref000:=(eq_ref00 P):((P (x0 (g x1)))->(P (x0 (g x1))))
% Found (eq_ref00 P) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((eq_ref0 (x0 (g x1))) P) as proof of ((P (x0 (g x1)))->(P x1))
% Found (((eq_ref fofType) (x0 (g x1))) P) as proof of ((P (x0 (g x1)))->(P x1))
% Found (((eq_ref fofType) (x0 (g x1))) P) as proof of ((P (x0 (g x1)))->(P x1))
% Found (fun (P:(fofType->Prop))=> (((eq_ref fofType) (x0 (g x1))) P)) as proof of ((P (x0 (g x1)))->(P x1))
% Found eq_ref000:=(eq_ref00 P):((P (x0 (g x1)))->(P (x0 (g x1))))
% Found (eq_ref00 P) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((eq_ref0 (x0 (g x1))) P) as proof of ((P (x0 (g x1)))->(P x1))
% Found (((eq_ref fofType) (x0 (g x1))) P) as proof of ((P (x0 (g x1)))->(P x1))
% Found (((eq_ref fofType) (x0 (g x1))) P) as proof of ((P (x0 (g x1)))->(P x1))
% Found (fun (P:(fofType->Prop))=> (((eq_ref fofType) (x0 (g x1))) P)) as proof of ((P (x0 (g x1)))->(P x1))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (x20 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((x2 x1) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (((x (x0 (g x1))) x1) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (x20 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((x2 x1) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (((x (x0 (g x1))) x1) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((eq_sym10 x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((eq_sym1 (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((eq_sym10 x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((eq_sym1 (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (fun (Xh:(fofType->fofType))=> (((eq (fofType->fofType)) (fun (Xx:fofType)=> (Xh (g Xx)))) (fun (Xx:fofType)=> Xx)))):(((eq ((fofType->fofType)->Prop)) (fun (Xh:(fofType->fofType))=> (((eq (fofType->fofType)) (fun (Xx:fofType)=> (Xh (g Xx)))) (fun (Xx:fofType)=> Xx)))) (fun (Xh:(fofType->fofType))=> (((eq (fofType->fofType)) (fun (Xx:fofType)=> (Xh (g Xx)))) (fun (Xx:fofType)=> Xx))))
% Found (eq_ref0 (fun (Xh:(fofType->fofType))=> (((eq (fofType->fofType)) (fun (Xx:fofType)=> (Xh (g Xx)))) (fun (Xx:fofType)=> Xx)))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (Xh:(fofType->fofType))=> (((eq (fofType->fofType)) (fun (Xx:fofType)=> (Xh (g Xx)))) (fun (Xx:fofType)=> Xx)))) b)
% Found ((eq_ref ((fofType->fofType)->Prop)) (fun (Xh:(fofType->fofType))=> (((eq (fofType->fofType)) (fun (Xx:fofType)=> (Xh (g Xx)))) (fun (Xx:fofType)=> Xx)))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (Xh:(fofType->fofType))=> (((eq (fofType->fofType)) (fun (Xx:fofType)=> (Xh (g Xx)))) (fun (Xx:fofType)=> Xx)))) b)
% Found ((eq_ref ((fofType->fofType)->Prop)) (fun (Xh:(fofType->fofType))=> (((eq (fofType->fofType)) (fun (Xx:fofType)=> (Xh (g Xx)))) (fun (Xx:fofType)=> Xx)))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (Xh:(fofType->fofType))=> (((eq (fofType->fofType)) (fun (Xx:fofType)=> (Xh (g Xx)))) (fun (Xx:fofType)=> Xx)))) b)
% Found ((eq_ref ((fofType->fofType)->Prop)) (fun (Xh:(fofType->fofType))=> (((eq (fofType->fofType)) (fun (Xx:fofType)=> (Xh (g Xx)))) (fun (Xx:fofType)=> Xx)))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (Xh:(fofType->fofType))=> (((eq (fofType->fofType)) (fun (Xx:fofType)=> (Xh (g Xx)))) (fun (Xx:fofType)=> Xx)))) b)
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym010 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym01 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x20 (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((x2 (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (eq_sym000 (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_sym00 (x0 (g x1))) (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (((eq_sym0 x1) (x0 (g x1))) (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((((eq_sym fofType) x1) (x0 (g x1))) (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym010 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym01 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x20 (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((x2 (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (eq_sym000 (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_sym00 (x0 (g x1))) (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (((eq_sym0 x1) (x0 (g x1))) (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((((eq_sym fofType) x1) (x0 (g x1))) (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym10 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x20 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((x2 (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym10 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x20 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((x2 (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (((eq (fofType->fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) (fun (Xx:fofType)=> Xx)))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (((eq (fofType->fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) (fun (Xx:fofType)=> Xx)))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (((eq (fofType->fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) (fun (Xx:fofType)=> Xx)))
% Found (fun (x0:(fofType->fofType))=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (((eq (fofType->fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) (fun (Xx:fofType)=> Xx)))
% Found (fun (x0:(fofType->fofType))=> ((eq_ref Prop) (f x0))) as proof of (forall (x:(fofType->fofType)), (((eq Prop) (f x)) (((eq (fofType->fofType)) (fun (Xx:fofType)=> (x (g Xx)))) (fun (Xx:fofType)=> Xx))))
% Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (((eq (fofType->fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) (fun (Xx:fofType)=> Xx)))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (((eq (fofType->fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) (fun (Xx:fofType)=> Xx)))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (((eq (fofType->fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) (fun (Xx:fofType)=> Xx)))
% Found (fun (x0:(fofType->fofType))=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (((eq (fofType->fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) (fun (Xx:fofType)=> Xx)))
% Found (fun (x0:(fofType->fofType))=> ((eq_ref Prop) (f x0))) as proof of (forall (x:(fofType->fofType)), (((eq Prop) (f x)) (((eq (fofType->fofType)) (fun (Xx:fofType)=> (x (g Xx)))) (fun (Xx:fofType)=> Xx))))
% Found eta_expansion0000:=(eta_expansion000 P):((P (fun (Xx:fofType)=> (x0 (g Xx))))->(P (fun (x:fofType)=> (x0 (g x)))))
% Found (eta_expansion000 P) as proof of (P0 (fun (Xx:fofType)=> (x0 (g Xx))))
% Found ((eta_expansion00 (fun (Xx:fofType)=> (x0 (g Xx)))) P) as proof of (P0 (fun (Xx:fofType)=> (x0 (g Xx))))
% Found (((eta_expansion0 fofType) (fun (Xx:fofType)=> (x0 (g Xx)))) P) as proof of (P0 (fun (Xx:fofType)=> (x0 (g Xx))))
% Found ((((eta_expansion fofType) fofType) (fun (Xx:fofType)=> (x0 (g Xx)))) P) as proof of (P0 (fun (Xx:fofType)=> (x0 (g Xx))))
% Found ((((eta_expansion fofType) fofType) (fun (Xx:fofType)=> (x0 (g Xx)))) P) as proof of (P0 (fun (Xx:fofType)=> (x0 (g Xx))))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (Xx:fofType)=> (x0 (g Xx))))->(P (fun (x:fofType)=> (x0 (g x)))))
% Found (eta_expansion_dep000 P) as proof of (P0 (fun (Xx:fofType)=> (x0 (g Xx))))
% Found ((eta_expansion_dep00 (fun (Xx:fofType)=> (x0 (g Xx)))) P) as proof of (P0 (fun (Xx:fofType)=> (x0 (g Xx))))
% Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) P) as proof of (P0 (fun (Xx:fofType)=> (x0 (g Xx))))
% Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) P) as proof of (P0 (fun (Xx:fofType)=> (x0 (g Xx))))
% Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) P) as proof of (P0 (fun (Xx:fofType)=> (x0 (g Xx))))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (Xx:fofType)=> (x0 (g Xx))))->(P (fun (x:fofType)=> (x0 (g x)))))
% Found (eta_expansion_dep000 P) as proof of (P0 (fun (Xx:fofType)=> (x0 (g Xx))))
% Found ((eta_expansion_dep00 (fun (Xx:fofType)=> (x0 (g Xx)))) P) as proof of (P0 (fun (Xx:fofType)=> (x0 (g Xx))))
% Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) P) as proof of (P0 (fun (Xx:fofType)=> (x0 (g Xx))))
% Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) P) as proof of (P0 (fun (Xx:fofType)=> (x0 (g Xx))))
% Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) P) as proof of (P0 (fun (Xx:fofType)=> (x0 (g Xx))))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found eq_ref000:=(eq_ref00 P1):((P1 (x0 (g x1)))->(P1 (x0 (g x1))))
% Found (eq_ref00 P1) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found ((eq_ref0 (x0 (g x1))) P1) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found (((eq_ref fofType) (x0 (g x1))) P1) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found (((eq_ref fofType) (x0 (g x1))) P1) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found (fun (P1:(fofType->Prop))=> (((eq_ref fofType) (x0 (g x1))) P1)) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found eq_ref000:=(eq_ref00 P1):((P1 (x0 (g x1)))->(P1 (x0 (g x1))))
% Found (eq_ref00 P1) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found ((eq_ref0 (x0 (g x1))) P1) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found (((eq_ref fofType) (x0 (g x1))) P1) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found (((eq_ref fofType) (x0 (g x1))) P1) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found (fun (P1:(fofType->Prop))=> (((eq_ref fofType) (x0 (g x1))) P1)) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found eq_ref000:=(eq_ref00 P1):((P1 (x0 (g x1)))->(P1 (x0 (g x1))))
% Found (eq_ref00 P1) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found ((eq_ref0 (x0 (g x1))) P1) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found (((eq_ref fofType) (x0 (g x1))) P1) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found (((eq_ref fofType) (x0 (g x1))) P1) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found (fun (P1:(fofType->Prop))=> (((eq_ref fofType) (x0 (g x1))) P1)) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found eq_ref000:=(eq_ref00 P1):((P1 (x0 (g x1)))->(P1 (x0 (g x1))))
% Found (eq_ref00 P1) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found ((eq_ref0 (x0 (g x1))) P1) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found (((eq_ref fofType) (x0 (g x1))) P1) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found (((eq_ref fofType) (x0 (g x1))) P1) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found (fun (P1:(fofType->Prop))=> (((eq_ref fofType) (x0 (g x1))) P1)) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xx:fofType)=> (x0 (g Xx)))):(((eq (fofType->fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) (fun (x:fofType)=> (x0 (g x))))
% Found (eta_expansion_dep00 (fun (Xx:fofType)=> (x0 (g Xx)))) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) b)
% Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) b)
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) b)
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) b)
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq (fofType->fofType)) b) b)
% Found (eq_ref0 b) as proof of (((eq (fofType->fofType)) b) (fun (Xx:fofType)=> Xx))
% Found ((eq_ref (fofType->fofType)) b) as proof of (((eq (fofType->fofType)) b) (fun (Xx:fofType)=> Xx))
% Found ((eq_ref (fofType->fofType)) b) as proof of (((eq (fofType->fofType)) b) (fun (Xx:fofType)=> Xx))
% Found ((eq_ref (fofType->fofType)) b) as proof of (((eq (fofType->fofType)) b) (fun (Xx:fofType)=> Xx))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (x200 ((eq_ref fofType) (g (x0 (g x1))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found (x200 ((eq_ref fofType) (g (x0 (g x1))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((fun (x3:(((eq fofType) (g (x0 (g x1)))) (g x1)))=> ((x20 x3) P)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((fun (x3:(((eq fofType) (g (x0 (g x1)))) (g x1)))=> (((x2 x1) x3) P)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((fun (x3:(((eq fofType) (g (x0 (g x1)))) (g x1)))=> ((((x (x0 (g x1))) x1) x3) P)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found (fun (P:(fofType->Prop))=> ((fun (x3:(((eq fofType) (g (x0 (g x1)))) (g x1)))=> ((((x (x0 (g x1))) x1) x3) P)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (x200 ((eq_ref fofType) (g (x0 (g x1))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found (x200 ((eq_ref fofType) (g (x0 (g x1))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((fun (x3:(((eq fofType) (g (x0 (g x1)))) (g x1)))=> ((x20 x3) P)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((fun (x3:(((eq fofType) (g (x0 (g x1)))) (g x1)))=> (((x2 x1) x3) P)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((fun (x3:(((eq fofType) (g (x0 (g x1)))) (g x1)))=> ((((x (x0 (g x1))) x1) x3) P)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found (fun (P:(fofType->Prop))=> ((fun (x3:(((eq fofType) (g (x0 (g x1)))) (g x1)))=> ((((x (x0 (g x1))) x1) x3) P)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (x20 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((x2 x1) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (((x (x0 (g x1))) x1) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (x20 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((x2 x1) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (((x (x0 (g x1))) x1) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (x20 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((x2 x1) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (((x (x0 (g x1))) x1) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (x20 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((x2 x1) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (((x (x0 (g x1))) x1) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found eq_ref00:=(eq_ref0 (x0 (g x2))):(((eq fofType) (x0 (g x2))) (x0 (g x2)))
% Found (eq_ref0 (x0 (g x2))) as proof of (((eq fofType) (x0 (g x2))) x1)
% Found ((eq_ref fofType) (x0 (g x2))) as proof of (((eq fofType) (x0 (g x2))) x1)
% Found (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2)))) as proof of (((eq fofType) (x0 (g x2))) x1)
% Found (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2)))) as proof of (forall (x:fofType), (((eq fofType) (x0 (g x))) x1))
% Found (functional_extensionality00010 (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found (functional_extensionality00010 (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> ((functional_extensionality0001 x2) (fun (x3:(fofType->fofType))=> (P (x0 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> (((functional_extensionality000 (fun (x4:fofType)=> x1)) x2) (fun (x3:(fofType->fofType))=> (P (x0 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> (((functional_extensionality000 (fun (x4:fofType)=> x1)) x2) (fun (x3:(fofType->fofType))=> (P (x0 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found (fun (P:(fofType->Prop))=> ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> (((functional_extensionality000 (fun (x4:fofType)=> x1)) x2) (fun (x3:(fofType->fofType))=> (P (x0 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2)))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found eq_ref00:=(eq_ref0 (x0 (g x2))):(((eq fofType) (x0 (g x2))) (x0 (g x2)))
% Found (eq_ref0 (x0 (g x2))) as proof of (((eq fofType) (x0 (g x2))) x1)
% Found ((eq_ref fofType) (x0 (g x2))) as proof of (((eq fofType) (x0 (g x2))) x1)
% Found (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2)))) as proof of (((eq fofType) (x0 (g x2))) x1)
% Found (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2)))) as proof of (forall (x:fofType), (((eq fofType) (x0 (g x))) x1))
% Found (functional_extensionality00010 (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found (functional_extensionality00010 (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> ((functional_extensionality0001 x2) (fun (x3:(fofType->fofType))=> (P (x3 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> (((functional_extensionality000 (fun (x4:fofType)=> x1)) x2) (fun (x3:(fofType->fofType))=> (P (x3 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> (((functional_extensionality000 (fun (x4:fofType)=> x1)) x2) (fun (x3:(fofType->fofType))=> (P (x3 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found (fun (P:(fofType->Prop))=> ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> (((functional_extensionality000 (fun (x4:fofType)=> x1)) x2) (fun (x3:(fofType->fofType))=> (P (x3 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2)))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found eq_ref00:=(eq_ref0 (x0 (g x2))):(((eq fofType) (x0 (g x2))) (x0 (g x2)))
% Found (eq_ref0 (x0 (g x2))) as proof of (((eq fofType) (x0 (g x2))) x1)
% Found ((eq_ref fofType) (x0 (g x2))) as proof of (((eq fofType) (x0 (g x2))) x1)
% Found (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2)))) as proof of (((eq fofType) (x0 (g x2))) x1)
% Found (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2)))) as proof of (forall (x:fofType), (((eq fofType) (x0 (g x))) x1))
% Found (functional_extensionality_dep00010 (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found (functional_extensionality_dep00010 (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> ((functional_extensionality_dep0001 x2) (fun (x3:(fofType->fofType))=> (P (x0 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> (((functional_extensionality_dep000 (fun (x4:fofType)=> x1)) x2) (fun (x3:(fofType->fofType))=> (P (x0 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> (((functional_extensionality_dep000 (fun (x4:fofType)=> x1)) x2) (fun (x3:(fofType->fofType))=> (P (x0 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found (fun (P:(fofType->Prop))=> ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> (((functional_extensionality_dep000 (fun (x4:fofType)=> x1)) x2) (fun (x3:(fofType->fofType))=> (P (x0 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2)))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found eq_ref00:=(eq_ref0 (x0 (g x2))):(((eq fofType) (x0 (g x2))) (x0 (g x2)))
% Found (eq_ref0 (x0 (g x2))) as proof of (((eq fofType) (x0 (g x2))) x1)
% Found ((eq_ref fofType) (x0 (g x2))) as proof of (((eq fofType) (x0 (g x2))) x1)
% Found (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2)))) as proof of (((eq fofType) (x0 (g x2))) x1)
% Found (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2)))) as proof of (forall (x:fofType), (((eq fofType) (x0 (g x))) x1))
% Found (functional_extensionality_dep00010 (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found (functional_extensionality_dep00010 (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> ((functional_extensionality_dep0001 x2) (fun (x3:(fofType->fofType))=> (P (x3 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> (((functional_extensionality_dep000 (fun (x4:fofType)=> x1)) x2) (fun (x3:(fofType->fofType))=> (P (x3 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> (((functional_extensionality_dep000 (fun (x4:fofType)=> x1)) x2) (fun (x3:(fofType->fofType))=> (P (x3 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found (fun (P:(fofType->Prop))=> ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> (((functional_extensionality_dep000 (fun (x4:fofType)=> x1)) x2) (fun (x3:(fofType->fofType))=> (P (x3 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2)))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found eta_expansion0000:=(eta_expansion000 P):((P (fun (Xx:fofType)=> Xx))->(P (fun (x:fofType)=> x)))
% Found (eta_expansion000 P) as proof of (P0 (fun (Xx:fofType)=> Xx))
% Found ((eta_expansion00 (fun (Xx:fofType)=> Xx)) P) as proof of (P0 (fun (Xx:fofType)=> Xx))
% Found (((eta_expansion0 fofType) (fun (Xx:fofType)=> Xx)) P) as proof of (P0 (fun (Xx:fofType)=> Xx))
% Found ((((eta_expansion fofType) fofType) (fun (Xx:fofType)=> Xx)) P) as proof of (P0 (fun (Xx:fofType)=> Xx))
% Found ((((eta_expansion fofType) fofType) (fun (Xx:fofType)=> Xx)) P) as proof of (P0 (fun (Xx:fofType)=> Xx))
% Found eta_expansion0000:=(eta_expansion000 P):((P (fun (Xx:fofType)=> Xx))->(P (fun (x:fofType)=> x)))
% Found (eta_expansion000 P) as proof of (P0 (fun (Xx:fofType)=> Xx))
% Found ((eta_expansion00 (fun (Xx:fofType)=> Xx)) P) as proof of (P0 (fun (Xx:fofType)=> Xx))
% Found (((eta_expansion0 fofType) (fun (Xx:fofType)=> Xx)) P) as proof of (P0 (fun (Xx:fofType)=> Xx))
% Found ((((eta_expansion fofType) fofType) (fun (Xx:fofType)=> Xx)) P) as proof of (P0 (fun (Xx:fofType)=> Xx))
% Found ((((eta_expansion fofType) fofType) (fun (Xx:fofType)=> Xx)) P) as proof of (P0 (fun (Xx:fofType)=> Xx))
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xx:fofType)=> Xx)):(((eq (fofType->fofType)) (fun (Xx:fofType)=> Xx)) (fun (x:fofType)=> x))
% Found (eta_expansion_dep00 (fun (Xx:fofType)=> Xx)) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> Xx)) b)
% Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (Xx:fofType)=> Xx)) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> Xx)) b)
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (Xx:fofType)=> Xx)) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> Xx)) b)
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (Xx:fofType)=> Xx)) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> Xx)) b)
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (Xx:fofType)=> Xx)) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> Xx)) b)
% Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->fofType)) b) (fun (x:fofType)=> (b x)))
% Found (eta_expansion00 b) as proof of (((eq (fofType->fofType)) b) (fun (Xx:fofType)=> (x0 (g Xx))))
% Found ((eta_expansion0 fofType) b) as proof of (((eq (fofType->fofType)) b) (fun (Xx:fofType)=> (x0 (g Xx))))
% Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (fun (Xx:fofType)=> (x0 (g Xx))))
% Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (fun (Xx:fofType)=> (x0 (g Xx))))
% Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (fun (Xx:fofType)=> (x0 (g Xx))))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) x1)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x1)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x1)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x1)
% Found ((eq_trans0000 ((eq_ref fofType) (x0 (g x1)))) ((eq_ref fofType) b)) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (((eq_trans000 x1) ((eq_ref fofType) (x0 (g x1)))) ((eq_ref fofType) x1)) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((((fun (b:fofType)=> ((eq_trans00 b) x1)) x1) ((eq_ref fofType) (x0 (g x1)))) ((eq_ref fofType) x1)) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((((fun (b:fofType)=> (((eq_trans0 (x0 (g x1))) b) x1)) x1) ((eq_ref fofType) (x0 (g x1)))) ((eq_ref fofType) x1)) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((((fun (b:fofType)=> ((((eq_trans fofType) (x0 (g x1))) b) x1)) x1) ((eq_ref fofType) (x0 (g x1)))) ((eq_ref fofType) x1)) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) x1)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x1)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x1)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x1)
% Found ((eq_trans0000 ((eq_ref fofType) (x0 (g x1)))) ((eq_ref fofType) b)) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (((eq_trans000 x1) ((eq_ref fofType) (x0 (g x1)))) ((eq_ref fofType) x1)) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((((fun (b:fofType)=> ((eq_trans00 b) x1)) x1) ((eq_ref fofType) (x0 (g x1)))) ((eq_ref fofType) x1)) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((((fun (b:fofType)=> (((eq_trans0 (x0 (g x1))) b) x1)) x1) ((eq_ref fofType) (x0 (g x1)))) ((eq_ref fofType) x1)) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((((fun (b:fofType)=> ((((eq_trans fofType) (x0 (g x1))) b) x1)) x1) ((eq_ref fofType) (x0 (g x1)))) ((eq_ref fofType) x1)) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found eq_ref000:=(eq_ref00 P):((P x1)->(P x1))
% Found (eq_ref00 P) as proof of (P0 x1)
% Found ((eq_ref0 x1) P) as proof of (P0 x1)
% Found (((eq_ref fofType) x1) P) as proof of (P0 x1)
% Found (((eq_ref fofType) x1) P) as proof of (P0 x1)
% Found eq_ref000:=(eq_ref00 P):((P x1)->(P x1))
% Found (eq_ref00 P) as proof of (P0 x1)
% Found ((eq_ref0 x1) P) as proof of (P0 x1)
% Found (((eq_ref fofType) x1) P) as proof of (P0 x1)
% Found (((eq_ref fofType) x1) P) as proof of (P0 x1)
% Found eq_ref000:=(eq_ref00 P):((P (x0 (g x1)))->(P (x0 (g x1))))
% Found (eq_ref00 P) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((eq_ref0 (x0 (g x1))) P) as proof of ((P (x0 (g x1)))->(P x1))
% Found (((eq_ref fofType) (x0 (g x1))) P) as proof of ((P (x0 (g x1)))->(P x1))
% Found (((eq_ref fofType) (x0 (g x1))) P) as proof of ((P (x0 (g x1)))->(P x1))
% Found (fun (P:(fofType->Prop))=> (((eq_ref fofType) (x0 (g x1))) P)) as proof of ((P (x0 (g x1)))->(P x1))
% Found (fun (P:(fofType->Prop))=> (((eq_ref fofType) (x0 (g x1))) P)) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found eq_ref000:=(eq_ref00 P):((P (x0 (g x1)))->(P (x0 (g x1))))
% Found (eq_ref00 P) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((eq_ref0 (x0 (g x1))) P) as proof of ((P (x0 (g x1)))->(P x1))
% Found (((eq_ref fofType) (x0 (g x1))) P) as proof of ((P (x0 (g x1)))->(P x1))
% Found (((eq_ref fofType) (x0 (g x1))) P) as proof of ((P (x0 (g x1)))->(P x1))
% Found (fun (P:(fofType->Prop))=> (((eq_ref fofType) (x0 (g x1))) P)) as proof of ((P (x0 (g x1)))->(P x1))
% Found (fun (P:(fofType->Prop))=> (((eq_ref fofType) (x0 (g x1))) P)) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found eq_ref000:=(eq_ref00 P):((P (x0 (g x1)))->(P (x0 (g x1))))
% Found (eq_ref00 P) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((eq_ref0 (x0 (g x1))) P) as proof of ((P (x0 (g x1)))->(P x1))
% Found (((eq_ref fofType) (x0 (g x1))) P) as proof of ((P (x0 (g x1)))->(P x1))
% Found (((eq_ref fofType) (x0 (g x1))) P) as proof of ((P (x0 (g x1)))->(P x1))
% Found (fun (P:(fofType->Prop))=> (((eq_ref fofType) (x0 (g x1))) P)) as proof of ((P (x0 (g x1)))->(P x1))
% Found eq_ref000:=(eq_ref00 P):((P (x0 (g x1)))->(P (x0 (g x1))))
% Found (eq_ref00 P) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((eq_ref0 (x0 (g x1))) P) as proof of ((P (x0 (g x1)))->(P x1))
% Found (((eq_ref fofType) (x0 (g x1))) P) as proof of ((P (x0 (g x1)))->(P x1))
% Found (((eq_ref fofType) (x0 (g x1))) P) as proof of ((P (x0 (g x1)))->(P x1))
% Found (fun (P:(fofType->Prop))=> (((eq_ref fofType) (x0 (g x1))) P)) as proof of ((P (x0 (g x1)))->(P x1))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (eq_sym1000 ((eq_ref fofType) (x0 (g x1)))) as proof of ((P x1)->(P (x0 (g x1))))
% Found (eq_sym1000 ((eq_ref fofType) (x0 (g x1)))) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> ((eq_sym100 x2) P)) ((eq_ref fofType) (x0 (g x1)))) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((eq_sym10 x1) x2) P)) ((eq_ref fofType) (x0 (g x1)))) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> ((((eq_sym1 (x0 (g x1))) x1) x2) P)) ((eq_ref fofType) (x0 (g x1)))) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((((eq_sym fofType) (x0 (g x1))) x1) x2) P)) ((eq_ref fofType) (x0 (g x1)))) as proof of ((P x1)->(P (x0 (g x1))))
% Found (fun (P:(fofType->Prop))=> ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((((eq_sym fofType) (x0 (g x1))) x1) x2) P)) ((eq_ref fofType) (x0 (g x1))))) as proof of ((P x1)->(P (x0 (g x1))))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (eq_sym1000 ((eq_ref fofType) (x0 (g x1)))) as proof of ((P x1)->(P (x0 (g x1))))
% Found (eq_sym1000 ((eq_ref fofType) (x0 (g x1)))) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> ((eq_sym100 x2) P)) ((eq_ref fofType) (x0 (g x1)))) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((eq_sym10 x1) x2) P)) ((eq_ref fofType) (x0 (g x1)))) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> ((((eq_sym1 (x0 (g x1))) x1) x2) P)) ((eq_ref fofType) (x0 (g x1)))) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((((eq_sym fofType) (x0 (g x1))) x1) x2) P)) ((eq_ref fofType) (x0 (g x1)))) as proof of ((P x1)->(P (x0 (g x1))))
% Found (fun (P:(fofType->Prop))=> ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((((eq_sym fofType) (x0 (g x1))) x1) x2) P)) ((eq_ref fofType) (x0 (g x1))))) as proof of ((P x1)->(P (x0 (g x1))))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((eq_sym10 x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((eq_sym1 (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((eq_sym10 x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((eq_sym1 (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((eq_sym10 x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((eq_sym1 (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((eq_sym10 x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((eq_sym1 (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((eq_sym10 x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((eq_sym1 (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((eq_sym10 x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((eq_sym1 (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((eq_sym10 x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((eq_sym1 (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((eq_sym10 x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((eq_sym1 (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (x20 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found ((x2 x1) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found (((x (x0 (g x1))) x1) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found (((x (x0 (g x1))) x1) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (x20 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found ((x2 x1) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found (((x (x0 (g x1))) x1) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found (((x (x0 (g x1))) x1) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found eq_ref000:=(eq_ref00 P):((P x1)->(P x1))
% Found (eq_ref00 P) as proof of (P0 x1)
% Found ((eq_ref0 x1) P) as proof of (P0 x1)
% Found (((eq_ref fofType) x1) P) as proof of (P0 x1)
% Found (((eq_ref fofType) x1) P) as proof of (P0 x1)
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_sym1000 ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((eq_sym1000 ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> ((eq_sym100 x2) (fun (x4:fofType)=> ((P x1)->(P x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((eq_sym10 x1) x2) (fun (x4:fofType)=> ((P x1)->(P x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> ((((eq_sym1 (x0 (g x1))) x1) x2) (fun (x4:fofType)=> ((P x1)->(P x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((((eq_sym fofType) (x0 (g x1))) x1) x2) (fun (x4:fofType)=> ((P x1)->(P x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found (fun (P:(fofType->Prop))=> (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((((eq_sym fofType) (x0 (g x1))) x1) x2) (fun (x4:fofType)=> ((P x1)->(P x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P))) as proof of ((P x1)->(P (x0 (g x1))))
% Found eq_ref000:=(eq_ref00 P):((P x1)->(P x1))
% Found (eq_ref00 P) as proof of (P0 x1)
% Found ((eq_ref0 x1) P) as proof of (P0 x1)
% Found (((eq_ref fofType) x1) P) as proof of (P0 x1)
% Found (((eq_ref fofType) x1) P) as proof of (P0 x1)
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_sym1000 ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((eq_sym1000 ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> ((eq_sym100 x2) (fun (x4:fofType)=> ((P x1)->(P x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((eq_sym10 x1) x2) (fun (x4:fofType)=> ((P x1)->(P x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> ((((eq_sym1 (x0 (g x1))) x1) x2) (fun (x4:fofType)=> ((P x1)->(P x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((((eq_sym fofType) (x0 (g x1))) x1) x2) (fun (x4:fofType)=> ((P x1)->(P x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found (fun (P:(fofType->Prop))=> (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((((eq_sym fofType) (x0 (g x1))) x1) x2) (fun (x4:fofType)=> ((P x1)->(P x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P))) as proof of ((P x1)->(P (x0 (g x1))))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (x20 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((x2 x1) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (((x (x0 (g x1))) x1) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (x20 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((x2 x1) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (((x (x0 (g x1))) x1) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym010 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym01 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x20 (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((x2 (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (eq_sym0000 (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found (eq_sym0000 (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((fun (x2:(((eq fofType) x1) (x0 (g x1))))=> ((eq_sym000 x2) P)) (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((fun (x2:(((eq fofType) x1) (x0 (g x1))))=> (((eq_sym00 (x0 (g x1))) x2) P)) (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((fun (x2:(((eq fofType) x1) (x0 (g x1))))=> ((((eq_sym0 x1) (x0 (g x1))) x2) P)) (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((fun (x2:(((eq fofType) x1) (x0 (g x1))))=> (((((eq_sym fofType) x1) (x0 (g x1))) x2) P)) (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found (fun (P:(fofType->Prop))=> ((fun (x2:(((eq fofType) x1) (x0 (g x1))))=> (((((eq_sym fofType) x1) (x0 (g x1))) x2) P)) (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym010 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym01 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x20 (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((x2 (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (eq_sym0000 (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found (eq_sym0000 (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((fun (x2:(((eq fofType) x1) (x0 (g x1))))=> ((eq_sym000 x2) P)) (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((fun (x2:(((eq fofType) x1) (x0 (g x1))))=> (((eq_sym00 (x0 (g x1))) x2) P)) (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((fun (x2:(((eq fofType) x1) (x0 (g x1))))=> ((((eq_sym0 x1) (x0 (g x1))) x2) P)) (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((fun (x2:(((eq fofType) x1) (x0 (g x1))))=> (((((eq_sym fofType) x1) (x0 (g x1))) x2) P)) (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found (fun (P:(fofType->Prop))=> ((fun (x2:(((eq fofType) x1) (x0 (g x1))))=> (((((eq_sym fofType) x1) (x0 (g x1))) x2) P)) (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found eq_ref00:=(eq_ref0 x1):(((eq fofType) x1) x1)
% Found (eq_ref0 x1) as proof of (((eq fofType) x1) b)
% Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 x1):(((eq fofType) x1) x1)
% Found (eq_ref0 x1) as proof of (((eq fofType) x1) b)
% Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym010 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym01 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x20 (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((x2 (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (eq_sym000 (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_sym00 (x0 (g x1))) (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (((eq_sym0 x1) (x0 (g x1))) (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((((eq_sym fofType) x1) (x0 (g x1))) (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym010 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym01 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x20 (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((x2 (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (eq_sym000 (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_sym00 (x0 (g x1))) (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (((eq_sym0 x1) (x0 (g x1))) (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((((eq_sym fofType) x1) (x0 (g x1))) (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym010 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym01 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x20 (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((x2 (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (eq_sym000 (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_sym00 (x0 (g x1))) (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (((eq_sym0 x1) (x0 (g x1))) (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((((eq_sym fofType) x1) (x0 (g x1))) (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym010 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym01 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x20 (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((x2 (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (eq_sym000 (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_sym00 (x0 (g x1))) (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (((eq_sym0 x1) (x0 (g x1))) (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((((eq_sym fofType) x1) (x0 (g x1))) (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym10 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x200 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P x1)->(P (x0 (g x1))))
% Found (x200 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((x20 x3) P)) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> (((x2 (x0 (g x1))) x3) P)) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((((x x1) (x0 (g x1))) x3) P)) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P x1)->(P (x0 (g x1))))
% Found (fun (P:(fofType->Prop))=> ((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((((x x1) (x0 (g x1))) x3) P)) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of ((P x1)->(P (x0 (g x1))))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym10 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((x200 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((x200 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found (((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((x20 x3) (fun (x5:fofType)=> ((P x1)->(P x5))))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found (((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> (((x2 (x0 (g x1))) x3) (fun (x5:fofType)=> ((P x1)->(P x5))))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found (((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((((x x1) (x0 (g x1))) x3) (fun (x5:fofType)=> ((P x1)->(P x5))))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found (fun (P:(fofType->Prop))=> (((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((((x x1) (x0 (g x1))) x3) (fun (x5:fofType)=> ((P x1)->(P x5))))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P))) as proof of ((P x1)->(P (x0 (g x1))))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym10 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x200 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P x1)->(P (x0 (g x1))))
% Found (x200 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((x20 x3) P)) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> (((x2 (x0 (g x1))) x3) P)) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((((x x1) (x0 (g x1))) x3) P)) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P x1)->(P (x0 (g x1))))
% Found (fun (P:(fofType->Prop))=> ((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((((x x1) (x0 (g x1))) x3) P)) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of ((P x1)->(P (x0 (g x1))))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym10 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((x200 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((x200 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found (((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((x20 x3) (fun (x5:fofType)=> ((P x1)->(P x5))))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found (((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> (((x2 (x0 (g x1))) x3) (fun (x5:fofType)=> ((P x1)->(P x5))))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found (((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((((x x1) (x0 (g x1))) x3) (fun (x5:fofType)=> ((P x1)->(P x5))))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found (fun (P:(fofType->Prop))=> (((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((((x x1) (x0 (g x1))) x3) (fun (x5:fofType)=> ((P x1)->(P x5))))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P))) as proof of ((P x1)->(P (x0 (g x1))))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym10 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x20 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((x2 (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym10 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x20 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((x2 (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym10 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x20 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((x2 (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym10 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x20 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((x2 (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym10 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x20 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((x2 (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym10 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x20 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((x2 (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym10 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x20 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((x2 (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym10 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x20 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((x2 (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_sym10 b) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found (((eq_sym1 (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_trans0000 ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((eq_trans000 x1) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((fun (b:fofType)=> ((eq_trans00 b) (x0 (g x1)))) x1) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((fun (b:fofType)=> (((eq_trans0 x1) b) (x0 (g x1)))) x1) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((fun (b:fofType)=> ((((eq_trans fofType) x1) b) (x0 (g x1)))) x1) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_sym10 b) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found (((eq_sym1 (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_trans0000 ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((eq_trans000 x1) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((fun (b:fofType)=> ((eq_trans00 b) (x0 (g x1)))) x1) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((fun (b:fofType)=> (((eq_trans0 x1) b) (x0 (g x1)))) x1) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((fun (b:fofType)=> ((((eq_trans fofType) x1) b) (x0 (g x1)))) x1) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref000:=(eq_ref00 P):((P (x0 (g x1)))->(P (x0 (g x1))))
% Found (eq_ref00 P) as proof of ((P (x0 (g x1)))->(P (b x1)))
% Found ((eq_ref0 (x0 (g x1))) P) as proof of ((P (x0 (g x1)))->(P (b x1)))
% Found (((eq_ref fofType) (x0 (g x1))) P) as proof of ((P (x0 (g x1)))->(P (b x1)))
% Found (((eq_ref fofType) (x0 (g x1))) P) as proof of ((P (x0 (g x1)))->(P (b x1)))
% Found (fun (P:(fofType->Prop))=> (((eq_ref fofType) (x0 (g x1))) P)) as proof of ((P (x0 (g x1)))->(P (b x1)))
% Found eq_ref000:=(eq_ref00 P):((P (x0 (g x1)))->(P (x0 (g x1))))
% Found (eq_ref00 P) as proof of ((P (x0 (g x1)))->(P (b x1)))
% Found ((eq_ref0 (x0 (g x1))) P) as proof of ((P (x0 (g x1)))->(P (b x1)))
% Found (((eq_ref fofType) (x0 (g x1))) P) as proof of ((P (x0 (g x1)))->(P (b x1)))
% Found (((eq_ref fofType) (x0 (g x1))) P) as proof of ((P (x0 (g x1)))->(P (b x1)))
% Found (fun (P:(fofType->Prop))=> (((eq_ref fofType) (x0 (g x1))) P)) as proof of ((P (x0 (g x1)))->(P (b x1)))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found ((eq_sym10 (b x1)) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found (((eq_sym1 (x0 (g x1))) (b x1)) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) (b x1)) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found ((eq_sym10 (b x1)) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found (((eq_sym1 (x0 (g x1))) (b x1)) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) (b x1)) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found ((eq_sym10 x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found (((eq_sym1 (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found ((eq_sym10 x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found (((eq_sym1 (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((eq_sym10 x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((eq_sym1 (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((eq_sym10 x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((eq_sym1 (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((eq_sym10 x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((eq_sym1 (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((eq_sym10 x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((eq_sym1 (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found (x20 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((x2 (b x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found (((x (x0 (g x1))) (b x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found (x20 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((x2 (b x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found (((x (x0 (g x1))) (b x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym010 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym01 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x20 (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((x2 (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (eq_sym000 (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found ((eq_sym00 (x0 (g x1))) (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found (((eq_sym0 x1) (x0 (g x1))) (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found ((((eq_sym fofType) x1) (x0 (g x1))) (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found ((((eq_sym fofType) x1) (x0 (g x1))) (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym010 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym01 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x20 (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((x2 (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (eq_sym000 (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found ((eq_sym00 (x0 (g x1))) (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found (((eq_sym0 x1) (x0 (g x1))) (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found ((((eq_sym fofType) x1) (x0 (g x1))) (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found ((((eq_sym fofType) x1) (x0 (g x1))) (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym010 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym01 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x20 (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((x2 (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (eq_sym000 (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_sym00 (x0 (g x1))) (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (((eq_sym0 x1) (x0 (g x1))) (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((((eq_sym fofType) x1) (x0 (g x1))) (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym010 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym01 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x20 (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((x2 (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (eq_sym000 (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_sym00 (x0 (g x1))) (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (((eq_sym0 x1) (x0 (g x1))) (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((((eq_sym fofType) x1) (x0 (g x1))) (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g (b x1))) (g (x0 (g x1))))
% Found ((eq_sym10 (g (b x1))) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g (b x1))) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g (b x1))) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g (b x1))) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g (b x1))) (g (x0 (g x1))))
% Found (x20 ((((eq_sym fofType) (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found ((x2 (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found (((x (b x1)) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g (b x1))) (g (x0 (g x1))))
% Found ((eq_sym10 (g (b x1))) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g (b x1))) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g (b x1))) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g (b x1))) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g (b x1))) (g (x0 (g x1))))
% Found (x20 ((((eq_sym fofType) (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found ((x2 (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found (((x (b x1)) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym10 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x20 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found ((x2 (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym10 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x20 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found ((x2 (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym10 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x20 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((x2 (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym10 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x20 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((x2 (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym10 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x20 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((x2 (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym10 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x20 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((x2 (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eta_expansion0000:=(eta_expansion000 P):((P (fun (Xx:fofType)=> (x0 (g Xx))))->(P (fun (x:fofType)=> (x0 (g x)))))
% Found (eta_expansion000 P) as proof of (P0 (fun (Xx:fofType)=> (x0 (g Xx))))
% Found ((eta_expansion00 (fun (Xx:fofType)=> (x0 (g Xx)))) P) as proof of (P0 (fun (Xx:fofType)=> (x0 (g Xx))))
% Found (((eta_expansion0 fofType) (fun (Xx:fofType)=> (x0 (g Xx)))) P) as proof of (P0 (fun (Xx:fofType)=> (x0 (g Xx))))
% Found ((((eta_expansion fofType) fofType) (fun (Xx:fofType)=> (x0 (g Xx)))) P) as proof of (P0 (fun (Xx:fofType)=> (x0 (g Xx))))
% Found ((((eta_expansion fofType) fofType) (fun (Xx:fofType)=> (x0 (g Xx)))) P) as proof of (P0 (fun (Xx:fofType)=> (x0 (g Xx))))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (Xx:fofType)=> (x0 (g Xx))))->(P (fun (x:fofType)=> (x0 (g x)))))
% Found (eta_expansion_dep000 P) as proof of (P0 (fun (Xx:fofType)=> (x0 (g Xx))))
% Found ((eta_expansion_dep00 (fun (Xx:fofType)=> (x0 (g Xx)))) P) as proof of (P0 (fun (Xx:fofType)=> (x0 (g Xx))))
% Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) P) as proof of (P0 (fun (Xx:fofType)=> (x0 (g Xx))))
% Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) P) as proof of (P0 (fun (Xx:fofType)=> (x0 (g Xx))))
% Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) P) as proof of (P0 (fun (Xx:fofType)=> (x0 (g Xx))))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (Xx:fofType)=> (x0 (g Xx))))->(P (fun (x:fofType)=> (x0 (g x)))))
% Found (eta_expansion_dep000 P) as proof of (P0 (fun (Xx:fofType)=> (x0 (g Xx))))
% Found ((eta_expansion_dep00 (fun (Xx:fofType)=> (x0 (g Xx)))) P) as proof of (P0 (fun (Xx:fofType)=> (x0 (g Xx))))
% Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) P) as proof of (P0 (fun (Xx:fofType)=> (x0 (g Xx))))
% Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) P) as proof of (P0 (fun (Xx:fofType)=> (x0 (g Xx))))
% Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) P) as proof of (P0 (fun (Xx:fofType)=> (x0 (g Xx))))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found eq_ref000:=(eq_ref00 P1):((P1 (x0 (g x1)))->(P1 (x0 (g x1))))
% Found (eq_ref00 P1) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found ((eq_ref0 (x0 (g x1))) P1) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found (((eq_ref fofType) (x0 (g x1))) P1) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found (((eq_ref fofType) (x0 (g x1))) P1) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found (fun (P1:(fofType->Prop))=> (((eq_ref fofType) (x0 (g x1))) P1)) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found (fun (P1:(fofType->Prop))=> (((eq_ref fofType) (x0 (g x1))) P1)) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found eq_ref000:=(eq_ref00 P1):((P1 (x0 (g x1)))->(P1 (x0 (g x1))))
% Found (eq_ref00 P1) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found ((eq_ref0 (x0 (g x1))) P1) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found (((eq_ref fofType) (x0 (g x1))) P1) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found (((eq_ref fofType) (x0 (g x1))) P1) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found (fun (P1:(fofType->Prop))=> (((eq_ref fofType) (x0 (g x1))) P1)) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found (fun (P1:(fofType->Prop))=> (((eq_ref fofType) (x0 (g x1))) P1)) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found eq_ref000:=(eq_ref00 P1):((P1 (x0 (g x1)))->(P1 (x0 (g x1))))
% Found (eq_ref00 P1) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found ((eq_ref0 (x0 (g x1))) P1) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found (((eq_ref fofType) (x0 (g x1))) P1) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found (((eq_ref fofType) (x0 (g x1))) P1) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found (fun (P1:(fofType->Prop))=> (((eq_ref fofType) (x0 (g x1))) P1)) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found (fun (P1:(fofType->Prop))=> (((eq_ref fofType) (x0 (g x1))) P1)) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found eq_ref000:=(eq_ref00 P1):((P1 (x0 (g x1)))->(P1 (x0 (g x1))))
% Found (eq_ref00 P1) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found ((eq_ref0 (x0 (g x1))) P1) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found (((eq_ref fofType) (x0 (g x1))) P1) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found (((eq_ref fofType) (x0 (g x1))) P1) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found (fun (P1:(fofType->Prop))=> (((eq_ref fofType) (x0 (g x1))) P1)) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found (fun (P1:(fofType->Prop))=> (((eq_ref fofType) (x0 (g x1))) P1)) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found eq_ref000:=(eq_ref00 P1):((P1 (x0 (g x1)))->(P1 (x0 (g x1))))
% Found (eq_ref00 P1) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found ((eq_ref0 (x0 (g x1))) P1) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found (((eq_ref fofType) (x0 (g x1))) P1) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found (((eq_ref fofType) (x0 (g x1))) P1) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found (fun (P1:(fofType->Prop))=> (((eq_ref fofType) (x0 (g x1))) P1)) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found eq_ref000:=(eq_ref00 P1):((P1 (x0 (g x1)))->(P1 (x0 (g x1))))
% Found (eq_ref00 P1) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found ((eq_ref0 (x0 (g x1))) P1) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found (((eq_ref fofType) (x0 (g x1))) P1) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found (((eq_ref fofType) (x0 (g x1))) P1) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found (fun (P1:(fofType->Prop))=> (((eq_ref fofType) (x0 (g x1))) P1)) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found eq_ref000:=(eq_ref00 P1):((P1 (x0 (g x1)))->(P1 (x0 (g x1))))
% Found (eq_ref00 P1) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found ((eq_ref0 (x0 (g x1))) P1) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found (((eq_ref fofType) (x0 (g x1))) P1) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found (((eq_ref fofType) (x0 (g x1))) P1) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found (fun (P1:(fofType->Prop))=> (((eq_ref fofType) (x0 (g x1))) P1)) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found eq_ref000:=(eq_ref00 P1):((P1 (x0 (g x1)))->(P1 (x0 (g x1))))
% Found (eq_ref00 P1) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found ((eq_ref0 (x0 (g x1))) P1) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found (((eq_ref fofType) (x0 (g x1))) P1) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found (((eq_ref fofType) (x0 (g x1))) P1) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found (fun (P1:(fofType->Prop))=> (((eq_ref fofType) (x0 (g x1))) P1)) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found eta_expansion000:=(eta_expansion00 a):(((eq ((fofType->fofType)->Prop)) a) (fun (x:(fofType->fofType))=> (a x)))
% Found (eta_expansion00 a) as proof of (((eq ((fofType->fofType)->Prop)) a) b)
% Found ((eta_expansion0 Prop) a) as proof of (((eq ((fofType->fofType)->Prop)) a) b)
% Found (((eta_expansion (fofType->fofType)) Prop) a) as proof of (((eq ((fofType->fofType)->Prop)) a) b)
% Found (((eta_expansion (fofType->fofType)) Prop) a) as proof of (((eq ((fofType->fofType)->Prop)) a) b)
% Found (((eta_expansion (fofType->fofType)) Prop) a) as proof of (((eq ((fofType->fofType)->Prop)) a) b)
% Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq ((fofType->fofType)->Prop)) b) (fun (x:(fofType->fofType))=> (b x)))
% Found (eta_expansion_dep00 b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (Xh:(fofType->fofType))=> (((eq (fofType->fofType)) (fun (Xx:fofType)=> (Xh (g Xx)))) (fun (Xx:fofType)=> Xx))))
% Found ((eta_expansion_dep0 (fun (x1:(fofType->fofType))=> Prop)) b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (Xh:(fofType->fofType))=> (((eq (fofType->fofType)) (fun (Xx:fofType)=> (Xh (g Xx)))) (fun (Xx:fofType)=> Xx))))
% Found (((eta_expansion_dep (fofType->fofType)) (fun (x1:(fofType->fofType))=> Prop)) b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (Xh:(fofType->fofType))=> (((eq (fofType->fofType)) (fun (Xx:fofType)=> (Xh (g Xx)))) (fun (Xx:fofType)=> Xx))))
% Found (((eta_expansion_dep (fofType->fofType)) (fun (x1:(fofType->fofType))=> Prop)) b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (Xh:(fofType->fofType))=> (((eq (fofType->fofType)) (fun (Xx:fofType)=> (Xh (g Xx)))) (fun (Xx:fofType)=> Xx))))
% Found (((eta_expansion_dep (fofType->fofType)) (fun (x1:(fofType->fofType))=> Prop)) b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (Xh:(fofType->fofType))=> (((eq (fofType->fofType)) (fun (Xx:fofType)=> (Xh (g Xx)))) (fun (Xx:fofType)=> Xx))))
% Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->fofType)->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (Xh:(fofType->fofType))=> (((eq (fofType->fofType)) (fun (Xx:fofType)=> (Xh (g Xx)))) (fun (Xx:fofType)=> Xx))))
% Found ((eq_ref ((fofType->fofType)->Prop)) b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (Xh:(fofType->fofType))=> (((eq (fofType->fofType)) (fun (Xx:fofType)=> (Xh (g Xx)))) (fun (Xx:fofType)=> Xx))))
% Found ((eq_ref ((fofType->fofType)->Prop)) b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (Xh:(fofType->fofType))=> (((eq (fofType->fofType)) (fun (Xx:fofType)=> (Xh (g Xx)))) (fun (Xx:fofType)=> Xx))))
% Found ((eq_ref ((fofType->fofType)->Prop)) b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (Xh:(fofType->fofType))=> (((eq (fofType->fofType)) (fun (Xx:fofType)=> (Xh (g Xx)))) (fun (Xx:fofType)=> Xx))))
% Found x1:(P (fun (Xx:fofType)=> (x0 (g Xx))))
% Instantiate: b:=(fun (Xx:fofType)=> (x0 (g Xx))):(fofType->fofType)
% Found x1 as proof of (P0 b)
% Found eta_expansion000:=(eta_expansion00 (fun (Xx:fofType)=> Xx)):(((eq (fofType->fofType)) (fun (Xx:fofType)=> Xx)) (fun (x:fofType)=> x))
% Found (eta_expansion00 (fun (Xx:fofType)=> Xx)) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> Xx)) b)
% Found ((eta_expansion0 fofType) (fun (Xx:fofType)=> Xx)) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> Xx)) b)
% Found (((eta_expansion fofType) fofType) (fun (Xx:fofType)=> Xx)) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> Xx)) b)
% Found (((eta_expansion fofType) fofType) (fun (Xx:fofType)=> Xx)) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> Xx)) b)
% Found (((eta_expansion fofType) fofType) (fun (Xx:fofType)=> Xx)) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> Xx)) b)
% Found eq_ref00:=(eq_ref0 (fun (Xx:fofType)=> (x0 (g Xx)))):(((eq (fofType->fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) (fun (Xx:fofType)=> (x0 (g Xx))))
% Found (eq_ref0 (fun (Xx:fofType)=> (x0 (g Xx)))) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) b)
% Found ((eq_ref (fofType->fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) b)
% Found ((eq_ref (fofType->fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) b)
% Found ((eq_ref (fofType->fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq (fofType->fofType)) b) b)
% Found (eq_ref0 b) as proof of (((eq (fofType->fofType)) b) (fun (Xx:fofType)=> Xx))
% Found ((eq_ref (fofType->fofType)) b) as proof of (((eq (fofType->fofType)) b) (fun (Xx:fofType)=> Xx))
% Found ((eq_ref (fofType->fofType)) b) as proof of (((eq (fofType->fofType)) b) (fun (Xx:fofType)=> Xx))
% Found ((eq_ref (fofType->fofType)) b) as proof of (((eq (fofType->fofType)) b) (fun (Xx:fofType)=> Xx))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (x200 ((eq_ref fofType) (g (x0 (g x1))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found (x200 ((eq_ref fofType) (g (x0 (g x1))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((fun (x3:(((eq fofType) (g (x0 (g x1)))) (g x1)))=> ((x20 x3) P)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((fun (x3:(((eq fofType) (g (x0 (g x1)))) (g x1)))=> (((x2 x1) x3) P)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((fun (x3:(((eq fofType) (g (x0 (g x1)))) (g x1)))=> ((((x (x0 (g x1))) x1) x3) P)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found (fun (P:(fofType->Prop))=> ((fun (x3:(((eq fofType) (g (x0 (g x1)))) (g x1)))=> ((((x (x0 (g x1))) x1) x3) P)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found (fun (P:(fofType->Prop))=> ((fun (x3:(((eq fofType) (g (x0 (g x1)))) (g x1)))=> ((((x (x0 (g x1))) x1) x3) P)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (x200 ((eq_ref fofType) (g (x0 (g x1))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found (x200 ((eq_ref fofType) (g (x0 (g x1))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((fun (x3:(((eq fofType) (g (x0 (g x1)))) (g x1)))=> ((x20 x3) P)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((fun (x3:(((eq fofType) (g (x0 (g x1)))) (g x1)))=> (((x2 x1) x3) P)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((fun (x3:(((eq fofType) (g (x0 (g x1)))) (g x1)))=> ((((x (x0 (g x1))) x1) x3) P)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found (fun (P:(fofType->Prop))=> ((fun (x3:(((eq fofType) (g (x0 (g x1)))) (g x1)))=> ((((x (x0 (g x1))) x1) x3) P)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found (fun (P:(fofType->Prop))=> ((fun (x3:(((eq fofType) (g (x0 (g x1)))) (g x1)))=> ((((x (x0 (g x1))) x1) x3) P)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (x20 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found ((x2 x1) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found (((x (x0 (g x1))) x1) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found (((x (x0 (g x1))) x1) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (x20 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found ((x2 x1) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found (((x (x0 (g x1))) x1) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found (((x (x0 (g x1))) x1) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (x20 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found ((x2 x1) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found (((x (x0 (g x1))) x1) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found (((x (x0 (g x1))) x1) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (x200 ((eq_ref fofType) (g (x0 (g x1))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found (x200 ((eq_ref fofType) (g (x0 (g x1))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((fun (x3:(((eq fofType) (g (x0 (g x1)))) (g x1)))=> ((x20 x3) P)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((fun (x3:(((eq fofType) (g (x0 (g x1)))) (g x1)))=> (((x2 x1) x3) P)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((fun (x3:(((eq fofType) (g (x0 (g x1)))) (g x1)))=> ((((x (x0 (g x1))) x1) x3) P)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found (fun (P:(fofType->Prop))=> ((fun (x3:(((eq fofType) (g (x0 (g x1)))) (g x1)))=> ((((x (x0 (g x1))) x1) x3) P)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (x20 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found ((x2 x1) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found (((x (x0 (g x1))) x1) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found (((x (x0 (g x1))) x1) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (x200 ((eq_ref fofType) (g (x0 (g x1))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found (x200 ((eq_ref fofType) (g (x0 (g x1))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((fun (x3:(((eq fofType) (g (x0 (g x1)))) (g x1)))=> ((x20 x3) P)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((fun (x3:(((eq fofType) (g (x0 (g x1)))) (g x1)))=> (((x2 x1) x3) P)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((fun (x3:(((eq fofType) (g (x0 (g x1)))) (g x1)))=> ((((x (x0 (g x1))) x1) x3) P)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found (fun (P:(fofType->Prop))=> ((fun (x3:(((eq fofType) (g (x0 (g x1)))) (g x1)))=> ((((x (x0 (g x1))) x1) x3) P)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (x20 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((x2 x1) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (((x (x0 (g x1))) x1) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (x20 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((x2 x1) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (((x (x0 (g x1))) x1) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (x20 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((x2 x1) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (((x (x0 (g x1))) x1) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (x20 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((x2 x1) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (((x (x0 (g x1))) x1) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found eq_ref00:=(eq_ref0 (x0 (g x2))):(((eq fofType) (x0 (g x2))) (x0 (g x2)))
% Found (eq_ref0 (x0 (g x2))) as proof of (((eq fofType) (x0 (g x2))) x1)
% Found ((eq_ref fofType) (x0 (g x2))) as proof of (((eq fofType) (x0 (g x2))) x1)
% Found (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2)))) as proof of (((eq fofType) (x0 (g x2))) x1)
% Found (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2)))) as proof of (forall (x:fofType), (((eq fofType) (x0 (g x))) x1))
% Found (functional_extensionality00010 (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found (functional_extensionality00010 (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> ((functional_extensionality0001 x2) (fun (x3:(fofType->fofType))=> (P (x0 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> (((functional_extensionality000 (fun (x4:fofType)=> x1)) x2) (fun (x3:(fofType->fofType))=> (P (x0 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> (((functional_extensionality000 (fun (x4:fofType)=> x1)) x2) (fun (x3:(fofType->fofType))=> (P (x0 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found (fun (P:(fofType->Prop))=> ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> (((functional_extensionality000 (fun (x4:fofType)=> x1)) x2) (fun (x3:(fofType->fofType))=> (P (x0 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2)))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found eq_ref00:=(eq_ref0 (x0 (g x2))):(((eq fofType) (x0 (g x2))) (x0 (g x2)))
% Found (eq_ref0 (x0 (g x2))) as proof of (((eq fofType) (x0 (g x2))) x1)
% Found ((eq_ref fofType) (x0 (g x2))) as proof of (((eq fofType) (x0 (g x2))) x1)
% Found (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2)))) as proof of (((eq fofType) (x0 (g x2))) x1)
% Found (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2)))) as proof of (forall (x:fofType), (((eq fofType) (x0 (g x))) x1))
% Found (functional_extensionality00010 (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found (functional_extensionality00010 (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> ((functional_extensionality0001 x2) (fun (x3:(fofType->fofType))=> (P (x3 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> (((functional_extensionality000 (fun (x4:fofType)=> x1)) x2) (fun (x3:(fofType->fofType))=> (P (x3 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> (((functional_extensionality000 (fun (x4:fofType)=> x1)) x2) (fun (x3:(fofType->fofType))=> (P (x3 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found (fun (P:(fofType->Prop))=> ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> (((functional_extensionality000 (fun (x4:fofType)=> x1)) x2) (fun (x3:(fofType->fofType))=> (P (x3 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2)))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found eq_ref00:=(eq_ref0 (x0 (g x2))):(((eq fofType) (x0 (g x2))) (x0 (g x2)))
% Found (eq_ref0 (x0 (g x2))) as proof of (((eq fofType) (x0 (g x2))) x1)
% Found ((eq_ref fofType) (x0 (g x2))) as proof of (((eq fofType) (x0 (g x2))) x1)
% Found (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2)))) as proof of (((eq fofType) (x0 (g x2))) x1)
% Found (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2)))) as proof of (forall (x:fofType), (((eq fofType) (x0 (g x))) x1))
% Found (functional_extensionality_dep00010 (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found (functional_extensionality_dep00010 (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> ((functional_extensionality_dep0001 x2) (fun (x3:(fofType->fofType))=> (P (x3 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> (((functional_extensionality_dep000 (fun (x4:fofType)=> x1)) x2) (fun (x3:(fofType->fofType))=> (P (x3 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> (((functional_extensionality_dep000 (fun (x4:fofType)=> x1)) x2) (fun (x3:(fofType->fofType))=> (P (x3 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found (fun (P:(fofType->Prop))=> ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> (((functional_extensionality_dep000 (fun (x4:fofType)=> x1)) x2) (fun (x3:(fofType->fofType))=> (P (x3 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2)))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found eq_ref00:=(eq_ref0 (x0 (g x2))):(((eq fofType) (x0 (g x2))) (x0 (g x2)))
% Found (eq_ref0 (x0 (g x2))) as proof of (((eq fofType) (x0 (g x2))) x1)
% Found ((eq_ref fofType) (x0 (g x2))) as proof of (((eq fofType) (x0 (g x2))) x1)
% Found (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2)))) as proof of (((eq fofType) (x0 (g x2))) x1)
% Found (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2)))) as proof of (forall (x:fofType), (((eq fofType) (x0 (g x))) x1))
% Found (functional_extensionality_dep00010 (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found (functional_extensionality_dep00010 (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> ((functional_extensionality_dep0001 x2) (fun (x3:(fofType->fofType))=> (P (x0 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> (((functional_extensionality_dep000 (fun (x4:fofType)=> x1)) x2) (fun (x3:(fofType->fofType))=> (P (x0 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> (((functional_extensionality_dep000 (fun (x4:fofType)=> x1)) x2) (fun (x3:(fofType->fofType))=> (P (x0 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found (fun (P:(fofType->Prop))=> ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> (((functional_extensionality_dep000 (fun (x4:fofType)=> x1)) x2) (fun (x3:(fofType->fofType))=> (P (x0 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2)))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found x1:(P (fun (Xx:fofType)=> (x0 (g Xx))))
% Instantiate: f:=(fun (Xx:fofType)=> (x0 (g Xx))):(fofType->fofType)
% Found x1 as proof of (P0 f)
% Found eq_ref00:=(eq_ref0 (f x2)):(((eq fofType) (f x2)) (f x2))
% Found (eq_ref0 (f x2)) as proof of (((eq fofType) (f x2)) x2)
% Found ((eq_ref fofType) (f x2)) as proof of (((eq fofType) (f x2)) x2)
% Found ((eq_ref fofType) (f x2)) as proof of (((eq fofType) (f x2)) x2)
% Found (fun (x2:fofType)=> ((eq_ref fofType) (f x2))) as proof of (((eq fofType) (f x2)) x2)
% Found (fun (x2:fofType)=> ((eq_ref fofType) (f x2))) as proof of (forall (x:fofType), (((eq fofType) (f x)) x))
% Found x1:(P (fun (Xx:fofType)=> (x0 (g Xx))))
% Instantiate: f:=(fun (Xx:fofType)=> (x0 (g Xx))):(fofType->fofType)
% Found x1 as proof of (P0 f)
% Found eq_ref00:=(eq_ref0 (f x2)):(((eq fofType) (f x2)) (f x2))
% Found (eq_ref0 (f x2)) as proof of (((eq fofType) (f x2)) x2)
% Found ((eq_ref fofType) (f x2)) as proof of (((eq fofType) (f x2)) x2)
% Found ((eq_ref fofType) (f x2)) as proof of (((eq fofType) (f x2)) x2)
% Found (fun (x2:fofType)=> ((eq_ref fofType) (f x2))) as proof of (((eq fofType) (f x2)) x2)
% Found (fun (x2:fofType)=> ((eq_ref fofType) (f x2))) as proof of (forall (x:fofType), (((eq fofType) (f x)) x))
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xx:fofType)=> (x0 (g Xx)))):(((eq (fofType->fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) (fun (x:fofType)=> (x0 (g x))))
% Found (eta_expansion_dep00 (fun (Xx:fofType)=> (x0 (g Xx)))) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) b)
% Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) b)
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) b)
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) b)
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) b)
% Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->fofType)) b) (fun (x:fofType)=> (b x)))
% Found (eta_expansion00 b) as proof of (((eq (fofType->fofType)) b) (fun (Xx:fofType)=> Xx))
% Found ((eta_expansion0 fofType) b) as proof of (((eq (fofType->fofType)) b) (fun (Xx:fofType)=> Xx))
% Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (fun (Xx:fofType)=> Xx))
% Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (fun (Xx:fofType)=> Xx))
% Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (fun (Xx:fofType)=> Xx))
% Found eta_expansion0000:=(eta_expansion000 P):((P (fun (Xx:fofType)=> Xx))->(P (fun (x:fofType)=> x)))
% Found (eta_expansion000 P) as proof of (P0 (fun (Xx:fofType)=> Xx))
% Found ((eta_expansion00 (fun (Xx:fofType)=> Xx)) P) as proof of (P0 (fun (Xx:fofType)=> Xx))
% Found (((eta_expansion0 fofType) (fun (Xx:fofType)=> Xx)) P) as proof of (P0 (fun (Xx:fofType)=> Xx))
% Found ((((eta_expansion fofType) fofType) (fun (Xx:fofType)=> Xx)) P) as proof of (P0 (fun (Xx:fofType)=> Xx))
% Found ((((eta_expansion fofType) fofType) (fun (Xx:fofType)=> Xx)) P) as proof of (P0 (fun (Xx:fofType)=> Xx))
% Found eta_expansion0000:=(eta_expansion000 P):((P (fun (Xx:fofType)=> Xx))->(P (fun (x:fofType)=> x)))
% Found (eta_expansion000 P) as proof of (P0 (fun (Xx:fofType)=> Xx))
% Found ((eta_expansion00 (fun (Xx:fofType)=> Xx)) P) as proof of (P0 (fun (Xx:fofType)=> Xx))
% Found (((eta_expansion0 fofType) (fun (Xx:fofType)=> Xx)) P) as proof of (P0 (fun (Xx:fofType)=> Xx))
% Found ((((eta_expansion fofType) fofType) (fun (Xx:fofType)=> Xx)) P) as proof of (P0 (fun (Xx:fofType)=> Xx))
% Found ((((eta_expansion fofType) fofType) (fun (Xx:fofType)=> Xx)) P) as proof of (P0 (fun (Xx:fofType)=> Xx))
% Found eq_ref00:=(eq_ref0 (x0 (g x2))):(((eq fofType) (x0 (g x2))) (x0 (g x2)))
% Found (eq_ref0 (x0 (g x2))) as proof of (((eq fofType) (x0 (g x2))) x1)
% Found ((eq_ref fofType) (x0 (g x2))) as proof of (((eq fofType) (x0 (g x2))) x1)
% Found (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2)))) as proof of (((eq fofType) (x0 (g x2))) x1)
% Found (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2)))) as proof of (forall (x:fofType), (((eq fofType) (x0 (g x))) x1))
% Found (functional_extensionality00010 (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found (functional_extensionality00010 (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> ((functional_extensionality0001 x2) (fun (x3:(fofType->fofType))=> (P (x0 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> (((functional_extensionality000 (fun (x4:fofType)=> x1)) x2) (fun (x3:(fofType->fofType))=> (P (x0 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> (((functional_extensionality000 (fun (x4:fofType)=> x1)) x2) (fun (x3:(fofType->fofType))=> (P (x0 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found (fun (P:(fofType->Prop))=> ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> (((functional_extensionality000 (fun (x4:fofType)=> x1)) x2) (fun (x3:(fofType->fofType))=> (P (x0 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2)))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found (fun (P:(fofType->Prop))=> ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> (((functional_extensionality000 (fun (x4:fofType)=> x1)) x2) (fun (x3:(fofType->fofType))=> (P (x0 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2)))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found eq_ref00:=(eq_ref0 (x0 (g x2))):(((eq fofType) (x0 (g x2))) (x0 (g x2)))
% Found (eq_ref0 (x0 (g x2))) as proof of (((eq fofType) (x0 (g x2))) x1)
% Found ((eq_ref fofType) (x0 (g x2))) as proof of (((eq fofType) (x0 (g x2))) x1)
% Found (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2)))) as proof of (((eq fofType) (x0 (g x2))) x1)
% Found (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2)))) as proof of (forall (x:fofType), (((eq fofType) (x0 (g x))) x1))
% Found (functional_extensionality00010 (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found (functional_extensionality00010 (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> ((functional_extensionality0001 x2) (fun (x3:(fofType->fofType))=> (P (x3 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> (((functional_extensionality000 (fun (x4:fofType)=> x1)) x2) (fun (x3:(fofType->fofType))=> (P (x3 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> (((functional_extensionality000 (fun (x4:fofType)=> x1)) x2) (fun (x3:(fofType->fofType))=> (P (x3 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found (fun (P:(fofType->Prop))=> ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> (((functional_extensionality000 (fun (x4:fofType)=> x1)) x2) (fun (x3:(fofType->fofType))=> (P (x3 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2)))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found (fun (P:(fofType->Prop))=> ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> (((functional_extensionality000 (fun (x4:fofType)=> x1)) x2) (fun (x3:(fofType->fofType))=> (P (x3 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2)))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found eta_expansion0000:=(eta_expansion000 P):((P (fun (Xx:fofType)=> Xx))->(P (fun (x:fofType)=> x)))
% Found (eta_expansion000 P) as proof of (P0 (fun (Xx:fofType)=> Xx))
% Found ((eta_expansion00 (fun (Xx:fofType)=> Xx)) P) as proof of (P0 (fun (Xx:fofType)=> Xx))
% Found (((eta_expansion0 fofType) (fun (Xx:fofType)=> Xx)) P) as proof of (P0 (fun (Xx:fofType)=> Xx))
% Found ((((eta_expansion fofType) fofType) (fun (Xx:fofType)=> Xx)) P) as proof of (P0 (fun (Xx:fofType)=> Xx))
% Found ((((eta_expansion fofType) fofType) (fun (Xx:fofType)=> Xx)) P) as proof of (P0 (fun (Xx:fofType)=> Xx))
% Found eq_ref00:=(eq_ref0 (x0 (g x2))):(((eq fofType) (x0 (g x2))) (x0 (g x2)))
% Found (eq_ref0 (x0 (g x2))) as proof of (((eq fofType) (x0 (g x2))) x1)
% Found ((eq_ref fofType) (x0 (g x2))) as proof of (((eq fofType) (x0 (g x2))) x1)
% Found (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2)))) as proof of (((eq fofType) (x0 (g x2))) x1)
% Found (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2)))) as proof of (forall (x:fofType), (((eq fofType) (x0 (g x))) x1))
% Found (functional_extensionality_dep00010 (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found (functional_extensionality_dep00010 (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> ((functional_extensionality_dep0001 x2) (fun (x3:(fofType->fofType))=> (P (x3 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> (((functional_extensionality_dep000 (fun (x4:fofType)=> x1)) x2) (fun (x3:(fofType->fofType))=> (P (x3 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> (((functional_extensionality_dep000 (fun (x4:fofType)=> x1)) x2) (fun (x3:(fofType->fofType))=> (P (x3 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found (fun (P:(fofType->Prop))=> ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> (((functional_extensionality_dep000 (fun (x4:fofType)=> x1)) x2) (fun (x3:(fofType->fofType))=> (P (x3 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2)))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found (fun (P:(fofType->Prop))=> ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> (((functional_extensionality_dep000 (fun (x4:fofType)=> x1)) x2) (fun (x3:(fofType->fofType))=> (P (x3 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2)))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found eq_ref00:=(eq_ref0 (x0 (g x2))):(((eq fofType) (x0 (g x2))) (x0 (g x2)))
% Found (eq_ref0 (x0 (g x2))) as proof of (((eq fofType) (x0 (g x2))) x1)
% Found ((eq_ref fofType) (x0 (g x2))) as proof of (((eq fofType) (x0 (g x2))) x1)
% Found (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2)))) as proof of (((eq fofType) (x0 (g x2))) x1)
% Found (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2)))) as proof of (forall (x:fofType), (((eq fofType) (x0 (g x))) x1))
% Found (functional_extensionality_dep00010 (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found (functional_extensionality_dep00010 (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> ((functional_extensionality_dep0001 x2) (fun (x3:(fofType->fofType))=> (P (x0 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> (((functional_extensionality_dep000 (fun (x4:fofType)=> x1)) x2) (fun (x3:(fofType->fofType))=> (P (x0 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> (((functional_extensionality_dep000 (fun (x4:fofType)=> x1)) x2) (fun (x3:(fofType->fofType))=> (P (x0 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found (fun (P:(fofType->Prop))=> ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> (((functional_extensionality_dep000 (fun (x4:fofType)=> x1)) x2) (fun (x3:(fofType->fofType))=> (P (x0 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2)))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found (fun (P:(fofType->Prop))=> ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> (((functional_extensionality_dep000 (fun (x4:fofType)=> x1)) x2) (fun (x3:(fofType->fofType))=> (P (x0 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2)))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found eta_expansion0000:=(eta_expansion000 P):((P (fun (Xx:fofType)=> Xx))->(P (fun (x:fofType)=> x)))
% Found (eta_expansion000 P) as proof of (P0 (fun (Xx:fofType)=> Xx))
% Found ((eta_expansion00 (fun (Xx:fofType)=> Xx)) P) as proof of (P0 (fun (Xx:fofType)=> Xx))
% Found (((eta_expansion0 fofType) (fun (Xx:fofType)=> Xx)) P) as proof of (P0 (fun (Xx:fofType)=> Xx))
% Found ((((eta_expansion fofType) fofType) (fun (Xx:fofType)=> Xx)) P) as proof of (P0 (fun (Xx:fofType)=> Xx))
% Found ((((eta_expansion fofType) fofType) (fun (Xx:fofType)=> Xx)) P) as proof of (P0 (fun (Xx:fofType)=> Xx))
% Found eta_expansion0000:=(eta_expansion000 P):((P (fun (Xx:fofType)=> (x0 (g Xx))))->(P (fun (x:fofType)=> (x0 (g x)))))
% Found (eta_expansion000 P) as proof of (P0 (fun (Xx:fofType)=> (x0 (g Xx))))
% Found ((eta_expansion00 (fun (Xx:fofType)=> (x0 (g Xx)))) P) as proof of (P0 (fun (Xx:fofType)=> (x0 (g Xx))))
% Found (((eta_expansion0 fofType) (fun (Xx:fofType)=> (x0 (g Xx)))) P) as proof of (P0 (fun (Xx:fofType)=> (x0 (g Xx))))
% Found ((((eta_expansion fofType) fofType) (fun (Xx:fofType)=> (x0 (g Xx)))) P) as proof of (P0 (fun (Xx:fofType)=> (x0 (g Xx))))
% Found ((((eta_expansion fofType) fofType) (fun (Xx:fofType)=> (x0 (g Xx)))) P) as proof of (P0 (fun (Xx:fofType)=> (x0 (g Xx))))
% Found eta_expansion000:=(eta_expansion00 (fun (Xx:fofType)=> (x0 (g Xx)))):(((eq (fofType->fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) (fun (x:fofType)=> (x0 (g x))))
% Found (eta_expansion00 (fun (Xx:fofType)=> (x0 (g Xx)))) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) b)
% Found ((eta_expansion0 fofType) (fun (Xx:fofType)=> (x0 (g Xx)))) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) b)
% Found (((eta_expansion fofType) fofType) (fun (Xx:fofType)=> (x0 (g Xx)))) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) b)
% Found (((eta_expansion fofType) fofType) (fun (Xx:fofType)=> (x0 (g Xx)))) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) b)
% Found (((eta_expansion fofType) fofType) (fun (Xx:fofType)=> (x0 (g Xx)))) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) b)
% Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->fofType)) b) (fun (x:fofType)=> (b x)))
% Found (eta_expansion00 b) as proof of (((eq (fofType->fofType)) b) (fun (Xx:fofType)=> Xx))
% Found ((eta_expansion0 fofType) b) as proof of (((eq (fofType->fofType)) b) (fun (Xx:fofType)=> Xx))
% Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (fun (Xx:fofType)=> Xx))
% Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (fun (Xx:fofType)=> Xx))
% Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (fun (Xx:fofType)=> Xx))
% Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->fofType)) b) (fun (x:fofType)=> (b x)))
% Found (eta_expansion00 b) as proof of (P b)
% Found ((eta_expansion0 fofType) b) as proof of (P b)
% Found (((eta_expansion fofType) fofType) b) as proof of (P b)
% Found (((eta_expansion fofType) fofType) b) as proof of (P b)
% Found (((eta_expansion fofType) fofType) b) as proof of (P b)
% Found eta_expansion000:=(eta_expansion00 (fun (Xx:fofType)=> Xx)):(((eq (fofType->fofType)) (fun (Xx:fofType)=> Xx)) (fun (x:fofType)=> x))
% Found (eta_expansion00 (fun (Xx:fofType)=> Xx)) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> Xx)) b)
% Found ((eta_expansion0 fofType) (fun (Xx:fofType)=> Xx)) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> Xx)) b)
% Found (((eta_expansion fofType) fofType) (fun (Xx:fofType)=> Xx)) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> Xx)) b)
% Found (((eta_expansion fofType) fofType) (fun (Xx:fofType)=> Xx)) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> Xx)) b)
% Found (((eta_expansion fofType) fofType) (fun (Xx:fofType)=> Xx)) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> Xx)) b)
% Found x1:(P (fun (Xx:fofType)=> Xx))
% Instantiate: b:=(fun (Xx:fofType)=> Xx):(fofType->fofType)
% Found x1 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (fun (Xx:fofType)=> (x0 (g Xx)))):(((eq (fofType->fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) (fun (Xx:fofType)=> (x0 (g Xx))))
% Found (eq_ref0 (fun (Xx:fofType)=> (x0 (g Xx)))) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) b)
% Found ((eq_ref (fofType->fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) b)
% Found ((eq_ref (fofType->fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) b)
% Found ((eq_ref (fofType->fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) b)
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (x200 ((eq_ref fofType) (g (x0 (g x1))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found (x200 ((eq_ref fofType) (g (x0 (g x1))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found ((fun (x3:(((eq fofType) (g (x0 (g x1)))) (g x1)))=> ((x20 x3) P1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found ((fun (x3:(((eq fofType) (g (x0 (g x1)))) (g x1)))=> (((x2 x1) x3) P1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found ((fun (x3:(((eq fofType) (g (x0 (g x1)))) (g x1)))=> ((((x (x0 (g x1))) x1) x3) P1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found (fun (P1:(fofType->Prop))=> ((fun (x3:(((eq fofType) (g (x0 (g x1)))) (g x1)))=> ((((x (x0 (g x1))) x1) x3) P1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (x200 ((eq_ref fofType) (g (x0 (g x1))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found (x200 ((eq_ref fofType) (g (x0 (g x1))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found ((fun (x3:(((eq fofType) (g (x0 (g x1)))) (g x1)))=> ((x20 x3) P1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found ((fun (x3:(((eq fofType) (g (x0 (g x1)))) (g x1)))=> (((x2 x1) x3) P1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found ((fun (x3:(((eq fofType) (g (x0 (g x1)))) (g x1)))=> ((((x (x0 (g x1))) x1) x3) P1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found (fun (P1:(fofType->Prop))=> ((fun (x3:(((eq fofType) (g (x0 (g x1)))) (g x1)))=> ((((x (x0 (g x1))) x1) x3) P1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (x200 ((eq_ref fofType) (g (x0 (g x1))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found (x200 ((eq_ref fofType) (g (x0 (g x1))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found ((fun (x3:(((eq fofType) (g (x0 (g x1)))) (g x1)))=> ((x20 x3) P1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found ((fun (x3:(((eq fofType) (g (x0 (g x1)))) (g x1)))=> (((x2 x1) x3) P1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found ((fun (x3:(((eq fofType) (g (x0 (g x1)))) (g x1)))=> ((((x (x0 (g x1))) x1) x3) P1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found (fun (P1:(fofType->Prop))=> ((fun (x3:(((eq fofType) (g (x0 (g x1)))) (g x1)))=> ((((x (x0 (g x1))) x1) x3) P1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (x200 ((eq_ref fofType) (g (x0 (g x1))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found (x200 ((eq_ref fofType) (g (x0 (g x1))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found ((fun (x3:(((eq fofType) (g (x0 (g x1)))) (g x1)))=> ((x20 x3) P1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found ((fun (x3:(((eq fofType) (g (x0 (g x1)))) (g x1)))=> (((x2 x1) x3) P1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found ((fun (x3:(((eq fofType) (g (x0 (g x1)))) (g x1)))=> ((((x (x0 (g x1))) x1) x3) P1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found (fun (P1:(fofType->Prop))=> ((fun (x3:(((eq fofType) (g (x0 (g x1)))) (g x1)))=> ((((x (x0 (g x1))) x1) x3) P1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found eq_ref00:=(eq_ref0 (fun (Xx:fofType)=> Xx)):(((eq (fofType->fofType)) (fun (Xx:fofType)=> Xx)) (fun (Xx:fofType)=> Xx))
% Found (eq_ref0 (fun (Xx:fofType)=> Xx)) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> Xx)) b)
% Found ((eq_ref (fofType->fofType)) (fun (Xx:fofType)=> Xx)) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> Xx)) b)
% Found ((eq_ref (fofType->fofType)) (fun (Xx:fofType)=> Xx)) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> Xx)) b)
% Found ((eq_ref (fofType->fofType)) (fun (Xx:fofType)=> Xx)) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> Xx)) b)
% Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->fofType)) b) (fun (x:fofType)=> (b x)))
% Found (eta_expansion00 b) as proof of (((eq (fofType->fofType)) b) (fun (Xx:fofType)=> (x0 (g Xx))))
% Found ((eta_expansion0 fofType) b) as proof of (((eq (fofType->fofType)) b) (fun (Xx:fofType)=> (x0 (g Xx))))
% Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (fun (Xx:fofType)=> (x0 (g Xx))))
% Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (fun (Xx:fofType)=> (x0 (g Xx))))
% Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (fun (Xx:fofType)=> (x0 (g Xx))))
% Found eq_ref00:=(eq_ref0 (fun (Xx:fofType)=> Xx)):(((eq (fofType->fofType)) (fun (Xx:fofType)=> Xx)) (fun (Xx:fofType)=> Xx))
% Found (eq_ref0 (fun (Xx:fofType)=> Xx)) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> Xx)) b)
% Found ((eq_ref (fofType->fofType)) (fun (Xx:fofType)=> Xx)) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> Xx)) b)
% Found ((eq_ref (fofType->fofType)) (fun (Xx:fofType)=> Xx)) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> Xx)) b)
% Found ((eq_ref (fofType->fofType)) (fun (Xx:fofType)=> Xx)) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> Xx)) b)
% Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->fofType)) b) (fun (x:fofType)=> (b x)))
% Found (eta_expansion00 b) as proof of (((eq (fofType->fofType)) b) (fun (Xx:fofType)=> (x0 (g Xx))))
% Found ((eta_expansion0 fofType) b) as proof of (((eq (fofType->fofType)) b) (fun (Xx:fofType)=> (x0 (g Xx))))
% Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (fun (Xx:fofType)=> (x0 (g Xx))))
% Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (fun (Xx:fofType)=> (x0 (g Xx))))
% Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (fun (Xx:fofType)=> (x0 (g Xx))))
% Found x2:(P (x0 (g x1)))
% Instantiate: Xx:=(x0 (g x1)):fofType
% Found x2 as proof of (P0 Xx)
% Found eq_ref00:=(eq_ref0 (g Xx)):(((eq fofType) (g Xx)) (g Xx))
% Found (eq_ref0 (g Xx)) as proof of (((eq fofType) (g Xx)) (g x1))
% Found ((eq_ref fofType) (g Xx)) as proof of (((eq fofType) (g Xx)) (g x1))
% Found ((eq_ref fofType) (g Xx)) as proof of (((eq fofType) (g Xx)) (g x1))
% Found ((eq_ref fofType) (g Xx)) as proof of (((eq fofType) (g Xx)) (g x1))
% Found x2:(P (x0 (g x1)))
% Instantiate: Xx:=(x0 (g x1)):fofType
% Found x2 as proof of (P0 Xx)
% Found eq_ref00:=(eq_ref0 (g Xx)):(((eq fofType) (g Xx)) (g Xx))
% Found (eq_ref0 (g Xx)) as proof of (((eq fofType) (g Xx)) (g x1))
% Found ((eq_ref fofType) (g Xx)) as proof of (((eq fofType) (g Xx)) (g x1))
% Found ((eq_ref fofType) (g Xx)) as proof of (((eq fofType) (g Xx)) (g x1))
% Found ((eq_ref fofType) (g Xx)) as proof of (((eq fofType) (g Xx)) (g x1))
% Found eq_ref00:=(eq_ref0 (x0 (g x2))):(((eq fofType) (x0 (g x2))) (x0 (g x2)))
% Found (eq_ref0 (x0 (g x2))) as proof of (((eq fofType) (x0 (g x2))) x1)
% Found ((eq_ref fofType) (x0 (g x2))) as proof of (((eq fofType) (x0 (g x2))) x1)
% Found (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2)))) as proof of (((eq fofType) (x0 (g x2))) x1)
% Found (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2)))) as proof of (forall (x:fofType), (((eq fofType) (x0 (g x))) x1))
% Found (functional_extensionality_dep00010 (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found (functional_extensionality_dep00010 (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> ((functional_extensionality_dep0001 x2) (fun (x3:(fofType->fofType))=> (P1 (x0 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> (((functional_extensionality_dep000 (fun (x4:fofType)=> x1)) x2) (fun (x3:(fofType->fofType))=> (P1 (x0 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> (((functional_extensionality_dep000 (fun (x4:fofType)=> x1)) x2) (fun (x3:(fofType->fofType))=> (P1 (x0 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found (fun (P1:(fofType->Prop))=> ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> (((functional_extensionality_dep000 (fun (x4:fofType)=> x1)) x2) (fun (x3:(fofType->fofType))=> (P1 (x0 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2)))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found eq_ref00:=(eq_ref0 (x0 (g x2))):(((eq fofType) (x0 (g x2))) (x0 (g x2)))
% Found (eq_ref0 (x0 (g x2))) as proof of (((eq fofType) (x0 (g x2))) x1)
% Found ((eq_ref fofType) (x0 (g x2))) as proof of (((eq fofType) (x0 (g x2))) x1)
% Found (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2)))) as proof of (((eq fofType) (x0 (g x2))) x1)
% Found (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2)))) as proof of (forall (x:fofType), (((eq fofType) (x0 (g x))) x1))
% Found (functional_extensionality_dep00010 (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found (functional_extensionality_dep00010 (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> ((functional_extensionality_dep0001 x2) (fun (x3:(fofType->fofType))=> (P1 (x3 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> (((functional_extensionality_dep000 (fun (x4:fofType)=> x1)) x2) (fun (x3:(fofType->fofType))=> (P1 (x3 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> (((functional_extensionality_dep000 (fun (x4:fofType)=> x1)) x2) (fun (x3:(fofType->fofType))=> (P1 (x3 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found (fun (P1:(fofType->Prop))=> ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> (((functional_extensionality_dep000 (fun (x4:fofType)=> x1)) x2) (fun (x3:(fofType->fofType))=> (P1 (x3 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2)))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found eq_ref00:=(eq_ref0 (x0 (g x2))):(((eq fofType) (x0 (g x2))) (x0 (g x2)))
% Found (eq_ref0 (x0 (g x2))) as proof of (((eq fofType) (x0 (g x2))) x1)
% Found ((eq_ref fofType) (x0 (g x2))) as proof of (((eq fofType) (x0 (g x2))) x1)
% Found (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2)))) as proof of (((eq fofType) (x0 (g x2))) x1)
% Found (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2)))) as proof of (forall (x:fofType), (((eq fofType) (x0 (g x))) x1))
% Found (functional_extensionality00010 (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found (functional_extensionality00010 (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> ((functional_extensionality0001 x2) (fun (x3:(fofType->fofType))=> (P1 (x3 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> (((functional_extensionality000 (fun (x4:fofType)=> x1)) x2) (fun (x3:(fofType->fofType))=> (P1 (x3 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> (((functional_extensionality000 (fun (x4:fofType)=> x1)) x2) (fun (x3:(fofType->fofType))=> (P1 (x3 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found (fun (P1:(fofType->Prop))=> ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> (((functional_extensionality000 (fun (x4:fofType)=> x1)) x2) (fun (x3:(fofType->fofType))=> (P1 (x3 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2)))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found eq_ref00:=(eq_ref0 (x0 (g x2))):(((eq fofType) (x0 (g x2))) (x0 (g x2)))
% Found (eq_ref0 (x0 (g x2))) as proof of (((eq fofType) (x0 (g x2))) x1)
% Found ((eq_ref fofType) (x0 (g x2))) as proof of (((eq fofType) (x0 (g x2))) x1)
% Found (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2)))) as proof of (((eq fofType) (x0 (g x2))) x1)
% Found (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2)))) as proof of (forall (x:fofType), (((eq fofType) (x0 (g x))) x1))
% Found (functional_extensionality00010 (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found (functional_extensionality00010 (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> ((functional_extensionality0001 x2) (fun (x3:(fofType->fofType))=> (P1 (x0 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> (((functional_extensionality000 (fun (x4:fofType)=> x1)) x2) (fun (x3:(fofType->fofType))=> (P1 (x0 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> (((functional_extensionality000 (fun (x4:fofType)=> x1)) x2) (fun (x3:(fofType->fofType))=> (P1 (x0 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found (fun (P1:(fofType->Prop))=> ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> (((functional_extensionality000 (fun (x4:fofType)=> x1)) x2) (fun (x3:(fofType->fofType))=> (P1 (x0 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2)))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found eq_ref00:=(eq_ref0 (x0 (g x2))):(((eq fofType) (x0 (g x2))) (x0 (g x2)))
% Found (eq_ref0 (x0 (g x2))) as proof of (((eq fofType) (x0 (g x2))) x1)
% Found ((eq_ref fofType) (x0 (g x2))) as proof of (((eq fofType) (x0 (g x2))) x1)
% Found (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2)))) as proof of (((eq fofType) (x0 (g x2))) x1)
% Found (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2)))) as proof of (forall (x:fofType), (((eq fofType) (x0 (g x))) x1))
% Found (functional_extensionality00010 (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found (functional_extensionality00010 (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> ((functional_extensionality0001 x2) (fun (x3:(fofType->fofType))=> (P1 (x3 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> (((functional_extensionality000 (fun (x4:fofType)=> x1)) x2) (fun (x3:(fofType->fofType))=> (P1 (x3 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> (((functional_extensionality000 (fun (x4:fofType)=> x1)) x2) (fun (x3:(fofType->fofType))=> (P1 (x3 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found (fun (P1:(fofType->Prop))=> ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> (((functional_extensionality000 (fun (x4:fofType)=> x1)) x2) (fun (x3:(fofType->fofType))=> (P1 (x3 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2)))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found eq_ref00:=(eq_ref0 (x0 (g x2))):(((eq fofType) (x0 (g x2))) (x0 (g x2)))
% Found (eq_ref0 (x0 (g x2))) as proof of (((eq fofType) (x0 (g x2))) x1)
% Found ((eq_ref fofType) (x0 (g x2))) as proof of (((eq fofType) (x0 (g x2))) x1)
% Found (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2)))) as proof of (((eq fofType) (x0 (g x2))) x1)
% Found (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2)))) as proof of (forall (x:fofType), (((eq fofType) (x0 (g x))) x1))
% Found (functional_extensionality00010 (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found (functional_extensionality00010 (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> ((functional_extensionality0001 x2) (fun (x3:(fofType->fofType))=> (P1 (x0 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> (((functional_extensionality000 (fun (x4:fofType)=> x1)) x2) (fun (x3:(fofType->fofType))=> (P1 (x0 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> (((functional_extensionality000 (fun (x4:fofType)=> x1)) x2) (fun (x3:(fofType->fofType))=> (P1 (x0 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found (fun (P1:(fofType->Prop))=> ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> (((functional_extensionality000 (fun (x4:fofType)=> x1)) x2) (fun (x3:(fofType->fofType))=> (P1 (x0 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2)))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found eq_ref00:=(eq_ref0 (x0 (g x2))):(((eq fofType) (x0 (g x2))) (x0 (g x2)))
% Found (eq_ref0 (x0 (g x2))) as proof of (((eq fofType) (x0 (g x2))) x1)
% Found ((eq_ref fofType) (x0 (g x2))) as proof of (((eq fofType) (x0 (g x2))) x1)
% Found (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2)))) as proof of (((eq fofType) (x0 (g x2))) x1)
% Found (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2)))) as proof of (forall (x:fofType), (((eq fofType) (x0 (g x))) x1))
% Found (functional_extensionality_dep00010 (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found (functional_extensionality_dep00010 (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> ((functional_extensionality_dep0001 x2) (fun (x3:(fofType->fofType))=> (P1 (x3 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> (((functional_extensionality_dep000 (fun (x4:fofType)=> x1)) x2) (fun (x3:(fofType->fofType))=> (P1 (x3 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> (((functional_extensionality_dep000 (fun (x4:fofType)=> x1)) x2) (fun (x3:(fofType->fofType))=> (P1 (x3 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found (fun (P1:(fofType->Prop))=> ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> (((functional_extensionality_dep000 (fun (x4:fofType)=> x1)) x2) (fun (x3:(fofType->fofType))=> (P1 (x3 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2)))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found eq_ref00:=(eq_ref0 (x0 (g x2))):(((eq fofType) (x0 (g x2))) (x0 (g x2)))
% Found (eq_ref0 (x0 (g x2))) as proof of (((eq fofType) (x0 (g x2))) x1)
% Found ((eq_ref fofType) (x0 (g x2))) as proof of (((eq fofType) (x0 (g x2))) x1)
% Found (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2)))) as proof of (((eq fofType) (x0 (g x2))) x1)
% Found (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2)))) as proof of (forall (x:fofType), (((eq fofType) (x0 (g x))) x1))
% Found (functional_extensionality_dep00010 (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found (functional_extensionality_dep00010 (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> ((functional_extensionality_dep0001 x2) (fun (x3:(fofType->fofType))=> (P1 (x0 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> (((functional_extensionality_dep000 (fun (x4:fofType)=> x1)) x2) (fun (x3:(fofType->fofType))=> (P1 (x0 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> (((functional_extensionality_dep000 (fun (x4:fofType)=> x1)) x2) (fun (x3:(fofType->fofType))=> (P1 (x0 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found (fun (P1:(fofType->Prop))=> ((fun (x2:(forall (x:fofType), (((eq fofType) (x0 (g x))) x1)))=> (((functional_extensionality_dep000 (fun (x4:fofType)=> x1)) x2) (fun (x3:(fofType->fofType))=> (P1 (x0 (g x1)))))) (fun (x2:fofType)=> ((eq_ref fofType) (x0 (g x2)))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found x2:(P (x0 (g x1)))
% Instantiate: b:=(x0 (g x1)):fofType
% Found x2 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 x1):(((eq fofType) x1) x1)
% Found (eq_ref0 x1) as proof of (((eq fofType) x1) b)
% Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% Found x2:(P (x0 (g x1)))
% Instantiate: b:=(x0 (g x1)):fofType
% Found x2 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 x1):(((eq fofType) x1) x1)
% Found (eq_ref0 x1) as proof of (((eq fofType) x1) b)
% Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) x1)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x1)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x1)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x1)
% Found ((eq_trans0000 ((eq_ref fofType) (x0 (g x1)))) ((eq_ref fofType) b)) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found (((eq_trans000 x1) ((eq_ref fofType) (x0 (g x1)))) ((eq_ref fofType) x1)) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found ((((fun (b:fofType)=> ((eq_trans00 b) x1)) x1) ((eq_ref fofType) (x0 (g x1)))) ((eq_ref fofType) x1)) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found ((((fun (b:fofType)=> (((eq_trans0 (x0 (g x1))) b) x1)) x1) ((eq_ref fofType) (x0 (g x1)))) ((eq_ref fofType) x1)) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found ((((fun (b:fofType)=> ((((eq_trans fofType) (x0 (g x1))) b) x1)) x1) ((eq_ref fofType) (x0 (g x1)))) ((eq_ref fofType) x1)) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found ((((fun (b:fofType)=> ((((eq_trans fofType) (x0 (g x1))) b) x1)) x1) ((eq_ref fofType) (x0 (g x1)))) ((eq_ref fofType) x1)) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) x1)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x1)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x1)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x1)
% Found ((eq_trans0000 ((eq_ref fofType) (x0 (g x1)))) ((eq_ref fofType) b)) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found (((eq_trans000 x1) ((eq_ref fofType) (x0 (g x1)))) ((eq_ref fofType) x1)) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found ((((fun (b:fofType)=> ((eq_trans00 b) x1)) x1) ((eq_ref fofType) (x0 (g x1)))) ((eq_ref fofType) x1)) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found ((((fun (b:fofType)=> (((eq_trans0 (x0 (g x1))) b) x1)) x1) ((eq_ref fofType) (x0 (g x1)))) ((eq_ref fofType) x1)) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found ((((fun (b:fofType)=> ((((eq_trans fofType) (x0 (g x1))) b) x1)) x1) ((eq_ref fofType) (x0 (g x1)))) ((eq_ref fofType) x1)) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found ((((fun (b:fofType)=> ((((eq_trans fofType) (x0 (g x1))) b) x1)) x1) ((eq_ref fofType) (x0 (g x1)))) ((eq_ref fofType) x1)) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) x1)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x1)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x1)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x1)
% Found ((eq_trans0000 ((eq_ref fofType) (x0 (g x1)))) ((eq_ref fofType) b)) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (((eq_trans000 x1) ((eq_ref fofType) (x0 (g x1)))) ((eq_ref fofType) x1)) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((((fun (b:fofType)=> ((eq_trans00 b) x1)) x1) ((eq_ref fofType) (x0 (g x1)))) ((eq_ref fofType) x1)) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((((fun (b:fofType)=> (((eq_trans0 (x0 (g x1))) b) x1)) x1) ((eq_ref fofType) (x0 (g x1)))) ((eq_ref fofType) x1)) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((((fun (b:fofType)=> ((((eq_trans fofType) (x0 (g x1))) b) x1)) x1) ((eq_ref fofType) (x0 (g x1)))) ((eq_ref fofType) x1)) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) x1)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x1)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x1)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x1)
% Found ((eq_trans0000 ((eq_ref fofType) (x0 (g x1)))) ((eq_ref fofType) b)) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (((eq_trans000 x1) ((eq_ref fofType) (x0 (g x1)))) ((eq_ref fofType) x1)) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((((fun (b:fofType)=> ((eq_trans00 b) x1)) x1) ((eq_ref fofType) (x0 (g x1)))) ((eq_ref fofType) x1)) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((((fun (b:fofType)=> (((eq_trans0 (x0 (g x1))) b) x1)) x1) ((eq_ref fofType) (x0 (g x1)))) ((eq_ref fofType) x1)) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((((fun (b:fofType)=> ((((eq_trans fofType) (x0 (g x1))) b) x1)) x1) ((eq_ref fofType) (x0 (g x1)))) ((eq_ref fofType) x1)) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (fun (Xx:fofType)=> Xx))->(P1 (fun (x:fofType)=> x)))
% Found (eta_expansion_dep000 P1) as proof of (P2 (fun (Xx:fofType)=> Xx))
% Found ((eta_expansion_dep00 (fun (Xx:fofType)=> Xx)) P1) as proof of (P2 (fun (Xx:fofType)=> Xx))
% Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (Xx:fofType)=> Xx)) P1) as proof of (P2 (fun (Xx:fofType)=> Xx))
% Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (Xx:fofType)=> Xx)) P1) as proof of (P2 (fun (Xx:fofType)=> Xx))
% Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (Xx:fofType)=> Xx)) P1) as proof of (P2 (fun (Xx:fofType)=> Xx))
% Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (fun (Xx:fofType)=> Xx))->(P1 (fun (x:fofType)=> x)))
% Found (eta_expansion_dep000 P1) as proof of (P2 (fun (Xx:fofType)=> Xx))
% Found ((eta_expansion_dep00 (fun (Xx:fofType)=> Xx)) P1) as proof of (P2 (fun (Xx:fofType)=> Xx))
% Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (Xx:fofType)=> Xx)) P1) as proof of (P2 (fun (Xx:fofType)=> Xx))
% Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (Xx:fofType)=> Xx)) P1) as proof of (P2 (fun (Xx:fofType)=> Xx))
% Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (Xx:fofType)=> Xx)) P1) as proof of (P2 (fun (Xx:fofType)=> Xx))
% Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (fun (Xx:fofType)=> Xx))->(P1 (fun (x:fofType)=> x)))
% Found (eta_expansion_dep000 P1) as proof of (P2 (fun (Xx:fofType)=> Xx))
% Found ((eta_expansion_dep00 (fun (Xx:fofType)=> Xx)) P1) as proof of (P2 (fun (Xx:fofType)=> Xx))
% Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (Xx:fofType)=> Xx)) P1) as proof of (P2 (fun (Xx:fofType)=> Xx))
% Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (Xx:fofType)=> Xx)) P1) as proof of (P2 (fun (Xx:fofType)=> Xx))
% Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (Xx:fofType)=> Xx)) P1) as proof of (P2 (fun (Xx:fofType)=> Xx))
% Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (fun (Xx:fofType)=> Xx))->(P1 (fun (x:fofType)=> x)))
% Found (eta_expansion_dep000 P1) as proof of (P2 (fun (Xx:fofType)=> Xx))
% Found ((eta_expansion_dep00 (fun (Xx:fofType)=> Xx)) P1) as proof of (P2 (fun (Xx:fofType)=> Xx))
% Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (Xx:fofType)=> Xx)) P1) as proof of (P2 (fun (Xx:fofType)=> Xx))
% Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (Xx:fofType)=> Xx)) P1) as proof of (P2 (fun (Xx:fofType)=> Xx))
% Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (Xx:fofType)=> Xx)) P1) as proof of (P2 (fun (Xx:fofType)=> Xx))
% Found eq_ref000:=(eq_ref00 P):((P x1)->(P x1))
% Found (eq_ref00 P) as proof of (P0 x1)
% Found ((eq_ref0 x1) P) as proof of (P0 x1)
% Found (((eq_ref fofType) x1) P) as proof of (P0 x1)
% Found (((eq_ref fofType) x1) P) as proof of (P0 x1)
% Found eq_ref000:=(eq_ref00 P):((P x1)->(P x1))
% Found (eq_ref00 P) as proof of (P0 x1)
% Found ((eq_ref0 x1) P) as proof of (P0 x1)
% Found (((eq_ref fofType) x1) P) as proof of (P0 x1)
% Found (((eq_ref fofType) x1) P) as proof of (P0 x1)
% Found eq_ref000:=(eq_ref00 P):((P x1)->(P x1))
% Found (eq_ref00 P) as proof of (P0 x1)
% Found ((eq_ref0 x1) P) as proof of (P0 x1)
% Found (((eq_ref fofType) x1) P) as proof of (P0 x1)
% Found (((eq_ref fofType) x1) P) as proof of (P0 x1)
% Found eq_ref000:=(eq_ref00 P):((P x1)->(P x1))
% Found (eq_ref00 P) as proof of (P0 x1)
% Found ((eq_ref0 x1) P) as proof of (P0 x1)
% Found (((eq_ref fofType) x1) P) as proof of (P0 x1)
% Found (((eq_ref fofType) x1) P) as proof of (P0 x1)
% Found eq_ref000:=(eq_ref00 P):((P x1)->(P x1))
% Found (eq_ref00 P) as proof of (P0 x1)
% Found ((eq_ref0 x1) P) as proof of (P0 x1)
% Found (((eq_ref fofType) x1) P) as proof of (P0 x1)
% Found (((eq_ref fofType) x1) P) as proof of (P0 x1)
% Found eq_ref000:=(eq_ref00 P):((P x1)->(P x1))
% Found (eq_ref00 P) as proof of (P0 x1)
% Found ((eq_ref0 x1) P) as proof of (P0 x1)
% Found (((eq_ref fofType) x1) P) as proof of (P0 x1)
% Found (((eq_ref fofType) x1) P) as proof of (P0 x1)
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref (fofType->fofType)) b) P) as proof of (P0 b)
% Found (((eq_ref (fofType->fofType)) b) P) as proof of (P0 b)
% Found eq_ref000:=(eq_ref00 P):((P (x0 (g x1)))->(P (x0 (g x1))))
% Found (eq_ref00 P) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((eq_ref0 (x0 (g x1))) P) as proof of ((P (x0 (g x1)))->(P x1))
% Found (((eq_ref fofType) (x0 (g x1))) P) as proof of ((P (x0 (g x1)))->(P x1))
% Found (((eq_ref fofType) (x0 (g x1))) P) as proof of ((P (x0 (g x1)))->(P x1))
% Found (fun (P:(fofType->Prop))=> (((eq_ref fofType) (x0 (g x1))) P)) as proof of ((P (x0 (g x1)))->(P x1))
% Found (fun (P:(fofType->Prop))=> (((eq_ref fofType) (x0 (g x1))) P)) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found eq_ref000:=(eq_ref00 P):((P (x0 (g x1)))->(P (x0 (g x1))))
% Found (eq_ref00 P) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((eq_ref0 (x0 (g x1))) P) as proof of ((P (x0 (g x1)))->(P x1))
% Found (((eq_ref fofType) (x0 (g x1))) P) as proof of ((P (x0 (g x1)))->(P x1))
% Found (((eq_ref fofType) (x0 (g x1))) P) as proof of ((P (x0 (g x1)))->(P x1))
% Found (fun (P:(fofType->Prop))=> (((eq_ref fofType) (x0 (g x1))) P)) as proof of ((P (x0 (g x1)))->(P x1))
% Found (fun (P:(fofType->Prop))=> (((eq_ref fofType) (x0 (g x1))) P)) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found x1:(P (fun (Xx:fofType)=> Xx))
% Instantiate: f:=(fun (Xx:fofType)=> Xx):(fofType->fofType)
% Found x1 as proof of (P0 f)
% Found eq_ref00:=(eq_ref0 (f x2)):(((eq fofType) (f x2)) (f x2))
% Found (eq_ref0 (f x2)) as proof of (((eq fofType) (f x2)) (x0 (g x2)))
% Found ((eq_ref fofType) (f x2)) as proof of (((eq fofType) (f x2)) (x0 (g x2)))
% Found ((eq_ref fofType) (f x2)) as proof of (((eq fofType) (f x2)) (x0 (g x2)))
% Found (fun (x2:fofType)=> ((eq_ref fofType) (f x2))) as proof of (((eq fofType) (f x2)) (x0 (g x2)))
% Found (fun (x2:fofType)=> ((eq_ref fofType) (f x2))) as proof of (forall (x:fofType), (((eq fofType) (f x)) (x0 (g x))))
% Found x1:(P (fun (Xx:fofType)=> Xx))
% Instantiate: f:=(fun (Xx:fofType)=> Xx):(fofType->fofType)
% Found x1 as proof of (P0 f)
% Found eq_ref00:=(eq_ref0 (f x2)):(((eq fofType) (f x2)) (f x2))
% Found (eq_ref0 (f x2)) as proof of (((eq fofType) (f x2)) (x0 (g x2)))
% Found ((eq_ref fofType) (f x2)) as proof of (((eq fofType) (f x2)) (x0 (g x2)))
% Found ((eq_ref fofType) (f x2)) as proof of (((eq fofType) (f x2)) (x0 (g x2)))
% Found (fun (x2:fofType)=> ((eq_ref fofType) (f x2))) as proof of (((eq fofType) (f x2)) (x0 (g x2)))
% Found (fun (x2:fofType)=> ((eq_ref fofType) (f x2))) as proof of (forall (x:fofType), (((eq fofType) (f x)) (x0 (g x))))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found (eq_sym110 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g (b x1))) (g (x0 (g x1))))
% Found ((eq_sym11 (g (b x1))) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g (b x1))) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g (b x1))) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g (b x1))) (g (x0 (g x1))))
% Found (x20 (((eq_sym1 (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found ((x2 (x0 (g x1))) (((eq_sym1 (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found (((x (b x1)) (x0 (g x1))) (((eq_sym1 (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found (((x (b x1)) (x0 (g x1))) (((eq_sym1 (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found (eq_sym100 (((x (b x1)) (x0 (g x1))) (((eq_sym1 (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_sym10 (x0 (g x1))) (((x (b x1)) (x0 (g x1))) (((eq_sym1 (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found (((eq_sym1 (b x1)) (x0 (g x1))) (((x (b x1)) (x0 (g x1))) (((eq_sym1 (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((((eq_sym fofType) (b x1)) (x0 (g x1))) (((x (b x1)) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found (eq_sym110 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g (b x1))) (g (x0 (g x1))))
% Found ((eq_sym11 (g (b x1))) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g (b x1))) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g (b x1))) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g (b x1))) (g (x0 (g x1))))
% Found (x20 (((eq_sym1 (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found ((x2 (x0 (g x1))) (((eq_sym1 (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found (((x (b x1)) (x0 (g x1))) (((eq_sym1 (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found (((x (b x1)) (x0 (g x1))) (((eq_sym1 (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found (eq_sym100 (((x (b x1)) (x0 (g x1))) (((eq_sym1 (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_sym10 (x0 (g x1))) (((x (b x1)) (x0 (g x1))) (((eq_sym1 (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found (((eq_sym1 (b x1)) (x0 (g x1))) (((x (b x1)) (x0 (g x1))) (((eq_sym1 (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((((eq_sym fofType) (b x1)) (x0 (g x1))) (((x (b x1)) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P b)->(P (fun (x:fofType)=> (b x))))
% Found (eta_expansion_dep000 P) as proof of (P0 b)
% Found ((eta_expansion_dep00 b) P) as proof of (P0 b)
% Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) b) P) as proof of (P0 b)
% Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) b) P) as proof of (P0 b)
% Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) b) P) as proof of (P0 b)
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref (fofType->fofType)) b) P) as proof of (P0 b)
% Found (((eq_ref (fofType->fofType)) b) P) as proof of (P0 b)
% Found eq_ref000:=(eq_ref00 P):((P (fun (Xx:fofType)=> Xx))->(P (fun (Xx:fofType)=> Xx)))
% Found (eq_ref00 P) as proof of (P0 (fun (Xx:fofType)=> Xx))
% Found ((eq_ref0 (fun (Xx:fofType)=> Xx)) P) as proof of (P0 (fun (Xx:fofType)=> Xx))
% Found (((eq_ref (fofType->fofType)) (fun (Xx:fofType)=> Xx)) P) as proof of (P0 (fun (Xx:fofType)=> Xx))
% Found (((eq_ref (fofType->fofType)) (fun (Xx:fofType)=> Xx)) P) as proof of (P0 (fun (Xx:fofType)=> Xx))
% Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->fofType)) b) (fun (x:fofType)=> (b x)))
% Found (eta_expansion00 b) as proof of (((eq (fofType->fofType)) b) (fun (Xx:fofType)=> (x0 (g Xx))))
% Found ((eta_expansion0 fofType) b) as proof of (((eq (fofType->fofType)) b) (fun (Xx:fofType)=> (x0 (g Xx))))
% Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (fun (Xx:fofType)=> (x0 (g Xx))))
% Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (fun (Xx:fofType)=> (x0 (g Xx))))
% Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (fun (Xx:fofType)=> (x0 (g Xx))))
% Found eq_ref00:=(eq_ref0 (fun (Xx:fofType)=> Xx)):(((eq (fofType->fofType)) (fun (Xx:fofType)=> Xx)) (fun (Xx:fofType)=> Xx))
% Found (eq_ref0 (fun (Xx:fofType)=> Xx)) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> Xx)) b)
% Found ((eq_ref (fofType->fofType)) (fun (Xx:fofType)=> Xx)) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> Xx)) b)
% Found ((eq_ref (fofType->fofType)) (fun (Xx:fofType)=> Xx)) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> Xx)) b)
% Found ((eq_ref (fofType->fofType)) (fun (Xx:fofType)=> Xx)) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> Xx)) b)
% Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->fofType)) b) (fun (x:fofType)=> (b x)))
% Found (eta_expansion00 b) as proof of (((eq (fofType->fofType)) b) (fun (Xx:fofType)=> (x0 (g Xx))))
% Found ((eta_expansion0 fofType) b) as proof of (((eq (fofType->fofType)) b) (fun (Xx:fofType)=> (x0 (g Xx))))
% Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (fun (Xx:fofType)=> (x0 (g Xx))))
% Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (fun (Xx:fofType)=> (x0 (g Xx))))
% Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (fun (Xx:fofType)=> (x0 (g Xx))))
% Found eq_ref00:=(eq_ref0 (fun (Xx:fofType)=> Xx)):(((eq (fofType->fofType)) (fun (Xx:fofType)=> Xx)) (fun (Xx:fofType)=> Xx))
% Found (eq_ref0 (fun (Xx:fofType)=> Xx)) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> Xx)) b)
% Found ((eq_ref (fofType->fofType)) (fun (Xx:fofType)=> Xx)) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> Xx)) b)
% Found ((eq_ref (fofType->fofType)) (fun (Xx:fofType)=> Xx)) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> Xx)) b)
% Found ((eq_ref (fofType->fofType)) (fun (Xx:fofType)=> Xx)) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> Xx)) b)
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xx:fofType)=> Xx)):(((eq (fofType->fofType)) (fun (Xx:fofType)=> Xx)) (fun (x:fofType)=> x))
% Found (eta_expansion_dep00 (fun (Xx:fofType)=> Xx)) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> Xx)) b)
% Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (Xx:fofType)=> Xx)) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> Xx)) b)
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (Xx:fofType)=> Xx)) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> Xx)) b)
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (Xx:fofType)=> Xx)) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> Xx)) b)
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (Xx:fofType)=> Xx)) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> Xx)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq (fofType->fofType)) b) b)
% Found (eq_ref0 b) as proof of (((eq (fofType->fofType)) b) (fun (Xx:fofType)=> (x0 (g Xx))))
% Found ((eq_ref (fofType->fofType)) b) as proof of (((eq (fofType->fofType)) b) (fun (Xx:fofType)=> (x0 (g Xx))))
% Found ((eq_ref (fofType->fofType)) b) as proof of (((eq (fofType->fofType)) b) (fun (Xx:fofType)=> (x0 (g Xx))))
% Found ((eq_ref (fofType->fofType)) b) as proof of (((eq (fofType->fofType)) b) (fun (Xx:fofType)=> (x0 (g Xx))))
% Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq (fofType->fofType)) b) (fun (x:fofType)=> (b x)))
% Found (eta_expansion_dep00 b) as proof of (((eq (fofType->fofType)) b) (fun (Xx:fofType)=> (x0 (g Xx))))
% Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) b) as proof of (((eq (fofType->fofType)) b) (fun (Xx:fofType)=> (x0 (g Xx))))
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) b) as proof of (((eq (fofType->fofType)) b) (fun (Xx:fofType)=> (x0 (g Xx))))
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) b) as proof of (((eq (fofType->fofType)) b) (fun (Xx:fofType)=> (x0 (g Xx))))
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) b) as proof of (((eq (fofType->fofType)) b) (fun (Xx:fofType)=> (x0 (g Xx))))
% Found eq_ref00:=(eq_ref0 (fun (Xx:fofType)=> Xx)):(((eq (fofType->fofType)) (fun (Xx:fofType)=> Xx)) (fun (Xx:fofType)=> Xx))
% Found (eq_ref0 (fun (Xx:fofType)=> Xx)) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> Xx)) b)
% Found ((eq_ref (fofType->fofType)) (fun (Xx:fofType)=> Xx)) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> Xx)) b)
% Found ((eq_ref (fofType->fofType)) (fun (Xx:fofType)=> Xx)) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> Xx)) b)
% Found ((eq_ref (fofType->fofType)) (fun (Xx:fofType)=> Xx)) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> Xx)) b)
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (eq_sym1000 ((eq_ref fofType) (x0 (g x1)))) as proof of ((P x1)->(P (x0 (g x1))))
% Found (eq_sym1000 ((eq_ref fofType) (x0 (g x1)))) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> ((eq_sym100 x2) P)) ((eq_ref fofType) (x0 (g x1)))) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((eq_sym10 x1) x2) P)) ((eq_ref fofType) (x0 (g x1)))) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> ((((eq_sym1 (x0 (g x1))) x1) x2) P)) ((eq_ref fofType) (x0 (g x1)))) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((((eq_sym fofType) (x0 (g x1))) x1) x2) P)) ((eq_ref fofType) (x0 (g x1)))) as proof of ((P x1)->(P (x0 (g x1))))
% Found (fun (P:(fofType->Prop))=> ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((((eq_sym fofType) (x0 (g x1))) x1) x2) P)) ((eq_ref fofType) (x0 (g x1))))) as proof of ((P x1)->(P (x0 (g x1))))
% Found (fun (P:(fofType->Prop))=> ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((((eq_sym fofType) (x0 (g x1))) x1) x2) P)) ((eq_ref fofType) (x0 (g x1))))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (eq_sym1000 ((eq_ref fofType) (x0 (g x1)))) as proof of ((P x1)->(P (x0 (g x1))))
% Found (eq_sym1000 ((eq_ref fofType) (x0 (g x1)))) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> ((eq_sym100 x2) P)) ((eq_ref fofType) (x0 (g x1)))) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((eq_sym10 x1) x2) P)) ((eq_ref fofType) (x0 (g x1)))) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> ((((eq_sym1 (x0 (g x1))) x1) x2) P)) ((eq_ref fofType) (x0 (g x1)))) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((((eq_sym fofType) (x0 (g x1))) x1) x2) P)) ((eq_ref fofType) (x0 (g x1)))) as proof of ((P x1)->(P (x0 (g x1))))
% Found (fun (P:(fofType->Prop))=> ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((((eq_sym fofType) (x0 (g x1))) x1) x2) P)) ((eq_ref fofType) (x0 (g x1))))) as proof of ((P x1)->(P (x0 (g x1))))
% Found (fun (P:(fofType->Prop))=> ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((((eq_sym fofType) (x0 (g x1))) x1) x2) P)) ((eq_ref fofType) (x0 (g x1))))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found ((eq_sym10 x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found (((eq_sym1 (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found ((eq_sym10 x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found (((eq_sym1 (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found ((eq_sym10 x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found (((eq_sym1 (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found ((eq_sym10 x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found (((eq_sym1 (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found ((eq_sym10 x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found (((eq_sym1 (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (eq_sym1000 ((eq_ref fofType) (x0 (g x1)))) as proof of ((P x1)->(P (x0 (g x1))))
% Found (eq_sym1000 ((eq_ref fofType) (x0 (g x1)))) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> ((eq_sym100 x2) P)) ((eq_ref fofType) (x0 (g x1)))) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((eq_sym10 x1) x2) P)) ((eq_ref fofType) (x0 (g x1)))) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> ((((eq_sym1 (x0 (g x1))) x1) x2) P)) ((eq_ref fofType) (x0 (g x1)))) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((((eq_sym fofType) (x0 (g x1))) x1) x2) P)) ((eq_ref fofType) (x0 (g x1)))) as proof of ((P x1)->(P (x0 (g x1))))
% Found (fun (P:(fofType->Prop))=> ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((((eq_sym fofType) (x0 (g x1))) x1) x2) P)) ((eq_ref fofType) (x0 (g x1))))) as proof of ((P x1)->(P (x0 (g x1))))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (eq_sym1000 ((eq_ref fofType) (x0 (g x1)))) as proof of ((P x1)->(P (x0 (g x1))))
% Found (eq_sym1000 ((eq_ref fofType) (x0 (g x1)))) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> ((eq_sym100 x2) P)) ((eq_ref fofType) (x0 (g x1)))) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((eq_sym10 x1) x2) P)) ((eq_ref fofType) (x0 (g x1)))) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> ((((eq_sym1 (x0 (g x1))) x1) x2) P)) ((eq_ref fofType) (x0 (g x1)))) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((((eq_sym fofType) (x0 (g x1))) x1) x2) P)) ((eq_ref fofType) (x0 (g x1)))) as proof of ((P x1)->(P (x0 (g x1))))
% Found (fun (P:(fofType->Prop))=> ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((((eq_sym fofType) (x0 (g x1))) x1) x2) P)) ((eq_ref fofType) (x0 (g x1))))) as proof of ((P x1)->(P (x0 (g x1))))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found ((eq_sym10 x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found (((eq_sym1 (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (eq_sym1000 ((eq_ref fofType) (x0 (g x1)))) as proof of ((P x1)->(P (x0 (g x1))))
% Found (eq_sym1000 ((eq_ref fofType) (x0 (g x1)))) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> ((eq_sym100 x2) P)) ((eq_ref fofType) (x0 (g x1)))) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((eq_sym10 x1) x2) P)) ((eq_ref fofType) (x0 (g x1)))) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> ((((eq_sym1 (x0 (g x1))) x1) x2) P)) ((eq_ref fofType) (x0 (g x1)))) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((((eq_sym fofType) (x0 (g x1))) x1) x2) P)) ((eq_ref fofType) (x0 (g x1)))) as proof of ((P x1)->(P (x0 (g x1))))
% Found (fun (P:(fofType->Prop))=> ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((((eq_sym fofType) (x0 (g x1))) x1) x2) P)) ((eq_ref fofType) (x0 (g x1))))) as proof of ((P x1)->(P (x0 (g x1))))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (eq_sym1000 ((eq_ref fofType) (x0 (g x1)))) as proof of ((P x1)->(P (x0 (g x1))))
% Found (eq_sym1000 ((eq_ref fofType) (x0 (g x1)))) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> ((eq_sym100 x2) P)) ((eq_ref fofType) (x0 (g x1)))) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((eq_sym10 x1) x2) P)) ((eq_ref fofType) (x0 (g x1)))) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> ((((eq_sym1 (x0 (g x1))) x1) x2) P)) ((eq_ref fofType) (x0 (g x1)))) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((((eq_sym fofType) (x0 (g x1))) x1) x2) P)) ((eq_ref fofType) (x0 (g x1)))) as proof of ((P x1)->(P (x0 (g x1))))
% Found (fun (P:(fofType->Prop))=> ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((((eq_sym fofType) (x0 (g x1))) x1) x2) P)) ((eq_ref fofType) (x0 (g x1))))) as proof of ((P x1)->(P (x0 (g x1))))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found ((eq_sym10 x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found (((eq_sym1 (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found ((eq_sym10 x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found (((eq_sym1 (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((eq_sym10 x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((eq_sym1 (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((eq_sym10 x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((eq_sym1 (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((eq_sym10 x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((eq_sym1 (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((eq_sym10 x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((eq_sym1 (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((eq_sym10 x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((eq_sym1 (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((eq_sym10 x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((eq_sym1 (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((eq_sym10 x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((eq_sym1 (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((eq_sym10 x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((eq_sym1 (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((eq_sym10 x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((eq_sym1 (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((eq_sym10 x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((eq_sym1 (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((eq_sym10 x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((eq_sym1 (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((eq_sym10 x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((eq_sym1 (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((eq_sym10 x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((eq_sym1 (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((eq_sym10 x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((eq_sym1 (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((eq_sym10 x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((eq_sym1 (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((eq_sym10 x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((eq_sym1 (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (x20 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found ((x2 x1) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found (((x (x0 (g x1))) x1) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found (((x (x0 (g x1))) x1) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (x20 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found ((x2 x1) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found (((x (x0 (g x1))) x1) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found (((x (x0 (g x1))) x1) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found eq_ref000:=(eq_ref00 P):((P x1)->(P x1))
% Found (eq_ref00 P) as proof of (P0 x1)
% Found ((eq_ref0 x1) P) as proof of (P0 x1)
% Found (((eq_ref fofType) x1) P) as proof of (P0 x1)
% Found (((eq_ref fofType) x1) P) as proof of (P0 x1)
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_sym1000 ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((eq_sym1000 ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> ((eq_sym100 x2) (fun (x4:fofType)=> ((P x1)->(P x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((eq_sym10 x1) x2) (fun (x4:fofType)=> ((P x1)->(P x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> ((((eq_sym1 (x0 (g x1))) x1) x2) (fun (x4:fofType)=> ((P x1)->(P x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((((eq_sym fofType) (x0 (g x1))) x1) x2) (fun (x4:fofType)=> ((P x1)->(P x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found (fun (P:(fofType->Prop))=> (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((((eq_sym fofType) (x0 (g x1))) x1) x2) (fun (x4:fofType)=> ((P x1)->(P x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P))) as proof of ((P x1)->(P (x0 (g x1))))
% Found (fun (P:(fofType->Prop))=> (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((((eq_sym fofType) (x0 (g x1))) x1) x2) (fun (x4:fofType)=> ((P x1)->(P x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found eq_ref000:=(eq_ref00 P):((P x1)->(P x1))
% Found (eq_ref00 P) as proof of (P0 x1)
% Found ((eq_ref0 x1) P) as proof of (P0 x1)
% Found (((eq_ref fofType) x1) P) as proof of (P0 x1)
% Found (((eq_ref fofType) x1) P) as proof of (P0 x1)
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_sym1000 ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((eq_sym1000 ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> ((eq_sym100 x2) (fun (x4:fofType)=> ((P x1)->(P x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((eq_sym10 x1) x2) (fun (x4:fofType)=> ((P x1)->(P x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> ((((eq_sym1 (x0 (g x1))) x1) x2) (fun (x4:fofType)=> ((P x1)->(P x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((((eq_sym fofType) (x0 (g x1))) x1) x2) (fun (x4:fofType)=> ((P x1)->(P x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found (fun (P:(fofType->Prop))=> (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((((eq_sym fofType) (x0 (g x1))) x1) x2) (fun (x4:fofType)=> ((P x1)->(P x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P))) as proof of ((P x1)->(P (x0 (g x1))))
% Found (fun (P:(fofType->Prop))=> (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((((eq_sym fofType) (x0 (g x1))) x1) x2) (fun (x4:fofType)=> ((P x1)->(P x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found eq_ref000:=(eq_ref00 P):((P x1)->(P x1))
% Found (eq_ref00 P) as proof of (P0 x1)
% Found ((eq_ref0 x1) P) as proof of (P0 x1)
% Found (((eq_ref fofType) x1) P) as proof of (P0 x1)
% Found (((eq_ref fofType) x1) P) as proof of (P0 x1)
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_sym1000 ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((eq_sym1000 ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> ((eq_sym100 x2) (fun (x4:fofType)=> ((P x1)->(P x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((eq_sym10 x1) x2) (fun (x4:fofType)=> ((P x1)->(P x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> ((((eq_sym1 (x0 (g x1))) x1) x2) (fun (x4:fofType)=> ((P x1)->(P x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((((eq_sym fofType) (x0 (g x1))) x1) x2) (fun (x4:fofType)=> ((P x1)->(P x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found (fun (P:(fofType->Prop))=> (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((((eq_sym fofType) (x0 (g x1))) x1) x2) (fun (x4:fofType)=> ((P x1)->(P x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P))) as proof of ((P x1)->(P (x0 (g x1))))
% Found eq_ref000:=(eq_ref00 P):((P x1)->(P x1))
% Found (eq_ref00 P) as proof of (P0 x1)
% Found ((eq_ref0 x1) P) as proof of (P0 x1)
% Found (((eq_ref fofType) x1) P) as proof of (P0 x1)
% Found (((eq_ref fofType) x1) P) as proof of (P0 x1)
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_sym1000 ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((eq_sym1000 ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> ((eq_sym100 x2) (fun (x4:fofType)=> ((P x1)->(P x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((eq_sym10 x1) x2) (fun (x4:fofType)=> ((P x1)->(P x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> ((((eq_sym1 (x0 (g x1))) x1) x2) (fun (x4:fofType)=> ((P x1)->(P x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((((eq_sym fofType) (x0 (g x1))) x1) x2) (fun (x4:fofType)=> ((P x1)->(P x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found (fun (P:(fofType->Prop))=> (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((((eq_sym fofType) (x0 (g x1))) x1) x2) (fun (x4:fofType)=> ((P x1)->(P x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P))) as proof of ((P x1)->(P (x0 (g x1))))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) x1)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x1)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x1)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x1)
% Found ((eq_trans00000 ((eq_ref fofType) (x0 (g x1)))) ((eq_ref fofType) b)) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((eq_trans00000 ((eq_ref fofType) (x0 (g x1)))) ((eq_ref fofType) b)) as proof of ((P (x0 (g x1)))->(P x1))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) b)) (x3:(((eq fofType) b) x1))=> (((eq_trans0000 x2) x3) P)) ((eq_ref fofType) (x0 (g x1)))) ((eq_ref fofType) b)) as proof of ((P (x0 (g x1)))->(P x1))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) x1)) (x3:(((eq fofType) x1) x1))=> ((((eq_trans000 x1) x2) x3) P)) ((eq_ref fofType) (x0 (g x1)))) ((eq_ref fofType) x1)) as proof of ((P (x0 (g x1)))->(P x1))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) x1)) (x3:(((eq fofType) x1) x1))=> (((((fun (b:fofType)=> ((eq_trans00 b) x1)) x1) x2) x3) P)) ((eq_ref fofType) (x0 (g x1)))) ((eq_ref fofType) x1)) as proof of ((P (x0 (g x1)))->(P x1))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) x1)) (x3:(((eq fofType) x1) x1))=> (((((fun (b:fofType)=> (((eq_trans0 (x0 (g x1))) b) x1)) x1) x2) x3) P)) ((eq_ref fofType) (x0 (g x1)))) ((eq_ref fofType) x1)) as proof of ((P (x0 (g x1)))->(P x1))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) x1)) (x3:(((eq fofType) x1) x1))=> (((((fun (b:fofType)=> ((((eq_trans fofType) (x0 (g x1))) b) x1)) x1) x2) x3) P)) ((eq_ref fofType) (x0 (g x1)))) ((eq_ref fofType) x1)) as proof of ((P (x0 (g x1)))->(P x1))
% Found (fun (P:(fofType->Prop))=> (((fun (x2:(((eq fofType) (x0 (g x1))) x1)) (x3:(((eq fofType) x1) x1))=> (((((fun (b:fofType)=> ((((eq_trans fofType) (x0 (g x1))) b) x1)) x1) x2) x3) P)) ((eq_ref fofType) (x0 (g x1)))) ((eq_ref fofType) x1))) as proof of ((P (x0 (g x1)))->(P x1))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) x1)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x1)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x1)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x1)
% Found ((eq_trans00000 ((eq_ref fofType) (x0 (g x1)))) ((eq_ref fofType) b)) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((eq_trans00000 ((eq_ref fofType) (x0 (g x1)))) ((eq_ref fofType) b)) as proof of ((P (x0 (g x1)))->(P x1))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) b)) (x3:(((eq fofType) b) x1))=> (((eq_trans0000 x2) x3) P)) ((eq_ref fofType) (x0 (g x1)))) ((eq_ref fofType) b)) as proof of ((P (x0 (g x1)))->(P x1))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) x1)) (x3:(((eq fofType) x1) x1))=> ((((eq_trans000 x1) x2) x3) P)) ((eq_ref fofType) (x0 (g x1)))) ((eq_ref fofType) x1)) as proof of ((P (x0 (g x1)))->(P x1))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) x1)) (x3:(((eq fofType) x1) x1))=> (((((fun (b:fofType)=> ((eq_trans00 b) x1)) x1) x2) x3) P)) ((eq_ref fofType) (x0 (g x1)))) ((eq_ref fofType) x1)) as proof of ((P (x0 (g x1)))->(P x1))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) x1)) (x3:(((eq fofType) x1) x1))=> (((((fun (b:fofType)=> (((eq_trans0 (x0 (g x1))) b) x1)) x1) x2) x3) P)) ((eq_ref fofType) (x0 (g x1)))) ((eq_ref fofType) x1)) as proof of ((P (x0 (g x1)))->(P x1))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) x1)) (x3:(((eq fofType) x1) x1))=> (((((fun (b:fofType)=> ((((eq_trans fofType) (x0 (g x1))) b) x1)) x1) x2) x3) P)) ((eq_ref fofType) (x0 (g x1)))) ((eq_ref fofType) x1)) as proof of ((P (x0 (g x1)))->(P x1))
% Found (fun (P:(fofType->Prop))=> (((fun (x2:(((eq fofType) (x0 (g x1))) x1)) (x3:(((eq fofType) x1) x1))=> (((((fun (b:fofType)=> ((((eq_trans fofType) (x0 (g x1))) b) x1)) x1) x2) x3) P)) ((eq_ref fofType) (x0 (g x1)))) ((eq_ref fofType) x1))) as proof of ((P (x0 (g x1)))->(P x1))
% Found eq_ref000:=(eq_ref00 P):((P x1)->(P x1))
% Found (eq_ref00 P) as proof of (P0 x1)
% Found ((eq_ref0 x1) P) as proof of (P0 x1)
% Found (((eq_ref fofType) x1) P) as proof of (P0 x1)
% Found (((eq_ref fofType) x1) P) as proof of (P0 x1)
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_sym1000 ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((eq_sym1000 ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> ((eq_sym100 x2) (fun (x4:fofType)=> ((P x1)->(P x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((eq_sym10 x1) x2) (fun (x4:fofType)=> ((P x1)->(P x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> ((((eq_sym1 (x0 (g x1))) x1) x2) (fun (x4:fofType)=> ((P x1)->(P x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((((eq_sym fofType) (x0 (g x1))) x1) x2) (fun (x4:fofType)=> ((P x1)->(P x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found (fun (P:(fofType->Prop))=> (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((((eq_sym fofType) (x0 (g x1))) x1) x2) (fun (x4:fofType)=> ((P x1)->(P x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P))) as proof of ((P x1)->(P (x0 (g x1))))
% Found eq_ref000:=(eq_ref00 P):((P x1)->(P x1))
% Found (eq_ref00 P) as proof of (P0 x1)
% Found ((eq_ref0 x1) P) as proof of (P0 x1)
% Found (((eq_ref fofType) x1) P) as proof of (P0 x1)
% Found (((eq_ref fofType) x1) P) as proof of (P0 x1)
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_sym1000 ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((eq_sym1000 ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> ((eq_sym100 x2) (fun (x4:fofType)=> ((P x1)->(P x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((eq_sym10 x1) x2) (fun (x4:fofType)=> ((P x1)->(P x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> ((((eq_sym1 (x0 (g x1))) x1) x2) (fun (x4:fofType)=> ((P x1)->(P x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((((eq_sym fofType) (x0 (g x1))) x1) x2) (fun (x4:fofType)=> ((P x1)->(P x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found (fun (P:(fofType->Prop))=> (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((((eq_sym fofType) (x0 (g x1))) x1) x2) (fun (x4:fofType)=> ((P x1)->(P x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P))) as proof of ((P x1)->(P (x0 (g x1))))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) x1)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x1)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x1)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x1)
% Found ((eq_trans0000 ((eq_ref fofType) (x0 (g x1)))) ((eq_ref fofType) b)) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (((eq_trans000 x1) ((eq_ref fofType) (x0 (g x1)))) ((eq_ref fofType) x1)) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((((fun (b:fofType)=> ((eq_trans00 b) x1)) x1) ((eq_ref fofType) (x0 (g x1)))) ((eq_ref fofType) x1)) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((((fun (b:fofType)=> (((eq_trans0 (x0 (g x1))) b) x1)) x1) ((eq_ref fofType) (x0 (g x1)))) ((eq_ref fofType) x1)) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((((fun (b:fofType)=> ((((eq_trans fofType) (x0 (g x1))) b) x1)) x1) ((eq_ref fofType) (x0 (g x1)))) ((eq_ref fofType) x1)) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) x1)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x1)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x1)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x1)
% Found ((eq_trans0000 ((eq_ref fofType) (x0 (g x1)))) ((eq_ref fofType) b)) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (((eq_trans000 x1) ((eq_ref fofType) (x0 (g x1)))) ((eq_ref fofType) x1)) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((((fun (b:fofType)=> ((eq_trans00 b) x1)) x1) ((eq_ref fofType) (x0 (g x1)))) ((eq_ref fofType) x1)) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((((fun (b:fofType)=> (((eq_trans0 (x0 (g x1))) b) x1)) x1) ((eq_ref fofType) (x0 (g x1)))) ((eq_ref fofType) x1)) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((((fun (b:fofType)=> ((((eq_trans fofType) (x0 (g x1))) b) x1)) x1) ((eq_ref fofType) (x0 (g x1)))) ((eq_ref fofType) x1)) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) x1)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x1)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x1)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x1)
% Found ((eq_trans0000 ((eq_ref fofType) (x0 (g x1)))) ((eq_ref fofType) b)) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (((eq_trans000 x1) ((eq_ref fofType) (x0 (g x1)))) ((eq_ref fofType) x1)) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((((fun (b:fofType)=> ((eq_trans00 b) x1)) x1) ((eq_ref fofType) (x0 (g x1)))) ((eq_ref fofType) x1)) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((((fun (b:fofType)=> (((eq_trans0 (x0 (g x1))) b) x1)) x1) ((eq_ref fofType) (x0 (g x1)))) ((eq_ref fofType) x1)) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((((fun (b:fofType)=> ((((eq_trans fofType) (x0 (g x1))) b) x1)) x1) ((eq_ref fofType) (x0 (g x1)))) ((eq_ref fofType) x1)) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) x1)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x1)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x1)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x1)
% Found ((eq_trans0000 ((eq_ref fofType) (x0 (g x1)))) ((eq_ref fofType) b)) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (((eq_trans000 x1) ((eq_ref fofType) (x0 (g x1)))) ((eq_ref fofType) x1)) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((((fun (b:fofType)=> ((eq_trans00 b) x1)) x1) ((eq_ref fofType) (x0 (g x1)))) ((eq_ref fofType) x1)) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((((fun (b:fofType)=> (((eq_trans0 (x0 (g x1))) b) x1)) x1) ((eq_ref fofType) (x0 (g x1)))) ((eq_ref fofType) x1)) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((((fun (b:fofType)=> ((((eq_trans fofType) (x0 (g x1))) b) x1)) x1) ((eq_ref fofType) (x0 (g x1)))) ((eq_ref fofType) x1)) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found eq_ref00:=(eq_ref0 b0):(((eq (fofType->fofType)) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq (fofType->fofType)) b0) (fun (Xx:fofType)=> (x0 (g Xx))))
% Found ((eq_ref (fofType->fofType)) b0) as proof of (((eq (fofType->fofType)) b0) (fun (Xx:fofType)=> (x0 (g Xx))))
% Found ((eq_ref (fofType->fofType)) b0) as proof of (((eq (fofType->fofType)) b0) (fun (Xx:fofType)=> (x0 (g Xx))))
% Found ((eq_ref (fofType->fofType)) b0) as proof of (((eq (fofType->fofType)) b0) (fun (Xx:fofType)=> (x0 (g Xx))))
% Found eta_expansion000:=(eta_expansion00 (fun (Xx:fofType)=> Xx)):(((eq (fofType->fofType)) (fun (Xx:fofType)=> Xx)) (fun (x:fofType)=> x))
% Found (eta_expansion00 (fun (Xx:fofType)=> Xx)) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> Xx)) b0)
% Found ((eta_expansion0 fofType) (fun (Xx:fofType)=> Xx)) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> Xx)) b0)
% Found (((eta_expansion fofType) fofType) (fun (Xx:fofType)=> Xx)) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> Xx)) b0)
% Found (((eta_expansion fofType) fofType) (fun (Xx:fofType)=> Xx)) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> Xx)) b0)
% Found (((eta_expansion fofType) fofType) (fun (Xx:fofType)=> Xx)) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> Xx)) b0)
% Found eq_ref00:=(eq_ref0 (x0 (g x2))):(((eq fofType) (x0 (g x2))) (x0 (g x2)))
% Found (eq_ref0 (x0 (g x2))) as proof of (((eq fofType) (x0 (g x2))) (b x2))
% Found ((eq_ref fofType) (x0 (g x2))) as proof of (((eq fofType) (x0 (g x2))) (b x2))
% Found ((eq_ref fofType) (x0 (g x2))) as proof of (((eq fofType) (x0 (g x2))) (b x2))
% Found eq_ref00:=(eq_ref0 (x0 (g x2))):(((eq fofType) (x0 (g x2))) (x0 (g x2)))
% Found (eq_ref0 (x0 (g x2))) as proof of (((eq fofType) (x0 (g x2))) (b x2))
% Found ((eq_ref fofType) (x0 (g x2))) as proof of (((eq fofType) (x0 (g x2))) (b x2))
% Found ((eq_ref fofType) (x0 (g x2))) as proof of (((eq fofType) (x0 (g x2))) (b x2))
% Found eq_ref000:=(eq_ref00 P1):((P1 x1)->(P1 x1))
% Found (eq_ref00 P1) as proof of (P2 x1)
% Found ((eq_ref0 x1) P1) as proof of (P2 x1)
% Found (((eq_ref fofType) x1) P1) as proof of (P2 x1)
% Found (((eq_ref fofType) x1) P1) as proof of (P2 x1)
% Found eq_ref000:=(eq_ref00 P1):((P1 x1)->(P1 x1))
% Found (eq_ref00 P1) as proof of (P2 x1)
% Found ((eq_ref0 x1) P1) as proof of (P2 x1)
% Found (((eq_ref fofType) x1) P1) as proof of (P2 x1)
% Found (((eq_ref fofType) x1) P1) as proof of (P2 x1)
% Found eq_ref000:=(eq_ref00 P1):((P1 x1)->(P1 x1))
% Found (eq_ref00 P1) as proof of (P2 x1)
% Found ((eq_ref0 x1) P1) as proof of (P2 x1)
% Found (((eq_ref fofType) x1) P1) as proof of (P2 x1)
% Found (((eq_ref fofType) x1) P1) as proof of (P2 x1)
% Found eq_ref000:=(eq_ref00 P1):((P1 x1)->(P1 x1))
% Found (eq_ref00 P1) as proof of (P2 x1)
% Found ((eq_ref0 x1) P1) as proof of (P2 x1)
% Found (((eq_ref fofType) x1) P1) as proof of (P2 x1)
% Found (((eq_ref fofType) x1) P1) as proof of (P2 x1)
% Found eq_ref000:=(eq_ref00 P1):((P1 x1)->(P1 x1))
% Found (eq_ref00 P1) as proof of (P2 x1)
% Found ((eq_ref0 x1) P1) as proof of (P2 x1)
% Found (((eq_ref fofType) x1) P1) as proof of (P2 x1)
% Found (((eq_ref fofType) x1) P1) as proof of (P2 x1)
% Found eq_ref000:=(eq_ref00 P1):((P1 x1)->(P1 x1))
% Found (eq_ref00 P1) as proof of (P2 x1)
% Found ((eq_ref0 x1) P1) as proof of (P2 x1)
% Found (((eq_ref fofType) x1) P1) as proof of (P2 x1)
% Found (((eq_ref fofType) x1) P1) as proof of (P2 x1)
% Found eq_ref000:=(eq_ref00 P1):((P1 x1)->(P1 x1))
% Found (eq_ref00 P1) as proof of (P2 x1)
% Found ((eq_ref0 x1) P1) as proof of (P2 x1)
% Found (((eq_ref fofType) x1) P1) as proof of (P2 x1)
% Found (((eq_ref fofType) x1) P1) as proof of (P2 x1)
% Found eq_ref000:=(eq_ref00 P1):((P1 x1)->(P1 x1))
% Found (eq_ref00 P1) as proof of (P2 x1)
% Found ((eq_ref0 x1) P1) as proof of (P2 x1)
% Found (((eq_ref fofType) x1) P1) as proof of (P2 x1)
% Found (((eq_ref fofType) x1) P1) as proof of (P2 x1)
% Found x2:(P x1)
% Instantiate: Xx:=x1:fofType
% Found x2 as proof of (P0 Xx)
% Found eq_ref00:=(eq_ref0 (g Xx)):(((eq fofType) (g Xx)) (g Xx))
% Found (eq_ref0 (g Xx)) as proof of (((eq fofType) (g Xx)) (g (x0 (g x1))))
% Found ((eq_ref fofType) (g Xx)) as proof of (((eq fofType) (g Xx)) (g (x0 (g x1))))
% Found ((eq_ref fofType) (g Xx)) as proof of (((eq fofType) (g Xx)) (g (x0 (g x1))))
% Found ((eq_ref fofType) (g Xx)) as proof of (((eq fofType) (g Xx)) (g (x0 (g x1))))
% Found x2:(P x1)
% Instantiate: Xx:=x1:fofType
% Found x2 as proof of (P0 Xx)
% Found eq_ref00:=(eq_ref0 (g Xx)):(((eq fofType) (g Xx)) (g Xx))
% Found (eq_ref0 (g Xx)) as proof of (((eq fofType) (g Xx)) (g (x0 (g x1))))
% Found ((eq_ref fofType) (g Xx)) as proof of (((eq fofType) (g Xx)) (g (x0 (g x1))))
% Found ((eq_ref fofType) (g Xx)) as proof of (((eq fofType) (g Xx)) (g (x0 (g x1))))
% Found ((eq_ref fofType) (g Xx)) as proof of (((eq fofType) (g Xx)) (g (x0 (g x1))))
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xx:fofType)=> (x0 (g Xx)))):(((eq (fofType->fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) (fun (x:fofType)=> (x0 (g x))))
% Found (eta_expansion_dep00 (fun (Xx:fofType)=> (x0 (g Xx)))) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) b0)
% Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) b0)
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) b0)
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) b0)
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) b0)
% Found eta_expansion_dep000:=(eta_expansion_dep00 b0):(((eq (fofType->fofType)) b0) (fun (x:fofType)=> (b0 x)))
% Found (eta_expansion_dep00 b0) as proof of (((eq (fofType->fofType)) b0) (fun (Xx:fofType)=> Xx))
% Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) b0) as proof of (((eq (fofType->fofType)) b0) (fun (Xx:fofType)=> Xx))
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) b0) as proof of (((eq (fofType->fofType)) b0) (fun (Xx:fofType)=> Xx))
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) b0) as proof of (((eq (fofType->fofType)) b0) (fun (Xx:fofType)=> Xx))
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) b0) as proof of (((eq (fofType->fofType)) b0) (fun (Xx:fofType)=> Xx))
% Found x2:(P x1)
% Instantiate: b:=x1:fofType
% Found x2 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_sym1000 ((eq_ref fofType) (x0 (g x1)))) x2) as proof of (P (x0 (g x1)))
% Found ((eq_sym1000 ((eq_ref fofType) (x0 (g x1)))) x2) as proof of (P (x0 (g x1)))
% Found (((fun (x3:(((eq fofType) (x0 (g x1))) b))=> ((eq_sym100 x3) P)) ((eq_ref fofType) (x0 (g x1)))) x2) as proof of (P (x0 (g x1)))
% Found (((fun (x3:(((eq fofType) (x0 (g x1))) x1))=> (((eq_sym10 x1) x3) P)) ((eq_ref fofType) (x0 (g x1)))) x2) as proof of (P (x0 (g x1)))
% Found (((fun (x3:(((eq fofType) (x0 (g x1))) x1))=> ((((eq_sym1 (x0 (g x1))) x1) x3) P)) ((eq_ref fofType) (x0 (g x1)))) x2) as proof of (P (x0 (g x1)))
% Found (((fun (x3:(((eq fofType) (x0 (g x1))) x1))=> (((((eq_sym fofType) (x0 (g x1))) x1) x3) P)) ((eq_ref fofType) (x0 (g x1)))) x2) as proof of (P (x0 (g x1)))
% Found (fun (x2:(P x1))=> (((fun (x3:(((eq fofType) (x0 (g x1))) x1))=> (((((eq_sym fofType) (x0 (g x1))) x1) x3) P)) ((eq_ref fofType) (x0 (g x1)))) x2)) as proof of (P (x0 (g x1)))
% Found (fun (P:(fofType->Prop)) (x2:(P x1))=> (((fun (x3:(((eq fofType) (x0 (g x1))) x1))=> (((((eq_sym fofType) (x0 (g x1))) x1) x3) P)) ((eq_ref fofType) (x0 (g x1)))) x2)) as proof of ((P x1)->(P (x0 (g x1))))
% Found x2:(P x1)
% Instantiate: b:=x1:fofType
% Found x2 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_sym1000 ((eq_ref fofType) (x0 (g x1)))) x2) as proof of (P (x0 (g x1)))
% Found ((eq_sym1000 ((eq_ref fofType) (x0 (g x1)))) x2) as proof of (P (x0 (g x1)))
% Found (((fun (x3:(((eq fofType) (x0 (g x1))) b))=> ((eq_sym100 x3) P)) ((eq_ref fofType) (x0 (g x1)))) x2) as proof of (P (x0 (g x1)))
% Found (((fun (x3:(((eq fofType) (x0 (g x1))) x1))=> (((eq_sym10 x1) x3) P)) ((eq_ref fofType) (x0 (g x1)))) x2) as proof of (P (x0 (g x1)))
% Found (((fun (x3:(((eq fofType) (x0 (g x1))) x1))=> ((((eq_sym1 (x0 (g x1))) x1) x3) P)) ((eq_ref fofType) (x0 (g x1)))) x2) as proof of (P (x0 (g x1)))
% Found (((fun (x3:(((eq fofType) (x0 (g x1))) x1))=> (((((eq_sym fofType) (x0 (g x1))) x1) x3) P)) ((eq_ref fofType) (x0 (g x1)))) x2) as proof of (P (x0 (g x1)))
% Found (fun (x2:(P x1))=> (((fun (x3:(((eq fofType) (x0 (g x1))) x1))=> (((((eq_sym fofType) (x0 (g x1))) x1) x3) P)) ((eq_ref fofType) (x0 (g x1)))) x2)) as proof of (P (x0 (g x1)))
% Found (fun (P:(fofType->Prop)) (x2:(P x1))=> (((fun (x3:(((eq fofType) (x0 (g x1))) x1))=> (((((eq_sym fofType) (x0 (g x1))) x1) x3) P)) ((eq_ref fofType) (x0 (g x1)))) x2)) as proof of ((P x1)->(P (x0 (g x1))))
% Found eq_ref00:=(eq_ref0 x1):(((eq fofType) x1) x1)
% Found (eq_ref0 x1) as proof of (((eq fofType) x1) b)
% Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 x1):(((eq fofType) x1) x1)
% Found (eq_ref0 x1) as proof of (((eq fofType) x1) b)
% Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 (g x1)))
% Found eq_ref000:=(eq_ref00 P1):((P1 (x0 (g x2)))->(P1 (x0 (g x2))))
% Found (eq_ref00 P1) as proof of ((P1 (x0 (g x2)))->(P1 (b x2)))
% Found ((eq_ref0 (x0 (g x2))) P1) as proof of ((P1 (x0 (g x2)))->(P1 (b x2)))
% Found (((eq_ref fofType) (x0 (g x2))) P1) as proof of ((P1 (x0 (g x2)))->(P1 (b x2)))
% Found (((eq_ref fofType) (x0 (g x2))) P1) as proof of ((P1 (x0 (g x2)))->(P1 (b x2)))
% Found (fun (P1:(fofType->Prop))=> (((eq_ref fofType) (x0 (g x2))) P1)) as proof of ((P1 (x0 (g x2)))->(P1 (b x2)))
% Found eq_ref000:=(eq_ref00 P1):((P1 (x0 (g x2)))->(P1 (x0 (g x2))))
% Found (eq_ref00 P1) as proof of ((P1 (x0 (g x2)))->(P1 (b x2)))
% Found ((eq_ref0 (x0 (g x2))) P1) as proof of ((P1 (x0 (g x2)))->(P1 (b x2)))
% Found (((eq_ref fofType) (x0 (g x2))) P1) as proof of ((P1 (x0 (g x2)))->(P1 (b x2)))
% Found (((eq_ref fofType) (x0 (g x2))) P1) as proof of ((P1 (x0 (g x2)))->(P1 (b x2)))
% Found (fun (P1:(fofType->Prop))=> (((eq_ref fofType) (x0 (g x2))) P1)) as proof of ((P1 (x0 (g x2)))->(P1 (b x2)))
% Found eq_ref00:=(eq_ref0 x1):(((eq fofType) x1) x1)
% Found (eq_ref0 x1) as proof of (((eq fofType) x1) b)
% Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 x1):(((eq fofType) x1) x1)
% Found (eq_ref0 x1) as proof of (((eq fofType) x1) b)
% Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 x1):(((eq fofType) x1) x1)
% Found (eq_ref0 x1) as proof of (((eq fofType) x1) b)
% Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 x1):(((eq fofType) x1) x1)
% Found (eq_ref0 x1) as proof of (((eq fofType) x1) b)
% Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym010 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym01 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x20 (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((x2 (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (eq_sym0000 (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found (eq_sym0000 (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((fun (x2:(((eq fofType) x1) (x0 (g x1))))=> ((eq_sym000 x2) P)) (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((fun (x2:(((eq fofType) x1) (x0 (g x1))))=> (((eq_sym00 (x0 (g x1))) x2) P)) (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((fun (x2:(((eq fofType) x1) (x0 (g x1))))=> ((((eq_sym0 x1) (x0 (g x1))) x2) P)) (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((fun (x2:(((eq fofType) x1) (x0 (g x1))))=> (((((eq_sym fofType) x1) (x0 (g x1))) x2) P)) (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found (fun (P:(fofType->Prop))=> ((fun (x2:(((eq fofType) x1) (x0 (g x1))))=> (((((eq_sym fofType) x1) (x0 (g x1))) x2) P)) (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found (fun (P:(fofType->Prop))=> ((fun (x2:(((eq fofType) x1) (x0 (g x1))))=> (((((eq_sym fofType) x1) (x0 (g x1))) x2) P)) (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym010 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym01 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x20 (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((x2 (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (eq_sym0000 (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found (eq_sym0000 (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((fun (x2:(((eq fofType) x1) (x0 (g x1))))=> ((eq_sym000 x2) P)) (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((fun (x2:(((eq fofType) x1) (x0 (g x1))))=> (((eq_sym00 (x0 (g x1))) x2) P)) (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((fun (x2:(((eq fofType) x1) (x0 (g x1))))=> ((((eq_sym0 x1) (x0 (g x1))) x2) P)) (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((fun (x2:(((eq fofType) x1) (x0 (g x1))))=> (((((eq_sym fofType) x1) (x0 (g x1))) x2) P)) (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found (fun (P:(fofType->Prop))=> ((fun (x2:(((eq fofType) x1) (x0 (g x1))))=> (((((eq_sym fofType) x1) (x0 (g x1))) x2) P)) (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found (fun (P:(fofType->Prop))=> ((fun (x2:(((eq fofType) x1) (x0 (g x1))))=> (((((eq_sym fofType) x1) (x0 (g x1))) x2) P)) (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym010 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym01 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x20 (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((x2 (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (eq_sym0000 (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found (eq_sym0000 (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((fun (x2:(((eq fofType) x1) (x0 (g x1))))=> ((eq_sym000 x2) P)) (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((fun (x2:(((eq fofType) x1) (x0 (g x1))))=> (((eq_sym00 (x0 (g x1))) x2) P)) (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((fun (x2:(((eq fofType) x1) (x0 (g x1))))=> ((((eq_sym0 x1) (x0 (g x1))) x2) P)) (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((fun (x2:(((eq fofType) x1) (x0 (g x1))))=> (((((eq_sym fofType) x1) (x0 (g x1))) x2) P)) (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found (fun (P:(fofType->Prop))=> ((fun (x2:(((eq fofType) x1) (x0 (g x1))))=> (((((eq_sym fofType) x1) (x0 (g x1))) x2) P)) (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym010 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym01 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x20 (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((x2 (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (eq_sym0000 (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found (eq_sym0000 (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((fun (x2:(((eq fofType) x1) (x0 (g x1))))=> ((eq_sym000 x2) P)) (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((fun (x2:(((eq fofType) x1) (x0 (g x1))))=> (((eq_sym00 (x0 (g x1))) x2) P)) (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((fun (x2:(((eq fofType) x1) (x0 (g x1))))=> ((((eq_sym0 x1) (x0 (g x1))) x2) P)) (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found ((fun (x2:(((eq fofType) x1) (x0 (g x1))))=> (((((eq_sym fofType) x1) (x0 (g x1))) x2) P)) (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found (fun (P:(fofType->Prop))=> ((fun (x2:(((eq fofType) x1) (x0 (g x1))))=> (((((eq_sym fofType) x1) (x0 (g x1))) x2) P)) (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))))) as proof of ((P (x0 (g x1)))->(P x1))
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref (fofType->fofType)) b) P) as proof of (P0 b)
% Found (((eq_ref (fofType->fofType)) b) P) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym010 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym01 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x20 (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((x2 (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (eq_sym000 (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found ((eq_sym00 (x0 (g x1))) (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found (((eq_sym0 x1) (x0 (g x1))) (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found ((((eq_sym fofType) x1) (x0 (g x1))) (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found ((((eq_sym fofType) x1) (x0 (g x1))) (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym010 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym01 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x20 (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((x2 (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (eq_sym000 (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found ((eq_sym00 (x0 (g x1))) (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found (((eq_sym0 x1) (x0 (g x1))) (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found ((((eq_sym fofType) x1) (x0 (g x1))) (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found ((((eq_sym fofType) x1) (x0 (g x1))) (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym010 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym01 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x20 (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((x2 (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (eq_sym000 (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found ((eq_sym00 (x0 (g x1))) (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found (((eq_sym0 x1) (x0 (g x1))) (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found ((((eq_sym fofType) x1) (x0 (g x1))) (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found ((((eq_sym fofType) x1) (x0 (g x1))) (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym010 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym01 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x20 (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((x2 (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (eq_sym000 (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found ((eq_sym00 (x0 (g x1))) (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found (((eq_sym0 x1) (x0 (g x1))) (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found ((((eq_sym fofType) x1) (x0 (g x1))) (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found ((((eq_sym fofType) x1) (x0 (g x1))) (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym010 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym01 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x20 (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((x2 (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (eq_sym000 (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_sym00 (x0 (g x1))) (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (((eq_sym0 x1) (x0 (g x1))) (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((((eq_sym fofType) x1) (x0 (g x1))) (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym010 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym01 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x20 (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((x2 (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (eq_sym000 (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_sym00 (x0 (g x1))) (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (((eq_sym0 x1) (x0 (g x1))) (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((((eq_sym fofType) x1) (x0 (g x1))) (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym010 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym01 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x20 (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((x2 (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (eq_sym000 (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_sym00 (x0 (g x1))) (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (((eq_sym0 x1) (x0 (g x1))) (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((((eq_sym fofType) x1) (x0 (g x1))) (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym010 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym01 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x20 (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((x2 (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (eq_sym000 (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_sym00 (x0 (g x1))) (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (((eq_sym0 x1) (x0 (g x1))) (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((((eq_sym fofType) x1) (x0 (g x1))) (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym10 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x200 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P x1)->(P (x0 (g x1))))
% Found (x200 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((x20 x3) P)) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> (((x2 (x0 (g x1))) x3) P)) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((((x x1) (x0 (g x1))) x3) P)) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P x1)->(P (x0 (g x1))))
% Found (fun (P:(fofType->Prop))=> ((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((((x x1) (x0 (g x1))) x3) P)) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of ((P x1)->(P (x0 (g x1))))
% Found (fun (P:(fofType->Prop))=> ((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((((x x1) (x0 (g x1))) x3) P)) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym10 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((x200 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((x200 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found (((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((x20 x3) (fun (x5:fofType)=> ((P x1)->(P x5))))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found (((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> (((x2 (x0 (g x1))) x3) (fun (x5:fofType)=> ((P x1)->(P x5))))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found (((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((((x x1) (x0 (g x1))) x3) (fun (x5:fofType)=> ((P x1)->(P x5))))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found (fun (P:(fofType->Prop))=> (((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((((x x1) (x0 (g x1))) x3) (fun (x5:fofType)=> ((P x1)->(P x5))))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P))) as proof of ((P x1)->(P (x0 (g x1))))
% Found (fun (P:(fofType->Prop))=> (((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((((x x1) (x0 (g x1))) x3) (fun (x5:fofType)=> ((P x1)->(P x5))))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym10 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((x200 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((x200 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found (((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((x20 x3) (fun (x5:fofType)=> ((P x1)->(P x5))))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found (((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> (((x2 (x0 (g x1))) x3) (fun (x5:fofType)=> ((P x1)->(P x5))))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found (((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((((x x1) (x0 (g x1))) x3) (fun (x5:fofType)=> ((P x1)->(P x5))))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found (fun (P:(fofType->Prop))=> (((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((((x x1) (x0 (g x1))) x3) (fun (x5:fofType)=> ((P x1)->(P x5))))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P))) as proof of ((P x1)->(P (x0 (g x1))))
% Found (fun (P:(fofType->Prop))=> (((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((((x x1) (x0 (g x1))) x3) (fun (x5:fofType)=> ((P x1)->(P x5))))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym10 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x200 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P x1)->(P (x0 (g x1))))
% Found (x200 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((x20 x3) P)) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> (((x2 (x0 (g x1))) x3) P)) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((((x x1) (x0 (g x1))) x3) P)) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P x1)->(P (x0 (g x1))))
% Found (fun (P:(fofType->Prop))=> ((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((((x x1) (x0 (g x1))) x3) P)) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of ((P x1)->(P (x0 (g x1))))
% Found (fun (P:(fofType->Prop))=> ((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((((x x1) (x0 (g x1))) x3) P)) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym10 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x20 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found ((x2 (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym10 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x20 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found ((x2 (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym10 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x20 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found ((x2 (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym10 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x20 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found ((x2 (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym10 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x20 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found ((x2 (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym10 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x20 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found ((x2 (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym10 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((x200 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((x200 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found (((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((x20 x3) (fun (x5:fofType)=> ((P x1)->(P x5))))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found (((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> (((x2 (x0 (g x1))) x3) (fun (x5:fofType)=> ((P x1)->(P x5))))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found (((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((((x x1) (x0 (g x1))) x3) (fun (x5:fofType)=> ((P x1)->(P x5))))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found (fun (P:(fofType->Prop))=> (((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((((x x1) (x0 (g x1))) x3) (fun (x5:fofType)=> ((P x1)->(P x5))))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P))) as proof of ((P x1)->(P (x0 (g x1))))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym10 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x200 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P x1)->(P (x0 (g x1))))
% Found (x200 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((x20 x3) P)) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> (((x2 (x0 (g x1))) x3) P)) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((((x x1) (x0 (g x1))) x3) P)) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P x1)->(P (x0 (g x1))))
% Found (fun (P:(fofType->Prop))=> ((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((((x x1) (x0 (g x1))) x3) P)) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of ((P x1)->(P (x0 (g x1))))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym10 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x200 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P x1)->(P (x0 (g x1))))
% Found (x200 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((x20 x3) P)) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> (((x2 (x0 (g x1))) x3) P)) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((((x x1) (x0 (g x1))) x3) P)) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P x1)->(P (x0 (g x1))))
% Found (fun (P:(fofType->Prop))=> ((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((((x x1) (x0 (g x1))) x3) P)) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of ((P x1)->(P (x0 (g x1))))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym10 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((x200 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((x200 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found (((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((x20 x3) (fun (x5:fofType)=> ((P x1)->(P x5))))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found (((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> (((x2 (x0 (g x1))) x3) (fun (x5:fofType)=> ((P x1)->(P x5))))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found (((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((((x x1) (x0 (g x1))) x3) (fun (x5:fofType)=> ((P x1)->(P x5))))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found (fun (P:(fofType->Prop))=> (((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((((x x1) (x0 (g x1))) x3) (fun (x5:fofType)=> ((P x1)->(P x5))))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P))) as proof of ((P x1)->(P (x0 (g x1))))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym10 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x20 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found ((x2 (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym10 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x200 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P x1)->(P (x0 (g x1))))
% Found (x200 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((x20 x3) P)) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> (((x2 (x0 (g x1))) x3) P)) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((((x x1) (x0 (g x1))) x3) P)) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P x1)->(P (x0 (g x1))))
% Found (fun (P:(fofType->Prop))=> ((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((((x x1) (x0 (g x1))) x3) P)) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of ((P x1)->(P (x0 (g x1))))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym10 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((x200 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((x200 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found (((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((x20 x3) (fun (x5:fofType)=> ((P x1)->(P x5))))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found (((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> (((x2 (x0 (g x1))) x3) (fun (x5:fofType)=> ((P x1)->(P x5))))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found (((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((((x x1) (x0 (g x1))) x3) (fun (x5:fofType)=> ((P x1)->(P x5))))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found (fun (P:(fofType->Prop))=> (((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((((x x1) (x0 (g x1))) x3) (fun (x5:fofType)=> ((P x1)->(P x5))))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P))) as proof of ((P x1)->(P (x0 (g x1))))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym10 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x20 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found ((x2 (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym10 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((x200 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((x200 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found (((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((x20 x3) (fun (x5:fofType)=> ((P x1)->(P x5))))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found (((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> (((x2 (x0 (g x1))) x3) (fun (x5:fofType)=> ((P x1)->(P x5))))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found (((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((((x x1) (x0 (g x1))) x3) (fun (x5:fofType)=> ((P x1)->(P x5))))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found (fun (P:(fofType->Prop))=> (((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((((x x1) (x0 (g x1))) x3) (fun (x5:fofType)=> ((P x1)->(P x5))))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P))) as proof of ((P x1)->(P (x0 (g x1))))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym10 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x200 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P x1)->(P (x0 (g x1))))
% Found (x200 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((x20 x3) P)) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> (((x2 (x0 (g x1))) x3) P)) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((((x x1) (x0 (g x1))) x3) P)) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P x1)->(P (x0 (g x1))))
% Found (fun (P:(fofType->Prop))=> ((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((((x x1) (x0 (g x1))) x3) P)) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of ((P x1)->(P (x0 (g x1))))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (eq_sym1000 ((eq_ref fofType) (x0 (g x1)))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (eq_sym1000 ((eq_ref fofType) (x0 (g x1)))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> ((eq_sym100 x2) P1)) ((eq_ref fofType) (x0 (g x1)))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((eq_sym10 x1) x2) P1)) ((eq_ref fofType) (x0 (g x1)))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> ((((eq_sym1 (x0 (g x1))) x1) x2) P1)) ((eq_ref fofType) (x0 (g x1)))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((((eq_sym fofType) (x0 (g x1))) x1) x2) P1)) ((eq_ref fofType) (x0 (g x1)))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (fun (P1:(fofType->Prop))=> ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((((eq_sym fofType) (x0 (g x1))) x1) x2) P1)) ((eq_ref fofType) (x0 (g x1))))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (eq_sym1000 ((eq_ref fofType) (x0 (g x1)))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (eq_sym1000 ((eq_ref fofType) (x0 (g x1)))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> ((eq_sym100 x2) P1)) ((eq_ref fofType) (x0 (g x1)))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((eq_sym10 x1) x2) P1)) ((eq_ref fofType) (x0 (g x1)))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> ((((eq_sym1 (x0 (g x1))) x1) x2) P1)) ((eq_ref fofType) (x0 (g x1)))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((((eq_sym fofType) (x0 (g x1))) x1) x2) P1)) ((eq_ref fofType) (x0 (g x1)))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (fun (P1:(fofType->Prop))=> ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((((eq_sym fofType) (x0 (g x1))) x1) x2) P1)) ((eq_ref fofType) (x0 (g x1))))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (eq_sym1000 ((eq_ref fofType) (x0 (g x1)))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (eq_sym1000 ((eq_ref fofType) (x0 (g x1)))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> ((eq_sym100 x2) P1)) ((eq_ref fofType) (x0 (g x1)))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((eq_sym10 x1) x2) P1)) ((eq_ref fofType) (x0 (g x1)))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> ((((eq_sym1 (x0 (g x1))) x1) x2) P1)) ((eq_ref fofType) (x0 (g x1)))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((((eq_sym fofType) (x0 (g x1))) x1) x2) P1)) ((eq_ref fofType) (x0 (g x1)))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (fun (P1:(fofType->Prop))=> ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((((eq_sym fofType) (x0 (g x1))) x1) x2) P1)) ((eq_ref fofType) (x0 (g x1))))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (eq_sym1000 ((eq_ref fofType) (x0 (g x1)))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (eq_sym1000 ((eq_ref fofType) (x0 (g x1)))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> ((eq_sym100 x2) P1)) ((eq_ref fofType) (x0 (g x1)))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((eq_sym10 x1) x2) P1)) ((eq_ref fofType) (x0 (g x1)))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> ((((eq_sym1 (x0 (g x1))) x1) x2) P1)) ((eq_ref fofType) (x0 (g x1)))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((((eq_sym fofType) (x0 (g x1))) x1) x2) P1)) ((eq_ref fofType) (x0 (g x1)))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (fun (P1:(fofType->Prop))=> ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((((eq_sym fofType) (x0 (g x1))) x1) x2) P1)) ((eq_ref fofType) (x0 (g x1))))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (eq_sym1000 ((eq_ref fofType) (x0 (g x1)))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (eq_sym1000 ((eq_ref fofType) (x0 (g x1)))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> ((eq_sym100 x2) P1)) ((eq_ref fofType) (x0 (g x1)))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((eq_sym10 x1) x2) P1)) ((eq_ref fofType) (x0 (g x1)))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> ((((eq_sym1 (x0 (g x1))) x1) x2) P1)) ((eq_ref fofType) (x0 (g x1)))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((((eq_sym fofType) (x0 (g x1))) x1) x2) P1)) ((eq_ref fofType) (x0 (g x1)))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (fun (P1:(fofType->Prop))=> ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((((eq_sym fofType) (x0 (g x1))) x1) x2) P1)) ((eq_ref fofType) (x0 (g x1))))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (eq_sym1000 ((eq_ref fofType) (x0 (g x1)))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (eq_sym1000 ((eq_ref fofType) (x0 (g x1)))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> ((eq_sym100 x2) P1)) ((eq_ref fofType) (x0 (g x1)))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((eq_sym10 x1) x2) P1)) ((eq_ref fofType) (x0 (g x1)))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> ((((eq_sym1 (x0 (g x1))) x1) x2) P1)) ((eq_ref fofType) (x0 (g x1)))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((((eq_sym fofType) (x0 (g x1))) x1) x2) P1)) ((eq_ref fofType) (x0 (g x1)))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (fun (P1:(fofType->Prop))=> ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((((eq_sym fofType) (x0 (g x1))) x1) x2) P1)) ((eq_ref fofType) (x0 (g x1))))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (eq_sym1000 ((eq_ref fofType) (x0 (g x1)))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (eq_sym1000 ((eq_ref fofType) (x0 (g x1)))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> ((eq_sym100 x2) P1)) ((eq_ref fofType) (x0 (g x1)))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((eq_sym10 x1) x2) P1)) ((eq_ref fofType) (x0 (g x1)))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> ((((eq_sym1 (x0 (g x1))) x1) x2) P1)) ((eq_ref fofType) (x0 (g x1)))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((((eq_sym fofType) (x0 (g x1))) x1) x2) P1)) ((eq_ref fofType) (x0 (g x1)))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (fun (P1:(fofType->Prop))=> ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((((eq_sym fofType) (x0 (g x1))) x1) x2) P1)) ((eq_ref fofType) (x0 (g x1))))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (eq_sym1000 ((eq_ref fofType) (x0 (g x1)))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (eq_sym1000 ((eq_ref fofType) (x0 (g x1)))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> ((eq_sym100 x2) P1)) ((eq_ref fofType) (x0 (g x1)))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((eq_sym10 x1) x2) P1)) ((eq_ref fofType) (x0 (g x1)))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> ((((eq_sym1 (x0 (g x1))) x1) x2) P1)) ((eq_ref fofType) (x0 (g x1)))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((((eq_sym fofType) (x0 (g x1))) x1) x2) P1)) ((eq_ref fofType) (x0 (g x1)))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (fun (P1:(fofType->Prop))=> ((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((((eq_sym fofType) (x0 (g x1))) x1) x2) P1)) ((eq_ref fofType) (x0 (g x1))))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym10 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x20 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((x2 (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym10 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x20 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((x2 (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym10 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x20 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((x2 (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym10 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x20 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((x2 (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym10 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x20 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((x2 (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym10 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x20 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((x2 (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym10 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x20 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((x2 (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym10 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x20 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((x2 (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym10 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x20 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((x2 (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym10 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x20 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((x2 (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym10 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x20 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((x2 (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym10 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x20 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((x2 (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym10 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x20 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((x2 (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym10 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x20 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((x2 (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym10 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x20 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((x2 (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym10 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x20 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((x2 (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((eq_sym10 x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((eq_sym1 (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((eq_sym10 x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((eq_sym1 (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((eq_sym10 x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((eq_sym1 (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((eq_sym10 x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((eq_sym1 (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((eq_sym10 x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((eq_sym1 (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((eq_sym10 x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((eq_sym1 (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((eq_sym10 x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((eq_sym1 (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((eq_sym10 x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((eq_sym1 (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref000:=(eq_ref00 P1):((P1 x1)->(P1 x1))
% Found (eq_ref00 P1) as proof of (P2 x1)
% Found ((eq_ref0 x1) P1) as proof of (P2 x1)
% Found (((eq_ref fofType) x1) P1) as proof of (P2 x1)
% Found (((eq_ref fofType) x1) P1) as proof of (P2 x1)
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_sym1000 ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found ((eq_sym1000 ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> ((eq_sym100 x2) (fun (x4:fofType)=> ((P1 x1)->(P1 x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((eq_sym10 x1) x2) (fun (x4:fofType)=> ((P1 x1)->(P1 x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> ((((eq_sym1 (x0 (g x1))) x1) x2) (fun (x4:fofType)=> ((P1 x1)->(P1 x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((((eq_sym fofType) (x0 (g x1))) x1) x2) (fun (x4:fofType)=> ((P1 x1)->(P1 x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (fun (P1:(fofType->Prop))=> (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((((eq_sym fofType) (x0 (g x1))) x1) x2) (fun (x4:fofType)=> ((P1 x1)->(P1 x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P1))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found eq_ref000:=(eq_ref00 P1):((P1 x1)->(P1 x1))
% Found (eq_ref00 P1) as proof of (P2 x1)
% Found ((eq_ref0 x1) P1) as proof of (P2 x1)
% Found (((eq_ref fofType) x1) P1) as proof of (P2 x1)
% Found (((eq_ref fofType) x1) P1) as proof of (P2 x1)
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_sym1000 ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found ((eq_sym1000 ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> ((eq_sym100 x2) (fun (x4:fofType)=> ((P1 x1)->(P1 x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((eq_sym10 x1) x2) (fun (x4:fofType)=> ((P1 x1)->(P1 x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> ((((eq_sym1 (x0 (g x1))) x1) x2) (fun (x4:fofType)=> ((P1 x1)->(P1 x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((((eq_sym fofType) (x0 (g x1))) x1) x2) (fun (x4:fofType)=> ((P1 x1)->(P1 x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (fun (P1:(fofType->Prop))=> (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((((eq_sym fofType) (x0 (g x1))) x1) x2) (fun (x4:fofType)=> ((P1 x1)->(P1 x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P1))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found eq_ref000:=(eq_ref00 P1):((P1 x1)->(P1 x1))
% Found (eq_ref00 P1) as proof of (P2 x1)
% Found ((eq_ref0 x1) P1) as proof of (P2 x1)
% Found (((eq_ref fofType) x1) P1) as proof of (P2 x1)
% Found (((eq_ref fofType) x1) P1) as proof of (P2 x1)
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_sym1000 ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found ((eq_sym1000 ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> ((eq_sym100 x2) (fun (x4:fofType)=> ((P1 x1)->(P1 x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((eq_sym10 x1) x2) (fun (x4:fofType)=> ((P1 x1)->(P1 x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> ((((eq_sym1 (x0 (g x1))) x1) x2) (fun (x4:fofType)=> ((P1 x1)->(P1 x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((((eq_sym fofType) (x0 (g x1))) x1) x2) (fun (x4:fofType)=> ((P1 x1)->(P1 x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (fun (P1:(fofType->Prop))=> (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((((eq_sym fofType) (x0 (g x1))) x1) x2) (fun (x4:fofType)=> ((P1 x1)->(P1 x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P1))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found eq_ref000:=(eq_ref00 P1):((P1 x1)->(P1 x1))
% Found (eq_ref00 P1) as proof of (P2 x1)
% Found ((eq_ref0 x1) P1) as proof of (P2 x1)
% Found (((eq_ref fofType) x1) P1) as proof of (P2 x1)
% Found (((eq_ref fofType) x1) P1) as proof of (P2 x1)
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_sym1000 ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found ((eq_sym1000 ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> ((eq_sym100 x2) (fun (x4:fofType)=> ((P1 x1)->(P1 x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((eq_sym10 x1) x2) (fun (x4:fofType)=> ((P1 x1)->(P1 x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> ((((eq_sym1 (x0 (g x1))) x1) x2) (fun (x4:fofType)=> ((P1 x1)->(P1 x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((((eq_sym fofType) (x0 (g x1))) x1) x2) (fun (x4:fofType)=> ((P1 x1)->(P1 x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (fun (P1:(fofType->Prop))=> (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((((eq_sym fofType) (x0 (g x1))) x1) x2) (fun (x4:fofType)=> ((P1 x1)->(P1 x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P1))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found eq_ref000:=(eq_ref00 P1):((P1 x1)->(P1 x1))
% Found (eq_ref00 P1) as proof of (P2 x1)
% Found ((eq_ref0 x1) P1) as proof of (P2 x1)
% Found (((eq_ref fofType) x1) P1) as proof of (P2 x1)
% Found (((eq_ref fofType) x1) P1) as proof of (P2 x1)
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_sym1000 ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found ((eq_sym1000 ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> ((eq_sym100 x2) (fun (x4:fofType)=> ((P1 x1)->(P1 x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((eq_sym10 x1) x2) (fun (x4:fofType)=> ((P1 x1)->(P1 x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> ((((eq_sym1 (x0 (g x1))) x1) x2) (fun (x4:fofType)=> ((P1 x1)->(P1 x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((((eq_sym fofType) (x0 (g x1))) x1) x2) (fun (x4:fofType)=> ((P1 x1)->(P1 x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (fun (P1:(fofType->Prop))=> (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((((eq_sym fofType) (x0 (g x1))) x1) x2) (fun (x4:fofType)=> ((P1 x1)->(P1 x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P1))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found eq_ref000:=(eq_ref00 P1):((P1 x1)->(P1 x1))
% Found (eq_ref00 P1) as proof of (P2 x1)
% Found ((eq_ref0 x1) P1) as proof of (P2 x1)
% Found (((eq_ref fofType) x1) P1) as proof of (P2 x1)
% Found (((eq_ref fofType) x1) P1) as proof of (P2 x1)
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_sym1000 ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found ((eq_sym1000 ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> ((eq_sym100 x2) (fun (x4:fofType)=> ((P1 x1)->(P1 x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((eq_sym10 x1) x2) (fun (x4:fofType)=> ((P1 x1)->(P1 x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> ((((eq_sym1 (x0 (g x1))) x1) x2) (fun (x4:fofType)=> ((P1 x1)->(P1 x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((((eq_sym fofType) (x0 (g x1))) x1) x2) (fun (x4:fofType)=> ((P1 x1)->(P1 x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (fun (P1:(fofType->Prop))=> (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((((eq_sym fofType) (x0 (g x1))) x1) x2) (fun (x4:fofType)=> ((P1 x1)->(P1 x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P1))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found eq_ref000:=(eq_ref00 P1):((P1 x1)->(P1 x1))
% Found (eq_ref00 P1) as proof of (P2 x1)
% Found ((eq_ref0 x1) P1) as proof of (P2 x1)
% Found (((eq_ref fofType) x1) P1) as proof of (P2 x1)
% Found (((eq_ref fofType) x1) P1) as proof of (P2 x1)
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_sym1000 ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found ((eq_sym1000 ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> ((eq_sym100 x2) (fun (x4:fofType)=> ((P1 x1)->(P1 x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((eq_sym10 x1) x2) (fun (x4:fofType)=> ((P1 x1)->(P1 x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> ((((eq_sym1 (x0 (g x1))) x1) x2) (fun (x4:fofType)=> ((P1 x1)->(P1 x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((((eq_sym fofType) (x0 (g x1))) x1) x2) (fun (x4:fofType)=> ((P1 x1)->(P1 x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (fun (P1:(fofType->Prop))=> (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((((eq_sym fofType) (x0 (g x1))) x1) x2) (fun (x4:fofType)=> ((P1 x1)->(P1 x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P1))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found eq_ref000:=(eq_ref00 P1):((P1 x1)->(P1 x1))
% Found (eq_ref00 P1) as proof of (P2 x1)
% Found ((eq_ref0 x1) P1) as proof of (P2 x1)
% Found (((eq_ref fofType) x1) P1) as proof of (P2 x1)
% Found (((eq_ref fofType) x1) P1) as proof of (P2 x1)
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_sym1000 ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found ((eq_sym1000 ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> ((eq_sym100 x2) (fun (x4:fofType)=> ((P1 x1)->(P1 x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((eq_sym10 x1) x2) (fun (x4:fofType)=> ((P1 x1)->(P1 x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> ((((eq_sym1 (x0 (g x1))) x1) x2) (fun (x4:fofType)=> ((P1 x1)->(P1 x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((((eq_sym fofType) (x0 (g x1))) x1) x2) (fun (x4:fofType)=> ((P1 x1)->(P1 x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (fun (P1:(fofType->Prop))=> (((fun (x2:(((eq fofType) (x0 (g x1))) x1))=> (((((eq_sym fofType) (x0 (g x1))) x1) x2) (fun (x4:fofType)=> ((P1 x1)->(P1 x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) x1) P1))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found eq_ref00:=(eq_ref0 (x0 (g x2))):(((eq fofType) (x0 (g x2))) (x0 (g x2)))
% Found (eq_ref0 (x0 (g x2))) as proof of (((eq fofType) (x0 (g x2))) (f x2))
% Found ((eq_ref fofType) (x0 (g x2))) as proof of (((eq fofType) (x0 (g x2))) (f x2))
% Found ((eq_ref fofType) (x0 (g x2))) as proof of (((eq fofType) (x0 (g x2))) (f x2))
% Found ((eq_ref fofType) (x0 (g x2))) as proof of (((eq fofType) (x0 (g x2))) (f x2))
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x2)))) as proof of (((eq fofType) (f x2)) (x0 (g x2)))
% Found ((eq_sym10 (f x2)) ((eq_ref fofType) (x0 (g x2)))) as proof of (((eq fofType) (f x2)) (x0 (g x2)))
% Found (((eq_sym1 (x0 (g x2))) (f x2)) ((eq_ref fofType) (x0 (g x2)))) as proof of (((eq fofType) (f x2)) (x0 (g x2)))
% Found ((((eq_sym fofType) (x0 (g x2))) (f x2)) ((eq_ref fofType) (x0 (g x2)))) as proof of (((eq fofType) (f x2)) (x0 (g x2)))
% Found eq_ref00:=(eq_ref0 (x0 (g x2))):(((eq fofType) (x0 (g x2))) (x0 (g x2)))
% Found (eq_ref0 (x0 (g x2))) as proof of (((eq fofType) (x0 (g x2))) (f x2))
% Found ((eq_ref fofType) (x0 (g x2))) as proof of (((eq fofType) (x0 (g x2))) (f x2))
% Found ((eq_ref fofType) (x0 (g x2))) as proof of (((eq fofType) (x0 (g x2))) (f x2))
% Found ((eq_ref fofType) (x0 (g x2))) as proof of (((eq fofType) (x0 (g x2))) (f x2))
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x2)))) as proof of (((eq fofType) (f x2)) (x0 (g x2)))
% Found ((eq_sym10 (f x2)) ((eq_ref fofType) (x0 (g x2)))) as proof of (((eq fofType) (f x2)) (x0 (g x2)))
% Found (((eq_sym1 (x0 (g x2))) (f x2)) ((eq_ref fofType) (x0 (g x2)))) as proof of (((eq fofType) (f x2)) (x0 (g x2)))
% Found ((((eq_sym fofType) (x0 (g x2))) (f x2)) ((eq_ref fofType) (x0 (g x2)))) as proof of (((eq fofType) (f x2)) (x0 (g x2)))
% Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (Xx:fofType)=> Xx))->(P (fun (x:fofType)=> x)))
% Found (eta_expansion_dep000 P) as proof of (P0 (fun (Xx:fofType)=> Xx))
% Found ((eta_expansion_dep00 (fun (Xx:fofType)=> Xx)) P) as proof of (P0 (fun (Xx:fofType)=> Xx))
% Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (Xx:fofType)=> Xx)) P) as proof of (P0 (fun (Xx:fofType)=> Xx))
% Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (Xx:fofType)=> Xx)) P) as proof of (P0 (fun (Xx:fofType)=> Xx))
% Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (Xx:fofType)=> Xx)) P) as proof of (P0 (fun (Xx:fofType)=> Xx))
% Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (Xx:fofType)=> Xx))->(P (fun (x:fofType)=> x)))
% Found (eta_expansion_dep000 P) as proof of (P0 (fun (Xx:fofType)=> Xx))
% Found ((eta_expansion_dep00 (fun (Xx:fofType)=> Xx)) P) as proof of (P0 (fun (Xx:fofType)=> Xx))
% Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (Xx:fofType)=> Xx)) P) as proof of (P0 (fun (Xx:fofType)=> Xx))
% Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (Xx:fofType)=> Xx)) P) as proof of (P0 (fun (Xx:fofType)=> Xx))
% Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (Xx:fofType)=> Xx)) P) as proof of (P0 (fun (Xx:fofType)=> Xx))
% Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P b)->(P (fun (x:fofType)=> (b x))))
% Found (eta_expansion_dep000 P) as proof of (P0 b)
% Found ((eta_expansion_dep00 b) P) as proof of (P0 b)
% Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) b) P) as proof of (P0 b)
% Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) b) P) as proof of (P0 b)
% Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) b) P) as proof of (P0 b)
% Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P b)->(P (fun (x:fofType)=> (b x))))
% Found (eta_expansion_dep000 P) as proof of (P0 b)
% Found ((eta_expansion_dep00 b) P) as proof of (P0 b)
% Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) b) P) as proof of (P0 b)
% Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) b) P) as proof of (P0 b)
% Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) b) P) as proof of (P0 b)
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xx:fofType)=> Xx)):(((eq (fofType->fofType)) (fun (Xx:fofType)=> Xx)) (fun (x:fofType)=> x))
% Found (eta_expansion_dep00 (fun (Xx:fofType)=> Xx)) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> Xx)) b0)
% Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (Xx:fofType)=> Xx)) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> Xx)) b0)
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (Xx:fofType)=> Xx)) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> Xx)) b0)
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (Xx:fofType)=> Xx)) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> Xx)) b0)
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (Xx:fofType)=> Xx)) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> Xx)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq (fofType->fofType)) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq (fofType->fofType)) b0) b)
% Found ((eq_ref (fofType->fofType)) b0) as proof of (((eq (fofType->fofType)) b0) b)
% Found ((eq_ref (fofType->fofType)) b0) as proof of (((eq (fofType->fofType)) b0) b)
% Found ((eq_ref (fofType->fofType)) b0) as proof of (((eq (fofType->fofType)) b0) b)
% Found eq_ref00:=(eq_ref0 (g (x0 (g x2)))):(((eq fofType) (g (x0 (g x2)))) (g (x0 (g x2))))
% Found (eq_ref0 (g (x0 (g x2)))) as proof of (((eq fofType) (g (x0 (g x2)))) (g (b x2)))
% Found ((eq_ref fofType) (g (x0 (g x2)))) as proof of (((eq fofType) (g (x0 (g x2)))) (g (b x2)))
% Found ((eq_ref fofType) (g (x0 (g x2)))) as proof of (((eq fofType) (g (x0 (g x2)))) (g (b x2)))
% Found ((eq_ref fofType) (g (x0 (g x2)))) as proof of (((eq fofType) (g (x0 (g x2)))) (g (b x2)))
% Found (x30 ((eq_ref fofType) (g (x0 (g x2))))) as proof of (((eq fofType) (x0 (g x2))) (b x2))
% Found ((x3 (b x2)) ((eq_ref fofType) (g (x0 (g x2))))) as proof of (((eq fofType) (x0 (g x2))) (b x2))
% Found (((x (x0 (g x2))) (b x2)) ((eq_ref fofType) (g (x0 (g x2))))) as proof of (((eq fofType) (x0 (g x2))) (b x2))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x2)))):(((eq fofType) (g (x0 (g x2)))) (g (x0 (g x2))))
% Found (eq_ref0 (g (x0 (g x2)))) as proof of (((eq fofType) (g (x0 (g x2)))) (g (b x2)))
% Found ((eq_ref fofType) (g (x0 (g x2)))) as proof of (((eq fofType) (g (x0 (g x2)))) (g (b x2)))
% Found ((eq_ref fofType) (g (x0 (g x2)))) as proof of (((eq fofType) (g (x0 (g x2)))) (g (b x2)))
% Found ((eq_ref fofType) (g (x0 (g x2)))) as proof of (((eq fofType) (g (x0 (g x2)))) (g (b x2)))
% Found (x30 ((eq_ref fofType) (g (x0 (g x2))))) as proof of (((eq fofType) (x0 (g x2))) (b x2))
% Found ((x3 (b x2)) ((eq_ref fofType) (g (x0 (g x2))))) as proof of (((eq fofType) (x0 (g x2))) (b x2))
% Found (((x (x0 (g x2))) (b x2)) ((eq_ref fofType) (g (x0 (g x2))))) as proof of (((eq fofType) (x0 (g x2))) (b x2))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P (b x1))))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P (b x1))))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P (b x1))))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P (b x1))))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P (b x1))))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P (b x1))))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P (b x1))))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P (b x1))))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found eq_ref000:=(eq_ref00 P):((P x1)->(P x1))
% Found (eq_ref00 P) as proof of (P0 x1)
% Found ((eq_ref0 x1) P) as proof of (P0 x1)
% Found (((eq_ref fofType) x1) P) as proof of (P0 x1)
% Found (((eq_ref fofType) x1) P) as proof of (P0 x1)
% Found eq_ref000:=(eq_ref00 P):((P x1)->(P x1))
% Found (eq_ref00 P) as proof of (P0 x1)
% Found ((eq_ref0 x1) P) as proof of (P0 x1)
% Found (((eq_ref fofType) x1) P) as proof of (P0 x1)
% Found (((eq_ref fofType) x1) P) as proof of (P0 x1)
% Found eq_ref00:=(eq_ref0 x1):(((eq fofType) x1) x1)
% Found (eq_ref0 x1) as proof of (((eq fofType) x1) b)
% Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 x1):(((eq fofType) x1) x1)
% Found (eq_ref0 x1) as proof of (((eq fofType) x1) b)
% Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 x1):(((eq fofType) x1) x1)
% Found (eq_ref0 x1) as proof of (((eq fofType) x1) b)
% Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 x1):(((eq fofType) x1) x1)
% Found (eq_ref0 x1) as proof of (((eq fofType) x1) b)
% Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 x1):(((eq fofType) x1) x1)
% Found (eq_ref0 x1) as proof of (((eq fofType) x1) b)
% Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 x1):(((eq fofType) x1) x1)
% Found (eq_ref0 x1) as proof of (((eq fofType) x1) b)
% Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 x1):(((eq fofType) x1) x1)
% Found (eq_ref0 x1) as proof of (((eq fofType) x1) b)
% Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 x1):(((eq fofType) x1) x1)
% Found (eq_ref0 x1) as proof of (((eq fofType) x1) b)
% Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 x1):(((eq fofType) x1) x1)
% Found (eq_ref0 x1) as proof of (((eq fofType) x1) b)
% Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 x1):(((eq fofType) x1) x1)
% Found (eq_ref0 x1) as proof of (((eq fofType) x1) b)
% Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 x1):(((eq fofType) x1) x1)
% Found (eq_ref0 x1) as proof of (((eq fofType) x1) b)
% Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 x1):(((eq fofType) x1) x1)
% Found (eq_ref0 x1) as proof of (((eq fofType) x1) b)
% Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym010 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym01 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x20 (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((x2 (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (eq_sym0000 (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found (eq_sym0000 (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found ((fun (x2:(((eq fofType) x1) (x0 (g x1))))=> ((eq_sym000 x2) P1)) (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found ((fun (x2:(((eq fofType) x1) (x0 (g x1))))=> (((eq_sym00 (x0 (g x1))) x2) P1)) (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found ((fun (x2:(((eq fofType) x1) (x0 (g x1))))=> ((((eq_sym0 x1) (x0 (g x1))) x2) P1)) (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found ((fun (x2:(((eq fofType) x1) (x0 (g x1))))=> (((((eq_sym fofType) x1) (x0 (g x1))) x2) P1)) (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found (fun (P1:(fofType->Prop))=> ((fun (x2:(((eq fofType) x1) (x0 (g x1))))=> (((((eq_sym fofType) x1) (x0 (g x1))) x2) P1)) (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym010 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym01 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x20 (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((x2 (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (eq_sym0000 (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found (eq_sym0000 (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found ((fun (x2:(((eq fofType) x1) (x0 (g x1))))=> ((eq_sym000 x2) P1)) (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found ((fun (x2:(((eq fofType) x1) (x0 (g x1))))=> (((eq_sym00 (x0 (g x1))) x2) P1)) (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found ((fun (x2:(((eq fofType) x1) (x0 (g x1))))=> ((((eq_sym0 x1) (x0 (g x1))) x2) P1)) (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found ((fun (x2:(((eq fofType) x1) (x0 (g x1))))=> (((((eq_sym fofType) x1) (x0 (g x1))) x2) P1)) (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found (fun (P1:(fofType->Prop))=> ((fun (x2:(((eq fofType) x1) (x0 (g x1))))=> (((((eq_sym fofType) x1) (x0 (g x1))) x2) P1)) (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym010 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym01 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x20 (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((x2 (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (eq_sym0000 (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found (eq_sym0000 (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found ((fun (x2:(((eq fofType) x1) (x0 (g x1))))=> ((eq_sym000 x2) P1)) (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found ((fun (x2:(((eq fofType) x1) (x0 (g x1))))=> (((eq_sym00 (x0 (g x1))) x2) P1)) (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found ((fun (x2:(((eq fofType) x1) (x0 (g x1))))=> ((((eq_sym0 x1) (x0 (g x1))) x2) P1)) (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found ((fun (x2:(((eq fofType) x1) (x0 (g x1))))=> (((((eq_sym fofType) x1) (x0 (g x1))) x2) P1)) (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found (fun (P1:(fofType->Prop))=> ((fun (x2:(((eq fofType) x1) (x0 (g x1))))=> (((((eq_sym fofType) x1) (x0 (g x1))) x2) P1)) (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym010 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym01 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x20 (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((x2 (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (eq_sym0000 (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found (eq_sym0000 (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found ((fun (x2:(((eq fofType) x1) (x0 (g x1))))=> ((eq_sym000 x2) P1)) (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found ((fun (x2:(((eq fofType) x1) (x0 (g x1))))=> (((eq_sym00 (x0 (g x1))) x2) P1)) (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found ((fun (x2:(((eq fofType) x1) (x0 (g x1))))=> ((((eq_sym0 x1) (x0 (g x1))) x2) P1)) (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found ((fun (x2:(((eq fofType) x1) (x0 (g x1))))=> (((((eq_sym fofType) x1) (x0 (g x1))) x2) P1)) (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found (fun (P1:(fofType->Prop))=> ((fun (x2:(((eq fofType) x1) (x0 (g x1))))=> (((((eq_sym fofType) x1) (x0 (g x1))) x2) P1)) (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))))) as proof of ((P1 (x0 (g x1)))->(P1 x1))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_sym10 b) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found (((eq_sym1 (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_trans0000 ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1))))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found (((eq_trans000 x1) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found ((((fun (b:fofType)=> ((eq_trans00 b) (x0 (g x1)))) x1) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found ((((fun (b:fofType)=> (((eq_trans0 x1) b) (x0 (g x1)))) x1) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found ((((fun (b:fofType)=> ((((eq_trans fofType) x1) b) (x0 (g x1)))) x1) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found ((((fun (b:fofType)=> ((((eq_trans fofType) x1) b) (x0 (g x1)))) x1) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_sym10 b) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found (((eq_sym1 (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_trans0000 ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1))))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found (((eq_trans000 x1) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found ((((fun (b:fofType)=> ((eq_trans00 b) (x0 (g x1)))) x1) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found ((((fun (b:fofType)=> (((eq_trans0 x1) b) (x0 (g x1)))) x1) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found ((((fun (b:fofType)=> ((((eq_trans fofType) x1) b) (x0 (g x1)))) x1) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found ((((fun (b:fofType)=> ((((eq_trans fofType) x1) b) (x0 (g x1)))) x1) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_sym10 b) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found (((eq_sym1 (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_trans0000 ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((eq_trans000 x1) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((fun (b:fofType)=> ((eq_trans00 b) (x0 (g x1)))) x1) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((fun (b:fofType)=> (((eq_trans0 x1) b) (x0 (g x1)))) x1) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((fun (b:fofType)=> ((((eq_trans fofType) x1) b) (x0 (g x1)))) x1) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_sym10 b) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found (((eq_sym1 (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_trans0000 ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((eq_trans000 x1) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((fun (b:fofType)=> ((eq_trans00 b) (x0 (g x1)))) x1) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((fun (b:fofType)=> (((eq_trans0 x1) b) (x0 (g x1)))) x1) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((fun (b:fofType)=> ((((eq_trans fofType) x1) b) (x0 (g x1)))) x1) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_sym10 b) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found (((eq_sym1 (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_trans0000 ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((eq_trans000 x1) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((fun (b:fofType)=> ((eq_trans00 b) (x0 (g x1)))) x1) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((fun (b:fofType)=> (((eq_trans0 x1) b) (x0 (g x1)))) x1) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((fun (b:fofType)=> ((((eq_trans fofType) x1) b) (x0 (g x1)))) x1) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_sym10 b) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found (((eq_sym1 (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_trans0000 ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((eq_trans000 x1) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((fun (b:fofType)=> ((eq_trans00 b) (x0 (g x1)))) x1) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((fun (b:fofType)=> (((eq_trans0 x1) b) (x0 (g x1)))) x1) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((fun (b:fofType)=> ((((eq_trans fofType) x1) b) (x0 (g x1)))) x1) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref000:=(eq_ref00 P):((P (x0 (g x1)))->(P (x0 (g x1))))
% Found (eq_ref00 P) as proof of ((P (x0 (g x1)))->(P (b x1)))
% Found ((eq_ref0 (x0 (g x1))) P) as proof of ((P (x0 (g x1)))->(P (b x1)))
% Found (((eq_ref fofType) (x0 (g x1))) P) as proof of ((P (x0 (g x1)))->(P (b x1)))
% Found (((eq_ref fofType) (x0 (g x1))) P) as proof of ((P (x0 (g x1)))->(P (b x1)))
% Found (fun (P:(fofType->Prop))=> (((eq_ref fofType) (x0 (g x1))) P)) as proof of ((P (x0 (g x1)))->(P (b x1)))
% Found (fun (P:(fofType->Prop))=> (((eq_ref fofType) (x0 (g x1))) P)) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P (b x1))))
% Found eq_ref000:=(eq_ref00 P):((P (x0 (g x1)))->(P (x0 (g x1))))
% Found (eq_ref00 P) as proof of ((P (x0 (g x1)))->(P (b x1)))
% Found ((eq_ref0 (x0 (g x1))) P) as proof of ((P (x0 (g x1)))->(P (b x1)))
% Found (((eq_ref fofType) (x0 (g x1))) P) as proof of ((P (x0 (g x1)))->(P (b x1)))
% Found (((eq_ref fofType) (x0 (g x1))) P) as proof of ((P (x0 (g x1)))->(P (b x1)))
% Found (fun (P:(fofType->Prop))=> (((eq_ref fofType) (x0 (g x1))) P)) as proof of ((P (x0 (g x1)))->(P (b x1)))
% Found (fun (P:(fofType->Prop))=> (((eq_ref fofType) (x0 (g x1))) P)) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P (b x1))))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (forall (P:(fofType->Prop)), ((P (b x1))->(P (x0 (g x1)))))
% Found ((eq_sym10 (b x1)) ((eq_ref fofType) (x0 (g x1)))) as proof of (forall (P:(fofType->Prop)), ((P (b x1))->(P (x0 (g x1)))))
% Found (((eq_sym1 (x0 (g x1))) (b x1)) ((eq_ref fofType) (x0 (g x1)))) as proof of (forall (P:(fofType->Prop)), ((P (b x1))->(P (x0 (g x1)))))
% Found ((((eq_sym fofType) (x0 (g x1))) (b x1)) ((eq_ref fofType) (x0 (g x1)))) as proof of (forall (P:(fofType->Prop)), ((P (b x1))->(P (x0 (g x1)))))
% Found ((((eq_sym fofType) (x0 (g x1))) (b x1)) ((eq_ref fofType) (x0 (g x1)))) as proof of (forall (P:(fofType->Prop)), ((P (b x1))->(P (x0 (g x1)))))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (forall (P:(fofType->Prop)), ((P (b x1))->(P (x0 (g x1)))))
% Found ((eq_sym10 (b x1)) ((eq_ref fofType) (x0 (g x1)))) as proof of (forall (P:(fofType->Prop)), ((P (b x1))->(P (x0 (g x1)))))
% Found (((eq_sym1 (x0 (g x1))) (b x1)) ((eq_ref fofType) (x0 (g x1)))) as proof of (forall (P:(fofType->Prop)), ((P (b x1))->(P (x0 (g x1)))))
% Found ((((eq_sym fofType) (x0 (g x1))) (b x1)) ((eq_ref fofType) (x0 (g x1)))) as proof of (forall (P:(fofType->Prop)), ((P (b x1))->(P (x0 (g x1)))))
% Found ((((eq_sym fofType) (x0 (g x1))) (b x1)) ((eq_ref fofType) (x0 (g x1)))) as proof of (forall (P:(fofType->Prop)), ((P (b x1))->(P (x0 (g x1)))))
% Found eq_ref000:=(eq_ref00 P):((P (x0 (g x1)))->(P (x0 (g x1))))
% Found (eq_ref00 P) as proof of ((P (x0 (g x1)))->(P (b x1)))
% Found ((eq_ref0 (x0 (g x1))) P) as proof of ((P (x0 (g x1)))->(P (b x1)))
% Found (((eq_ref fofType) (x0 (g x1))) P) as proof of ((P (x0 (g x1)))->(P (b x1)))
% Found (((eq_ref fofType) (x0 (g x1))) P) as proof of ((P (x0 (g x1)))->(P (b x1)))
% Found (fun (P:(fofType->Prop))=> (((eq_ref fofType) (x0 (g x1))) P)) as proof of ((P (x0 (g x1)))->(P (b x1)))
% Found eq_ref000:=(eq_ref00 P):((P (x0 (g x1)))->(P (x0 (g x1))))
% Found (eq_ref00 P) as proof of ((P (x0 (g x1)))->(P (b x1)))
% Found ((eq_ref0 (x0 (g x1))) P) as proof of ((P (x0 (g x1)))->(P (b x1)))
% Found (((eq_ref fofType) (x0 (g x1))) P) as proof of ((P (x0 (g x1)))->(P (b x1)))
% Found (((eq_ref fofType) (x0 (g x1))) P) as proof of ((P (x0 (g x1)))->(P (b x1)))
% Found (fun (P:(fofType->Prop))=> (((eq_ref fofType) (x0 (g x1))) P)) as proof of ((P (x0 (g x1)))->(P (b x1)))
% Found eq_ref000:=(eq_ref00 P):((P (x0 (g x1)))->(P (x0 (g x1))))
% Found (eq_ref00 P) as proof of ((P (x0 (g x1)))->(P (b x1)))
% Found ((eq_ref0 (x0 (g x1))) P) as proof of ((P (x0 (g x1)))->(P (b x1)))
% Found (((eq_ref fofType) (x0 (g x1))) P) as proof of ((P (x0 (g x1)))->(P (b x1)))
% Found (((eq_ref fofType) (x0 (g x1))) P) as proof of ((P (x0 (g x1)))->(P (b x1)))
% Found (fun (P:(fofType->Prop))=> (((eq_ref fofType) (x0 (g x1))) P)) as proof of ((P (x0 (g x1)))->(P (b x1)))
% Found eq_ref000:=(eq_ref00 P):((P (x0 (g x1)))->(P (x0 (g x1))))
% Found (eq_ref00 P) as proof of ((P (x0 (g x1)))->(P (b x1)))
% Found ((eq_ref0 (x0 (g x1))) P) as proof of ((P (x0 (g x1)))->(P (b x1)))
% Found (((eq_ref fofType) (x0 (g x1))) P) as proof of ((P (x0 (g x1)))->(P (b x1)))
% Found (((eq_ref fofType) (x0 (g x1))) P) as proof of ((P (x0 (g x1)))->(P (b x1)))
% Found (fun (P:(fofType->Prop))=> (((eq_ref fofType) (x0 (g x1))) P)) as proof of ((P (x0 (g x1)))->(P (b x1)))
% Found eq_ref000:=(eq_ref00 P):((P (x0 (g x1)))->(P (x0 (g x1))))
% Found (eq_ref00 P) as proof of ((P (x0 (g x1)))->(P (b x1)))
% Found ((eq_ref0 (x0 (g x1))) P) as proof of ((P (x0 (g x1)))->(P (b x1)))
% Found (((eq_ref fofType) (x0 (g x1))) P) as proof of ((P (x0 (g x1)))->(P (b x1)))
% Found (((eq_ref fofType) (x0 (g x1))) P) as proof of ((P (x0 (g x1)))->(P (b x1)))
% Found (fun (P:(fofType->Prop))=> (((eq_ref fofType) (x0 (g x1))) P)) as proof of ((P (x0 (g x1)))->(P (b x1)))
% Found eq_ref000:=(eq_ref00 P):((P (x0 (g x1)))->(P (x0 (g x1))))
% Found (eq_ref00 P) as proof of ((P (x0 (g x1)))->(P (b x1)))
% Found ((eq_ref0 (x0 (g x1))) P) as proof of ((P (x0 (g x1)))->(P (b x1)))
% Found (((eq_ref fofType) (x0 (g x1))) P) as proof of ((P (x0 (g x1)))->(P (b x1)))
% Found (((eq_ref fofType) (x0 (g x1))) P) as proof of ((P (x0 (g x1)))->(P (b x1)))
% Found (fun (P:(fofType->Prop))=> (((eq_ref fofType) (x0 (g x1))) P)) as proof of ((P (x0 (g x1)))->(P (b x1)))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found ((eq_sym10 (b x1)) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found (((eq_sym1 (x0 (g x1))) (b x1)) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) (b x1)) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found ((eq_sym10 (b x1)) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found (((eq_sym1 (x0 (g x1))) (b x1)) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) (b x1)) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found ((eq_sym10 (b x1)) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found (((eq_sym1 (x0 (g x1))) (b x1)) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) (b x1)) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found ((eq_sym10 (b x1)) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found (((eq_sym1 (x0 (g x1))) (b x1)) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) (b x1)) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found ((eq_sym10 (b x1)) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found (((eq_sym1 (x0 (g x1))) (b x1)) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) (b x1)) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found ((eq_sym10 (b x1)) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found (((eq_sym1 (x0 (g x1))) (b x1)) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) (b x1)) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (b x1)):(((eq fofType) (b x1)) (b x1))
% Found (eq_ref0 (b x1)) as proof of (((eq fofType) (b x1)) b0)
% Found ((eq_ref fofType) (b x1)) as proof of (((eq fofType) (b x1)) b0)
% Found ((eq_ref fofType) (b x1)) as proof of (((eq fofType) (b x1)) b0)
% Found ((eq_ref fofType) (b x1)) as proof of (((eq fofType) (b x1)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) x1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x1)
% Found eq_ref00:=(eq_ref0 (b x1)):(((eq fofType) (b x1)) (b x1))
% Found (eq_ref0 (b x1)) as proof of (((eq fofType) (b x1)) b0)
% Found ((eq_ref fofType) (b x1)) as proof of (((eq fofType) (b x1)) b0)
% Found ((eq_ref fofType) (b x1)) as proof of (((eq fofType) (b x1)) b0)
% Found ((eq_ref fofType) (b x1)) as proof of (((eq fofType) (b x1)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) x1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x1)
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym10 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((x200 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found ((x200 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((x20 x3) (fun (x5:fofType)=> ((P1 x1)->(P1 x5))))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> (((x2 (x0 (g x1))) x3) (fun (x5:fofType)=> ((P1 x1)->(P1 x5))))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((((x x1) (x0 (g x1))) x3) (fun (x5:fofType)=> ((P1 x1)->(P1 x5))))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (fun (P1:(fofType->Prop))=> (((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((((x x1) (x0 (g x1))) x3) (fun (x5:fofType)=> ((P1 x1)->(P1 x5))))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P1))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym10 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x200 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (x200 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found ((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((x20 x3) P1)) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found ((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> (((x2 (x0 (g x1))) x3) P1)) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found ((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((((x x1) (x0 (g x1))) x3) P1)) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (fun (P1:(fofType->Prop))=> ((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((((x x1) (x0 (g x1))) x3) P1)) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym10 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((x200 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found ((x200 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((x20 x3) (fun (x5:fofType)=> ((P1 x1)->(P1 x5))))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> (((x2 (x0 (g x1))) x3) (fun (x5:fofType)=> ((P1 x1)->(P1 x5))))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((((x x1) (x0 (g x1))) x3) (fun (x5:fofType)=> ((P1 x1)->(P1 x5))))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (fun (P1:(fofType->Prop))=> (((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((((x x1) (x0 (g x1))) x3) (fun (x5:fofType)=> ((P1 x1)->(P1 x5))))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P1))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym10 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x200 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (x200 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found ((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((x20 x3) P1)) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found ((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> (((x2 (x0 (g x1))) x3) P1)) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found ((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((((x x1) (x0 (g x1))) x3) P1)) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (fun (P1:(fofType->Prop))=> ((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((((x x1) (x0 (g x1))) x3) P1)) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym10 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x200 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (x200 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found ((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((x20 x3) P1)) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found ((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> (((x2 (x0 (g x1))) x3) P1)) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found ((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((((x x1) (x0 (g x1))) x3) P1)) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (fun (P1:(fofType->Prop))=> ((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((((x x1) (x0 (g x1))) x3) P1)) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym10 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((x200 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found ((x200 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((x20 x3) (fun (x5:fofType)=> ((P1 x1)->(P1 x5))))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> (((x2 (x0 (g x1))) x3) (fun (x5:fofType)=> ((P1 x1)->(P1 x5))))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((((x x1) (x0 (g x1))) x3) (fun (x5:fofType)=> ((P1 x1)->(P1 x5))))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (fun (P1:(fofType->Prop))=> (((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((((x x1) (x0 (g x1))) x3) (fun (x5:fofType)=> ((P1 x1)->(P1 x5))))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P1))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym10 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x200 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (x200 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found ((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((x20 x3) P1)) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found ((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> (((x2 (x0 (g x1))) x3) P1)) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found ((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((((x x1) (x0 (g x1))) x3) P1)) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (fun (P1:(fofType->Prop))=> ((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((((x x1) (x0 (g x1))) x3) P1)) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym10 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((x200 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found ((x200 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((x20 x3) (fun (x5:fofType)=> ((P1 x1)->(P1 x5))))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> (((x2 (x0 (g x1))) x3) (fun (x5:fofType)=> ((P1 x1)->(P1 x5))))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((((x x1) (x0 (g x1))) x3) (fun (x5:fofType)=> ((P1 x1)->(P1 x5))))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (fun (P1:(fofType->Prop))=> (((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((((x x1) (x0 (g x1))) x3) (fun (x5:fofType)=> ((P1 x1)->(P1 x5))))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P1))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym10 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x200 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (x200 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found ((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((x20 x3) P1)) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found ((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> (((x2 (x0 (g x1))) x3) P1)) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found ((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((((x x1) (x0 (g x1))) x3) P1)) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (fun (P1:(fofType->Prop))=> ((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((((x x1) (x0 (g x1))) x3) P1)) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym10 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((x200 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found ((x200 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((x20 x3) (fun (x5:fofType)=> ((P1 x1)->(P1 x5))))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> (((x2 (x0 (g x1))) x3) (fun (x5:fofType)=> ((P1 x1)->(P1 x5))))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((((x x1) (x0 (g x1))) x3) (fun (x5:fofType)=> ((P1 x1)->(P1 x5))))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (fun (P1:(fofType->Prop))=> (((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((((x x1) (x0 (g x1))) x3) (fun (x5:fofType)=> ((P1 x1)->(P1 x5))))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P1))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym10 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((x200 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found ((x200 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((x20 x3) (fun (x5:fofType)=> ((P1 x1)->(P1 x5))))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> (((x2 (x0 (g x1))) x3) (fun (x5:fofType)=> ((P1 x1)->(P1 x5))))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((((x x1) (x0 (g x1))) x3) (fun (x5:fofType)=> ((P1 x1)->(P1 x5))))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (fun (P1:(fofType->Prop))=> (((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((((x x1) (x0 (g x1))) x3) (fun (x5:fofType)=> ((P1 x1)->(P1 x5))))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P1))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym10 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x200 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (x200 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found ((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((x20 x3) P1)) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found ((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> (((x2 (x0 (g x1))) x3) P1)) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found ((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((((x x1) (x0 (g x1))) x3) P1)) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (fun (P1:(fofType->Prop))=> ((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((((x x1) (x0 (g x1))) x3) P1)) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym10 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x200 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (x200 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found ((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((x20 x3) P1)) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found ((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> (((x2 (x0 (g x1))) x3) P1)) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found ((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((((x x1) (x0 (g x1))) x3) P1)) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (fun (P1:(fofType->Prop))=> ((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((((x x1) (x0 (g x1))) x3) P1)) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym10 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((x200 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found ((x200 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((x20 x3) (fun (x5:fofType)=> ((P1 x1)->(P1 x5))))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> (((x2 (x0 (g x1))) x3) (fun (x5:fofType)=> ((P1 x1)->(P1 x5))))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((((x x1) (x0 (g x1))) x3) (fun (x5:fofType)=> ((P1 x1)->(P1 x5))))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (fun (P1:(fofType->Prop))=> (((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((((x x1) (x0 (g x1))) x3) (fun (x5:fofType)=> ((P1 x1)->(P1 x5))))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P1))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym10 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x200 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (x200 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found ((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((x20 x3) P1)) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found ((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> (((x2 (x0 (g x1))) x3) P1)) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found ((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((((x x1) (x0 (g x1))) x3) P1)) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (fun (P1:(fofType->Prop))=> ((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((((x x1) (x0 (g x1))) x3) P1)) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym10 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((x200 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found ((x200 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((x20 x3) (fun (x5:fofType)=> ((P1 x1)->(P1 x5))))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> (((x2 (x0 (g x1))) x3) (fun (x5:fofType)=> ((P1 x1)->(P1 x5))))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((((x x1) (x0 (g x1))) x3) (fun (x5:fofType)=> ((P1 x1)->(P1 x5))))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P1)) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found (fun (P1:(fofType->Prop))=> (((fun (x3:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((((x x1) (x0 (g x1))) x3) (fun (x5:fofType)=> ((P1 x1)->(P1 x5))))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) (((eq_ref fofType) x1) P1))) as proof of ((P1 x1)->(P1 (x0 (g x1))))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym10 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x20 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((x2 (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym10 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x20 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((x2 (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym10 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x20 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((x2 (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym10 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x20 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((x2 (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym10 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x20 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((x2 (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym10 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x20 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((x2 (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym10 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x20 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((x2 (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym10 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x20 ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((x2 (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found ((eq_sym10 x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found (((eq_sym1 (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found ((eq_sym10 x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found (((eq_sym1 (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found ((eq_sym10 x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found (((eq_sym1 (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found ((eq_sym10 x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found (((eq_sym1 (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P (x0 (g x1)))))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((eq_sym10 x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((eq_sym1 (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) x1)
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((eq_sym10 x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((eq_sym1 (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g Xx))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g Xx))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g Xx))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g Xx))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g Xx)) (g (x0 (g x1))))
% Found ((eq_sym10 (g Xx)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g Xx)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g Xx)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g Xx)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g Xx)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g Xx)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g Xx)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g Xx)) (g (x0 (g x1))))
% Found ((x300 ((((eq_sym fofType) (g (x0 (g x1)))) (g Xx)) ((eq_ref fofType) (g (x0 (g x1)))))) x2) as proof of (P (x0 (g x1)))
% Found ((x300 ((((eq_sym fofType) (g (x0 (g x1)))) (g Xx)) ((eq_ref fofType) (g (x0 (g x1)))))) x2) as proof of (P (x0 (g x1)))
% Found (((fun (x4:(((eq fofType) (g Xx)) (g (x0 (g x1)))))=> ((x30 x4) P)) ((((eq_sym fofType) (g (x0 (g x1)))) (g Xx)) ((eq_ref fofType) (g (x0 (g x1)))))) x2) as proof of (P (x0 (g x1)))
% Found (((fun (x4:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> (((x3 x1) x4) P)) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) x2) as proof of (P (x0 (g x1)))
% Found (((fun (x4:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((((fun (Xx:fofType)=> ((x Xx) (x0 (g x1)))) x1) x4) P)) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) x2) as proof of (P (x0 (g x1)))
% Found (fun (x2:(P x1))=> (((fun (x4:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((((fun (Xx:fofType)=> ((x Xx) (x0 (g x1)))) x1) x4) P)) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) x2)) as proof of (P (x0 (g x1)))
% Found (fun (P:(fofType->Prop)) (x2:(P x1))=> (((fun (x4:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((((fun (Xx:fofType)=> ((x Xx) (x0 (g x1)))) x1) x4) P)) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) x2)) as proof of ((P x1)->(P (x0 (g x1))))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g Xx))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g Xx))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g Xx))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g Xx))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g Xx)) (g (x0 (g x1))))
% Found ((eq_sym10 (g Xx)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g Xx)) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g Xx)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g Xx)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g Xx)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g Xx)) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g Xx)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g Xx)) (g (x0 (g x1))))
% Found ((x300 ((((eq_sym fofType) (g (x0 (g x1)))) (g Xx)) ((eq_ref fofType) (g (x0 (g x1)))))) x2) as proof of (P (x0 (g x1)))
% Found ((x300 ((((eq_sym fofType) (g (x0 (g x1)))) (g Xx)) ((eq_ref fofType) (g (x0 (g x1)))))) x2) as proof of (P (x0 (g x1)))
% Found (((fun (x4:(((eq fofType) (g Xx)) (g (x0 (g x1)))))=> ((x30 x4) P)) ((((eq_sym fofType) (g (x0 (g x1)))) (g Xx)) ((eq_ref fofType) (g (x0 (g x1)))))) x2) as proof of (P (x0 (g x1)))
% Found (((fun (x4:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> (((x3 x1) x4) P)) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) x2) as proof of (P (x0 (g x1)))
% Found (((fun (x4:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((((fun (Xx:fofType)=> ((x Xx) (x0 (g x1)))) x1) x4) P)) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) x2) as proof of (P (x0 (g x1)))
% Found (fun (x2:(P x1))=> (((fun (x4:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((((fun (Xx:fofType)=> ((x Xx) (x0 (g x1)))) x1) x4) P)) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) x2)) as proof of (P (x0 (g x1)))
% Found (fun (P:(fofType->Prop)) (x2:(P x1))=> (((fun (x4:(((eq fofType) (g x1)) (g (x0 (g x1)))))=> ((((fun (Xx:fofType)=> ((x Xx) (x0 (g x1)))) x1) x4) P)) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) x2)) as proof of ((P x1)->(P (x0 (g x1))))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x2)))):(((eq fofType) (g (x0 (g x2)))) (g (x0 (g x2))))
% Found (eq_ref0 (g (x0 (g x2)))) as proof of (((eq fofType) (g (x0 (g x2)))) (g (f x2)))
% Found ((eq_ref fofType) (g (x0 (g x2)))) as proof of (((eq fofType) (g (x0 (g x2)))) (g (f x2)))
% Found ((eq_ref fofType) (g (x0 (g x2)))) as proof of (((eq fofType) (g (x0 (g x2)))) (g (f x2)))
% Found ((eq_ref fofType) (g (x0 (g x2)))) as proof of (((eq fofType) (g (x0 (g x2)))) (g (f x2)))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x2))))) as proof of (((eq fofType) (g (f x2))) (g (x0 (g x2))))
% Found ((eq_sym10 (g (f x2))) ((eq_ref fofType) (g (x0 (g x2))))) as proof of (((eq fofType) (g (f x2))) (g (x0 (g x2))))
% Found (((eq_sym1 (g (x0 (g x2)))) (g (f x2))) ((eq_ref fofType) (g (x0 (g x2))))) as proof of (((eq fofType) (g (f x2))) (g (x0 (g x2))))
% Found ((((eq_sym fofType) (g (x0 (g x2)))) (g (f x2))) ((eq_ref fofType) (g (x0 (g x2))))) as proof of (((eq fofType) (g (f x2))) (g (x0 (g x2))))
% Found ((((eq_sym fofType) (g (x0 (g x2)))) (g (f x2))) ((eq_ref fofType) (g (x0 (g x2))))) as proof of (((eq fofType) (g (f x2))) (g (x0 (g x2))))
% Found (x30 ((((eq_sym fofType) (g (x0 (g x2)))) (g (f x2))) ((eq_ref fofType) (g (x0 (g x2)))))) as proof of (((eq fofType) (f x2)) (x0 (g x2)))
% Found ((x3 (x0 (g x2))) ((((eq_sym fofType) (g (x0 (g x2)))) (g (f x2))) ((eq_ref fofType) (g (x0 (g x2)))))) as proof of (((eq fofType) (f x2)) (x0 (g x2)))
% Found (((x (f x2)) (x0 (g x2))) ((((eq_sym fofType) (g (x0 (g x2)))) (g (f x2))) ((eq_ref fofType) (g (x0 (g x2)))))) as proof of (((eq fofType) (f x2)) (x0 (g x2)))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x2)))):(((eq fofType) (g (x0 (g x2)))) (g (x0 (g x2))))
% Found (eq_ref0 (g (x0 (g x2)))) as proof of (((eq fofType) (g (x0 (g x2)))) (g (f x2)))
% Found ((eq_ref fofType) (g (x0 (g x2)))) as proof of (((eq fofType) (g (x0 (g x2)))) (g (f x2)))
% Found ((eq_ref fofType) (g (x0 (g x2)))) as proof of (((eq fofType) (g (x0 (g x2)))) (g (f x2)))
% Found ((eq_ref fofType) (g (x0 (g x2)))) as proof of (((eq fofType) (g (x0 (g x2)))) (g (f x2)))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x2))))) as proof of (((eq fofType) (g (f x2))) (g (x0 (g x2))))
% Found ((eq_sym10 (g (f x2))) ((eq_ref fofType) (g (x0 (g x2))))) as proof of (((eq fofType) (g (f x2))) (g (x0 (g x2))))
% Found (((eq_sym1 (g (x0 (g x2)))) (g (f x2))) ((eq_ref fofType) (g (x0 (g x2))))) as proof of (((eq fofType) (g (f x2))) (g (x0 (g x2))))
% Found ((((eq_sym fofType) (g (x0 (g x2)))) (g (f x2))) ((eq_ref fofType) (g (x0 (g x2))))) as proof of (((eq fofType) (g (f x2))) (g (x0 (g x2))))
% Found ((((eq_sym fofType) (g (x0 (g x2)))) (g (f x2))) ((eq_ref fofType) (g (x0 (g x2))))) as proof of (((eq fofType) (g (f x2))) (g (x0 (g x2))))
% Found (x30 ((((eq_sym fofType) (g (x0 (g x2)))) (g (f x2))) ((eq_ref fofType) (g (x0 (g x2)))))) as proof of (((eq fofType) (f x2)) (x0 (g x2)))
% Found ((x3 (x0 (g x2))) ((((eq_sym fofType) (g (x0 (g x2)))) (g (f x2))) ((eq_ref fofType) (g (x0 (g x2)))))) as proof of (((eq fofType) (f x2)) (x0 (g x2)))
% Found (((x (f x2)) (x0 (g x2))) ((((eq_sym fofType) (g (x0 (g x2)))) (g (f x2))) ((eq_ref fofType) (g (x0 (g x2)))))) as proof of (((eq fofType) (f x2)) (x0 (g x2)))
% Found eq_ref000:=(eq_ref00 P):((P (g (b x1)))->(P (g (b x1))))
% Found (eq_ref00 P) as proof of (P0 (g (b x1)))
% Found ((eq_ref0 (g (b x1))) P) as proof of (P0 (g (b x1)))
% Found (((eq_ref fofType) (g (b x1))) P) as proof of (P0 (g (b x1)))
% Found (((eq_ref fofType) (g (b x1))) P) as proof of (P0 (g (b x1)))
% Found eq_ref000:=(eq_ref00 P):((P (g (b x1)))->(P (g (b x1))))
% Found (eq_ref00 P) as proof of (P0 (g (b x1)))
% Found ((eq_ref0 (g (b x1))) P) as proof of (P0 (g (b x1)))
% Found (((eq_ref fofType) (g (b x1))) P) as proof of (P0 (g (b x1)))
% Found (((eq_ref fofType) (g (b x1))) P) as proof of (P0 (g (b x1)))
% Found eq_ref000:=(eq_ref00 P):((P x1)->(P x1))
% Found (eq_ref00 P) as proof of (P0 x1)
% Found ((eq_ref0 x1) P) as proof of (P0 x1)
% Found (((eq_ref fofType) x1) P) as proof of (P0 x1)
% Found (((eq_ref fofType) x1) P) as proof of (P0 x1)
% Found eq_ref000:=(eq_ref00 P):((P x1)->(P x1))
% Found (eq_ref00 P) as proof of (P0 x1)
% Found ((eq_ref0 x1) P) as proof of (P0 x1)
% Found (((eq_ref fofType) x1) P) as proof of (P0 x1)
% Found (((eq_ref fofType) x1) P) as proof of (P0 x1)
% Found eq_ref000:=(eq_ref00 P):((P (b x1))->(P (b x1)))
% Found (eq_ref00 P) as proof of (P0 (b x1))
% Found ((eq_ref0 (b x1)) P) as proof of (P0 (b x1))
% Found (((eq_ref fofType) (b x1)) P) as proof of (P0 (b x1))
% Found (((eq_ref fofType) (b x1)) P) as proof of (P0 (b x1))
% Found eq_ref000:=(eq_ref00 P):((P (b x1))->(P (b x1)))
% Found (eq_ref00 P) as proof of (P0 (b x1))
% Found ((eq_ref0 (b x1)) P) as proof of (P0 (b x1))
% Found (((eq_ref fofType) (b x1)) P) as proof of (P0 (b x1))
% Found (((eq_ref fofType) (b x1)) P) as proof of (P0 (b x1))
% Found eq_ref000:=(eq_ref00 P):((P x1)->(P x1))
% Found (eq_ref00 P) as proof of (P0 x1)
% Found ((eq_ref0 x1) P) as proof of (P0 x1)
% Found (((eq_ref fofType) x1) P) as proof of (P0 x1)
% Found (((eq_ref fofType) x1) P) as proof of (P0 x1)
% Found eq_ref000:=(eq_ref00 P):((P x1)->(P x1))
% Found (eq_ref00 P) as proof of (P0 x1)
% Found ((eq_ref0 x1) P) as proof of (P0 x1)
% Found (((eq_ref fofType) x1) P) as proof of (P0 x1)
% Found (((eq_ref fofType) x1) P) as proof of (P0 x1)
% Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (Xx:fofType)=> (x0 (g Xx))))->(P (fun (x:fofType)=> (x0 (g x)))))
% Found (eta_expansion_dep000 P) as proof of (P0 (fun (Xx:fofType)=> (x0 (g Xx))))
% Found ((eta_expansion_dep00 (fun (Xx:fofType)=> (x0 (g Xx)))) P) as proof of (P0 (fun (Xx:fofType)=> (x0 (g Xx))))
% Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) P) as proof of (P0 (fun (Xx:fofType)=> (x0 (g Xx))))
% Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) P) as proof of (P0 (fun (Xx:fofType)=> (x0 (g Xx))))
% Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) P) as proof of (P0 (fun (Xx:fofType)=> (x0 (g Xx))))
% Found eq_ref000:=(eq_ref00 P):((P (fun (Xx:fofType)=> (x0 (g Xx))))->(P (fun (Xx:fofType)=> (x0 (g Xx)))))
% Found (eq_ref00 P) as proof of (P0 (fun (Xx:fofType)=> (x0 (g Xx))))
% Found ((eq_ref0 (fun (Xx:fofType)=> (x0 (g Xx)))) P) as proof of (P0 (fun (Xx:fofType)=> (x0 (g Xx))))
% Found (((eq_ref (fofType->fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) P) as proof of (P0 (fun (Xx:fofType)=> (x0 (g Xx))))
% Found (((eq_ref (fofType->fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) P) as proof of (P0 (fun (Xx:fofType)=> (x0 (g Xx))))
% Found eq_ref00:=(eq_ref0 b0):(((eq (fofType->fofType)) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq (fofType->fofType)) b0) b)
% Found ((eq_ref (fofType->fofType)) b0) as proof of (((eq (fofType->fofType)) b0) b)
% Found ((eq_ref (fofType->fofType)) b0) as proof of (((eq (fofType->fofType)) b0) b)
% Found ((eq_ref (fofType->fofType)) b0) as proof of (((eq (fofType->fofType)) b0) b)
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xx:fofType)=> (x0 (g Xx)))):(((eq (fofType->fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) (fun (x:fofType)=> (x0 (g x))))
% Found (eta_expansion_dep00 (fun (Xx:fofType)=> (x0 (g Xx)))) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) b0)
% Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) b0)
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) b0)
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) b0)
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) as proof of (((eq (fofType->fofType)) (fun (Xx:fofType)=> (x0 (g Xx)))) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) (g x1))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (g x1))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (g x1))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (g x1))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) (g x1))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (g x1))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (g x1))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (g x1))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) (g x1))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (g x1))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (g x1))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (g x1))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) (g x1))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (g x1))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (g x1))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (g x1))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found (x20 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P (b x1))))
% Found ((x2 (b x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P (b x1))))
% Found (((x (x0 (g x1))) (b x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P (b x1))))
% Found (((x (x0 (g x1))) (b x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P (b x1))))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found (x20 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P (b x1))))
% Found ((x2 (b x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P (b x1))))
% Found (((x (x0 (g x1))) (b x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P (b x1))))
% Found (((x (x0 (g x1))) (b x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P (b x1))))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found (x20 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((x2 (b x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found (((x (x0 (g x1))) (b x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found (x20 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((x2 (b x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found (((x (x0 (g x1))) (b x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found (x20 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((x2 (b x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found (((x (x0 (g x1))) (b x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found (x20 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((x2 (b x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found (((x (x0 (g x1))) (b x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found (x20 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((x2 (b x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found (((x (x0 (g x1))) (b x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found (x20 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((x2 (b x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found (((x (x0 (g x1))) (b x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym010 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym01 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x20 (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((x2 (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (eq_sym000 (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found ((eq_sym00 (x0 (g x1))) (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found (((eq_sym0 x1) (x0 (g x1))) (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found ((((eq_sym fofType) x1) (x0 (g x1))) (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found ((((eq_sym fofType) x1) (x0 (g x1))) (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g x1))
% Found (eq_sym010 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found ((eq_sym01 (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g x1)) (g (x0 (g x1))))
% Found (x20 (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((x2 (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (eq_sym000 (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found ((eq_sym00 (x0 (g x1))) (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found (((eq_sym0 x1) (x0 (g x1))) (((x x1) (x0 (g x1))) (((eq_sym0 (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found ((((eq_sym fofType) x1) (x0 (g x1))) (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found ((((eq_sym fofType) x1) (x0 (g x1))) (((x x1) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g x1)) ((eq_ref fofType) (g (x0 (g x1))))))) as proof of (forall (P:(fofType->Prop)), ((P (x0 (g x1)))->(P x1)))
% Found eq_ref00:=(eq_ref0 (g (b x1))):(((eq fofType) (g (b x1))) (g (b x1)))
% Found (eq_ref0 (g (b x1))) as proof of (((eq fofType) (g (b x1))) b0)
% Found ((eq_ref fofType) (g (b x1))) as proof of (((eq fofType) (g (b x1))) b0)
% Found ((eq_ref fofType) (g (b x1))) as proof of (((eq fofType) (g (b x1))) b0)
% Found ((eq_ref fofType) (g (b x1))) as proof of (((eq fofType) (g (b x1))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (g x1))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g x1))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g x1))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g x1))
% Found eq_ref00:=(eq_ref0 (g (b x1))):(((eq fofType) (g (b x1))) (g (b x1)))
% Found (eq_ref0 (g (b x1))) as proof of (((eq fofType) (g (b x1))) b0)
% Found ((eq_ref fofType) (g (b x1))) as proof of (((eq fofType) (g (b x1))) b0)
% Found ((eq_ref fofType) (g (b x1))) as proof of (((eq fofType) (g (b x1))) b0)
% Found ((eq_ref fofType) (g (b x1))) as proof of (((eq fofType) (g (b x1))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (g x1))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g x1))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g x1))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g x1))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_sym10 b) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found (((eq_sym1 (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_trans00000 ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1))))) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((eq_trans00000 ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1))))) as proof of ((P x1)->(P (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) x1) b)) (x3:(((eq fofType) b) (x0 (g x1))))=> (((eq_trans0000 x2) x3) P)) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1))))) as proof of ((P x1)->(P (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) x1) x1)) (x3:(((eq fofType) x1) (x0 (g x1))))=> ((((eq_trans000 x1) x2) x3) P)) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) as proof of ((P x1)->(P (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) x1) x1)) (x3:(((eq fofType) x1) (x0 (g x1))))=> (((((fun (b:fofType)=> ((eq_trans00 b) (x0 (g x1)))) x1) x2) x3) P)) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) as proof of ((P x1)->(P (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) x1) x1)) (x3:(((eq fofType) x1) (x0 (g x1))))=> (((((fun (b:fofType)=> (((eq_trans0 x1) b) (x0 (g x1)))) x1) x2) x3) P)) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) as proof of ((P x1)->(P (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) x1) x1)) (x3:(((eq fofType) x1) (x0 (g x1))))=> (((((fun (b:fofType)=> ((((eq_trans fofType) x1) b) (x0 (g x1)))) x1) x2) x3) P)) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) as proof of ((P x1)->(P (x0 (g x1))))
% Found (fun (P:(fofType->Prop))=> (((fun (x2:(((eq fofType) x1) x1)) (x3:(((eq fofType) x1) (x0 (g x1))))=> (((((fun (b:fofType)=> ((((eq_trans fofType) x1) b) (x0 (g x1)))) x1) x2) x3) P)) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))))) as proof of ((P x1)->(P (x0 (g x1))))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_sym10 b) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found (((eq_sym1 (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found (((eq_trans00000 ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1))))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found (((eq_trans00000 ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1))))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((((fun (x2:(((eq fofType) x1) b)) (x3:(((eq fofType) b) (x0 (g x1))))=> (((eq_trans0000 x2) x3) (fun (x5:fofType)=> ((P x1)->(P x5))))) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1))))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((((fun (x2:(((eq fofType) x1) x1)) (x3:(((eq fofType) x1) (x0 (g x1))))=> ((((eq_trans000 x1) x2) x3) (fun (x5:fofType)=> ((P x1)->(P x5))))) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((((fun (x2:(((eq fofType) x1) x1)) (x3:(((eq fofType) x1) (x0 (g x1))))=> (((((fun (b:fofType)=> ((eq_trans00 b) (x0 (g x1)))) x1) x2) x3) (fun (x5:fofType)=> ((P x1)->(P x5))))) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((((fun (x2:(((eq fofType) x1) x1)) (x3:(((eq fofType) x1) (x0 (g x1))))=> (((((fun (b:fofType)=> (((eq_trans0 x1) b) (x0 (g x1)))) x1) x2) x3) (fun (x5:fofType)=> ((P x1)->(P x5))))) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((((fun (x2:(((eq fofType) x1) x1)) (x3:(((eq fofType) x1) (x0 (g x1))))=> (((((fun (b:fofType)=> ((((eq_trans fofType) x1) b) (x0 (g x1)))) x1) x2) x3) (fun (x5:fofType)=> ((P x1)->(P x5))))) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found (fun (P:(fofType->Prop))=> ((((fun (x2:(((eq fofType) x1) x1)) (x3:(((eq fofType) x1) (x0 (g x1))))=> (((((fun (b:fofType)=> ((((eq_trans fofType) x1) b) (x0 (g x1)))) x1) x2) x3) (fun (x5:fofType)=> ((P x1)->(P x5))))) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) (((eq_ref fofType) x1) P))) as proof of ((P x1)->(P (x0 (g x1))))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_sym10 b) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found (((eq_sym1 (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found (((eq_trans00000 ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1))))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found (((eq_trans00000 ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1))))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((((fun (x2:(((eq fofType) x1) b)) (x3:(((eq fofType) b) (x0 (g x1))))=> (((eq_trans0000 x2) x3) (fun (x5:fofType)=> ((P x1)->(P x5))))) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1))))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((((fun (x2:(((eq fofType) x1) x1)) (x3:(((eq fofType) x1) (x0 (g x1))))=> ((((eq_trans000 x1) x2) x3) (fun (x5:fofType)=> ((P x1)->(P x5))))) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((((fun (x2:(((eq fofType) x1) x1)) (x3:(((eq fofType) x1) (x0 (g x1))))=> (((((fun (b:fofType)=> ((eq_trans00 b) (x0 (g x1)))) x1) x2) x3) (fun (x5:fofType)=> ((P x1)->(P x5))))) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((((fun (x2:(((eq fofType) x1) x1)) (x3:(((eq fofType) x1) (x0 (g x1))))=> (((((fun (b:fofType)=> (((eq_trans0 x1) b) (x0 (g x1)))) x1) x2) x3) (fun (x5:fofType)=> ((P x1)->(P x5))))) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((((fun (x2:(((eq fofType) x1) x1)) (x3:(((eq fofType) x1) (x0 (g x1))))=> (((((fun (b:fofType)=> ((((eq_trans fofType) x1) b) (x0 (g x1)))) x1) x2) x3) (fun (x5:fofType)=> ((P x1)->(P x5))))) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P (x0 (g x1))))
% Found (fun (P:(fofType->Prop))=> ((((fun (x2:(((eq fofType) x1) x1)) (x3:(((eq fofType) x1) (x0 (g x1))))=> (((((fun (b:fofType)=> ((((eq_trans fofType) x1) b) (x0 (g x1)))) x1) x2) x3) (fun (x5:fofType)=> ((P x1)->(P x5))))) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) (((eq_ref fofType) x1) P))) as proof of ((P x1)->(P (x0 (g x1))))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_sym10 b) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found (((eq_sym1 (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_trans00000 ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1))))) as proof of ((P x1)->(P (x0 (g x1))))
% Found ((eq_trans00000 ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1))))) as proof of ((P x1)->(P (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) x1) b)) (x3:(((eq fofType) b) (x0 (g x1))))=> (((eq_trans0000 x2) x3) P)) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1))))) as proof of ((P x1)->(P (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) x1) x1)) (x3:(((eq fofType) x1) (x0 (g x1))))=> ((((eq_trans000 x1) x2) x3) P)) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) as proof of ((P x1)->(P (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) x1) x1)) (x3:(((eq fofType) x1) (x0 (g x1))))=> (((((fun (b:fofType)=> ((eq_trans00 b) (x0 (g x1)))) x1) x2) x3) P)) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) as proof of ((P x1)->(P (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) x1) x1)) (x3:(((eq fofType) x1) (x0 (g x1))))=> (((((fun (b:fofType)=> (((eq_trans0 x1) b) (x0 (g x1)))) x1) x2) x3) P)) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) as proof of ((P x1)->(P (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) x1) x1)) (x3:(((eq fofType) x1) (x0 (g x1))))=> (((((fun (b:fofType)=> ((((eq_trans fofType) x1) b) (x0 (g x1)))) x1) x2) x3) P)) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) as proof of ((P x1)->(P (x0 (g x1))))
% Found (fun (P:(fofType->Prop))=> (((fun (x2:(((eq fofType) x1) x1)) (x3:(((eq fofType) x1) (x0 (g x1))))=> (((((fun (b:fofType)=> ((((eq_trans fofType) x1) b) (x0 (g x1)))) x1) x2) x3) P)) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1)))))) as proof of ((P x1)->(P (x0 (g x1))))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_sym10 b) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found (((eq_sym1 (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_trans0000 ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((eq_trans000 x1) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((fun (b:fofType)=> ((eq_trans00 b) (x0 (g x1)))) x1) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((fun (b:fofType)=> (((eq_trans0 x1) b) (x0 (g x1)))) x1) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((fun (b:fofType)=> ((((eq_trans fofType) x1) b) (x0 (g x1)))) x1) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_sym10 b) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found (((eq_sym1 (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_trans0000 ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((eq_trans000 x1) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((fun (b:fofType)=> ((eq_trans00 b) (x0 (g x1)))) x1) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((fun (b:fofType)=> (((eq_trans0 x1) b) (x0 (g x1)))) x1) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((fun (b:fofType)=> ((((eq_trans fofType) x1) b) (x0 (g x1)))) x1) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_sym10 b) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found (((eq_sym1 (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_trans0000 ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((eq_trans000 x1) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((fun (b:fofType)=> ((eq_trans00 b) (x0 (g x1)))) x1) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((fun (b:fofType)=> (((eq_trans0 x1) b) (x0 (g x1)))) x1) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((fun (b:fofType)=> ((((eq_trans fofType) x1) b) (x0 (g x1)))) x1) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_sym10 b) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found (((eq_sym1 (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_trans0000 ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((eq_trans000 x1) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((fun (b:fofType)=> ((eq_trans00 b) (x0 (g x1)))) x1) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((fun (b:fofType)=> (((eq_trans0 x1) b) (x0 (g x1)))) x1) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((fun (b:fofType)=> ((((eq_trans fofType) x1) b) (x0 (g x1)))) x1) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_sym10 b) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found (((eq_sym1 (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_trans0000 ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((eq_trans000 x1) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((fun (b:fofType)=> ((eq_trans00 b) (x0 (g x1)))) x1) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((fun (b:fofType)=> (((eq_trans0 x1) b) (x0 (g x1)))) x1) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((fun (b:fofType)=> ((((eq_trans fofType) x1) b) (x0 (g x1)))) x1) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_sym10 b) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found (((eq_sym1 (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_trans0000 ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((eq_trans000 x1) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((fun (b:fofType)=> ((eq_trans00 b) (x0 (g x1)))) x1) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((fun (b:fofType)=> (((eq_trans0 x1) b) (x0 (g x1)))) x1) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((fun (b:fofType)=> ((((eq_trans fofType) x1) b) (x0 (g x1)))) x1) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_sym10 b) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found (((eq_sym1 (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_trans0000 ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((eq_trans000 x1) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((fun (b:fofType)=> ((eq_trans00 b) (x0 (g x1)))) x1) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((fun (b:fofType)=> (((eq_trans0 x1) b) (x0 (g x1)))) x1) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((fun (b:fofType)=> ((((eq_trans fofType) x1) b) (x0 (g x1)))) x1) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) b)
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_sym10 b) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found (((eq_sym1 (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) b) (x0 (g x1)))
% Found ((eq_trans0000 ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) b) ((eq_ref fofType) (x0 (g x1))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found (((eq_trans000 x1) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((fun (b:fofType)=> ((eq_trans00 b) (x0 (g x1)))) x1) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((fun (b:fofType)=> (((eq_trans0 x1) b) (x0 (g x1)))) x1) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found ((((fun (b:fofType)=> ((((eq_trans fofType) x1) b) (x0 (g x1)))) x1) ((eq_ref fofType) x1)) ((((eq_sym fofType) (x0 (g x1))) x1) ((eq_ref fofType) (x0 (g x1))))) as proof of (((eq fofType) x1) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found (eq_sym1000 ((eq_ref fofType) (x0 (g x1)))) as proof of ((P (b x1))->(P (x0 (g x1))))
% Found (eq_sym1000 ((eq_ref fofType) (x0 (g x1)))) as proof of ((P (b x1))->(P (x0 (g x1))))
% Found ((fun (x2:(((eq fofType) (x0 (g x1))) (b x1)))=> ((eq_sym100 x2) P)) ((eq_ref fofType) (x0 (g x1)))) as proof of ((P (b x1))->(P (x0 (g x1))))
% Found ((fun (x2:(((eq fofType) (x0 (g x1))) (b x1)))=> (((eq_sym10 (b x1)) x2) P)) ((eq_ref fofType) (x0 (g x1)))) as proof of ((P (b x1))->(P (x0 (g x1))))
% Found ((fun (x2:(((eq fofType) (x0 (g x1))) (b x1)))=> ((((eq_sym1 (x0 (g x1))) (b x1)) x2) P)) ((eq_ref fofType) (x0 (g x1)))) as proof of ((P (b x1))->(P (x0 (g x1))))
% Found ((fun (x2:(((eq fofType) (x0 (g x1))) (b x1)))=> (((((eq_sym fofType) (x0 (g x1))) (b x1)) x2) P)) ((eq_ref fofType) (x0 (g x1)))) as proof of ((P (b x1))->(P (x0 (g x1))))
% Found (fun (P:(fofType->Prop))=> ((fun (x2:(((eq fofType) (x0 (g x1))) (b x1)))=> (((((eq_sym fofType) (x0 (g x1))) (b x1)) x2) P)) ((eq_ref fofType) (x0 (g x1))))) as proof of ((P (b x1))->(P (x0 (g x1))))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found (eq_sym1000 ((eq_ref fofType) (x0 (g x1)))) as proof of ((P (b x1))->(P (x0 (g x1))))
% Found (eq_sym1000 ((eq_ref fofType) (x0 (g x1)))) as proof of ((P (b x1))->(P (x0 (g x1))))
% Found ((fun (x2:(((eq fofType) (x0 (g x1))) (b x1)))=> ((eq_sym100 x2) P)) ((eq_ref fofType) (x0 (g x1)))) as proof of ((P (b x1))->(P (x0 (g x1))))
% Found ((fun (x2:(((eq fofType) (x0 (g x1))) (b x1)))=> (((eq_sym10 (b x1)) x2) P)) ((eq_ref fofType) (x0 (g x1)))) as proof of ((P (b x1))->(P (x0 (g x1))))
% Found ((fun (x2:(((eq fofType) (x0 (g x1))) (b x1)))=> ((((eq_sym1 (x0 (g x1))) (b x1)) x2) P)) ((eq_ref fofType) (x0 (g x1)))) as proof of ((P (b x1))->(P (x0 (g x1))))
% Found ((fun (x2:(((eq fofType) (x0 (g x1))) (b x1)))=> (((((eq_sym fofType) (x0 (g x1))) (b x1)) x2) P)) ((eq_ref fofType) (x0 (g x1)))) as proof of ((P (b x1))->(P (x0 (g x1))))
% Found (fun (P:(fofType->Prop))=> ((fun (x2:(((eq fofType) (x0 (g x1))) (b x1)))=> (((((eq_sym fofType) (x0 (g x1))) (b x1)) x2) P)) ((eq_ref fofType) (x0 (g x1))))) as proof of ((P (b x1))->(P (x0 (g x1))))
% Found eq_ref000:=(eq_ref00 P1):((P1 (x0 (g x1)))->(P1 (x0 (g x1))))
% Found (eq_ref00 P1) as proof of ((P1 (x0 (g x1)))->(P1 (b x1)))
% Found ((eq_ref0 (x0 (g x1))) P1) as proof of ((P1 (x0 (g x1)))->(P1 (b x1)))
% Found (((eq_ref fofType) (x0 (g x1))) P1) as proof of ((P1 (x0 (g x1)))->(P1 (b x1)))
% Found (((eq_ref fofType) (x0 (g x1))) P1) as proof of ((P1 (x0 (g x1)))->(P1 (b x1)))
% Found (fun (P1:(fofType->Prop))=> (((eq_ref fofType) (x0 (g x1))) P1)) as proof of ((P1 (x0 (g x1)))->(P1 (b x1)))
% Found eq_ref000:=(eq_ref00 P1):((P1 (x0 (g x1)))->(P1 (x0 (g x1))))
% Found (eq_ref00 P1) as proof of ((P1 (x0 (g x1)))->(P1 (b x1)))
% Found ((eq_ref0 (x0 (g x1))) P1) as proof of ((P1 (x0 (g x1)))->(P1 (b x1)))
% Found (((eq_ref fofType) (x0 (g x1))) P1) as proof of ((P1 (x0 (g x1)))->(P1 (b x1)))
% Found (((eq_ref fofType) (x0 (g x1))) P1) as proof of ((P1 (x0 (g x1)))->(P1 (b x1)))
% Found (fun (P1:(fofType->Prop))=> (((eq_ref fofType) (x0 (g x1))) P1)) as proof of ((P1 (x0 (g x1)))->(P1 (b x1)))
% Found eq_ref000:=(eq_ref00 P1):((P1 (x0 (g x1)))->(P1 (x0 (g x1))))
% Found (eq_ref00 P1) as proof of ((P1 (x0 (g x1)))->(P1 (b x1)))
% Found ((eq_ref0 (x0 (g x1))) P1) as proof of ((P1 (x0 (g x1)))->(P1 (b x1)))
% Found (((eq_ref fofType) (x0 (g x1))) P1) as proof of ((P1 (x0 (g x1)))->(P1 (b x1)))
% Found (((eq_ref fofType) (x0 (g x1))) P1) as proof of ((P1 (x0 (g x1)))->(P1 (b x1)))
% Found (fun (P1:(fofType->Prop))=> (((eq_ref fofType) (x0 (g x1))) P1)) as proof of ((P1 (x0 (g x1)))->(P1 (b x1)))
% Found eq_ref000:=(eq_ref00 P1):((P1 (x0 (g x1)))->(P1 (x0 (g x1))))
% Found (eq_ref00 P1) as proof of ((P1 (x0 (g x1)))->(P1 (b x1)))
% Found ((eq_ref0 (x0 (g x1))) P1) as proof of ((P1 (x0 (g x1)))->(P1 (b x1)))
% Found (((eq_ref fofType) (x0 (g x1))) P1) as proof of ((P1 (x0 (g x1)))->(P1 (b x1)))
% Found (((eq_ref fofType) (x0 (g x1))) P1) as proof of ((P1 (x0 (g x1)))->(P1 (b x1)))
% Found (fun (P1:(fofType->Prop))=> (((eq_ref fofType) (x0 (g x1))) P1)) as proof of ((P1 (x0 (g x1)))->(P1 (b x1)))
% Found eq_ref000:=(eq_ref00 P1):((P1 (x0 (g x1)))->(P1 (x0 (g x1))))
% Found (eq_ref00 P1) as proof of ((P1 (x0 (g x1)))->(P1 (b x1)))
% Found ((eq_ref0 (x0 (g x1))) P1) as proof of ((P1 (x0 (g x1)))->(P1 (b x1)))
% Found (((eq_ref fofType) (x0 (g x1))) P1) as proof of ((P1 (x0 (g x1)))->(P1 (b x1)))
% Found (((eq_ref fofType) (x0 (g x1))) P1) as proof of ((P1 (x0 (g x1)))->(P1 (b x1)))
% Found (fun (P1:(fofType->Prop))=> (((eq_ref fofType) (x0 (g x1))) P1)) as proof of ((P1 (x0 (g x1)))->(P1 (b x1)))
% Found eq_ref000:=(eq_ref00 P1):((P1 (x0 (g x1)))->(P1 (x0 (g x1))))
% Found (eq_ref00 P1) as proof of ((P1 (x0 (g x1)))->(P1 (b x1)))
% Found ((eq_ref0 (x0 (g x1))) P1) as proof of ((P1 (x0 (g x1)))->(P1 (b x1)))
% Found (((eq_ref fofType) (x0 (g x1))) P1) as proof of ((P1 (x0 (g x1)))->(P1 (b x1)))
% Found (((eq_ref fofType) (x0 (g x1))) P1) as proof of ((P1 (x0 (g x1)))->(P1 (b x1)))
% Found (fun (P1:(fofType->Prop))=> (((eq_ref fofType) (x0 (g x1))) P1)) as proof of ((P1 (x0 (g x1)))->(P1 (b x1)))
% Found eq_ref000:=(eq_ref00 P1):((P1 (x0 (g x1)))->(P1 (x0 (g x1))))
% Found (eq_ref00 P1) as proof of ((P1 (x0 (g x1)))->(P1 (b x1)))
% Found ((eq_ref0 (x0 (g x1))) P1) as proof of ((P1 (x0 (g x1)))->(P1 (b x1)))
% Found (((eq_ref fofType) (x0 (g x1))) P1) as proof of ((P1 (x0 (g x1)))->(P1 (b x1)))
% Found (((eq_ref fofType) (x0 (g x1))) P1) as proof of ((P1 (x0 (g x1)))->(P1 (b x1)))
% Found (fun (P1:(fofType->Prop))=> (((eq_ref fofType) (x0 (g x1))) P1)) as proof of ((P1 (x0 (g x1)))->(P1 (b x1)))
% Found eq_ref000:=(eq_ref00 P1):((P1 (x0 (g x1)))->(P1 (x0 (g x1))))
% Found (eq_ref00 P1) as proof of ((P1 (x0 (g x1)))->(P1 (b x1)))
% Found ((eq_ref0 (x0 (g x1))) P1) as proof of ((P1 (x0 (g x1)))->(P1 (b x1)))
% Found (((eq_ref fofType) (x0 (g x1))) P1) as proof of ((P1 (x0 (g x1)))->(P1 (b x1)))
% Found (((eq_ref fofType) (x0 (g x1))) P1) as proof of ((P1 (x0 (g x1)))->(P1 (b x1)))
% Found (fun (P1:(fofType->Prop))=> (((eq_ref fofType) (x0 (g x1))) P1)) as proof of ((P1 (x0 (g x1)))->(P1 (b x1)))
% Found eq_ref000:=(eq_ref00 P1):((P1 (x0 (g x1)))->(P1 (x0 (g x1))))
% Found (eq_ref00 P1) as proof of ((P1 (x0 (g x1)))->(P1 (b x1)))
% Found ((eq_ref0 (x0 (g x1))) P1) as proof of ((P1 (x0 (g x1)))->(P1 (b x1)))
% Found (((eq_ref fofType) (x0 (g x1))) P1) as proof of ((P1 (x0 (g x1)))->(P1 (b x1)))
% Found (((eq_ref fofType) (x0 (g x1))) P1) as proof of ((P1 (x0 (g x1)))->(P1 (b x1)))
% Found (fun (P1:(fofType->Prop))=> (((eq_ref fofType) (x0 (g x1))) P1)) as proof of ((P1 (x0 (g x1)))->(P1 (b x1)))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found ((eq_sym10 (b x1)) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found (((eq_sym1 (x0 (g x1))) (b x1)) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) (b x1)) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found ((eq_sym10 (b x1)) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found (((eq_sym1 (x0 (g x1))) (b x1)) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) (b x1)) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found ((eq_sym10 (b x1)) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found (((eq_sym1 (x0 (g x1))) (b x1)) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) (b x1)) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found ((eq_sym10 (b x1)) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found (((eq_sym1 (x0 (g x1))) (b x1)) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) (b x1)) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found eq_ref000:=(eq_ref00 P1):((P1 (x0 (g x1)))->(P1 (x0 (g x1))))
% Found (eq_ref00 P1) as proof of ((P1 (x0 (g x1)))->(P1 (b x1)))
% Found ((eq_ref0 (x0 (g x1))) P1) as proof of ((P1 (x0 (g x1)))->(P1 (b x1)))
% Found (((eq_ref fofType) (x0 (g x1))) P1) as proof of ((P1 (x0 (g x1)))->(P1 (b x1)))
% Found (((eq_ref fofType) (x0 (g x1))) P1) as proof of ((P1 (x0 (g x1)))->(P1 (b x1)))
% Found (fun (P1:(fofType->Prop))=> (((eq_ref fofType) (x0 (g x1))) P1)) as proof of ((P1 (x0 (g x1)))->(P1 (b x1)))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found ((eq_sym10 (b x1)) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found (((eq_sym1 (x0 (g x1))) (b x1)) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) (b x1)) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found (eq_sym100 ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found ((eq_sym10 (b x1)) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found (((eq_sym1 (x0 (g x1))) (b x1)) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found ((((eq_sym fofType) (x0 (g x1))) (b x1)) ((eq_ref fofType) (x0 (g x1)))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g (b x1))) (g (x0 (g x1))))
% Found ((eq_sym10 (g (b x1))) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g (b x1))) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g (b x1))) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g (b x1))) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g (b x1))) (g (x0 (g x1))))
% Found (x20 ((((eq_sym fofType) (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (forall (P:(fofType->Prop)), ((P (b x1))->(P (x0 (g x1)))))
% Found ((x2 (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (forall (P:(fofType->Prop)), ((P (b x1))->(P (x0 (g x1)))))
% Found (((x (b x1)) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (forall (P:(fofType->Prop)), ((P (b x1))->(P (x0 (g x1)))))
% Found (((x (b x1)) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (forall (P:(fofType->Prop)), ((P (b x1))->(P (x0 (g x1)))))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g (b x1))) (g (x0 (g x1))))
% Found ((eq_sym10 (g (b x1))) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g (b x1))) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g (b x1))) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g (b x1))) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g (b x1))) (g (x0 (g x1))))
% Found (x20 ((((eq_sym fofType) (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (forall (P:(fofType->Prop)), ((P (b x1))->(P (x0 (g x1)))))
% Found ((x2 (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (forall (P:(fofType->Prop)), ((P (b x1))->(P (x0 (g x1)))))
% Found (((x (b x1)) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (forall (P:(fofType->Prop)), ((P (b x1))->(P (x0 (g x1)))))
% Found (((x (b x1)) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (forall (P:(fofType->Prop)), ((P (b x1))->(P (x0 (g x1)))))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g (b x1))) (g (x0 (g x1))))
% Found ((eq_sym10 (g (b x1))) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g (b x1))) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g (b x1))) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g (b x1))) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g (b x1))) (g (x0 (g x1))))
% Found (x20 ((((eq_sym fofType) (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found ((x2 (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found (((x (b x1)) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g (b x1))) (g (x0 (g x1))))
% Found ((eq_sym10 (g (b x1))) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g (b x1))) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g (b x1))) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g (b x1))) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g (b x1))) (g (x0 (g x1))))
% Found (x20 ((((eq_sym fofType) (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found ((x2 (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found (((x (b x1)) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g (b x1))) (g (x0 (g x1))))
% Found ((eq_sym10 (g (b x1))) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g (b x1))) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g (b x1))) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g (b x1))) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g (b x1))) (g (x0 (g x1))))
% Found (x20 ((((eq_sym fofType) (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found ((x2 (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found (((x (b x1)) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g (b x1))) (g (x0 (g x1))))
% Found ((eq_sym10 (g (b x1))) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g (b x1))) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g (b x1))) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g (b x1))) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g (b x1))) (g (x0 (g x1))))
% Found (x20 ((((eq_sym fofType) (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found ((x2 (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found (((x (b x1)) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g (b x1))) (g (x0 (g x1))))
% Found ((eq_sym10 (g (b x1))) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g (b x1))) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g (b x1))) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g (b x1))) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g (b x1))) (g (x0 (g x1))))
% Found (x20 ((((eq_sym fofType) (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found ((x2 (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found (((x (b x1)) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found eq_ref00:=(eq_ref0 (g (x0 (g x1)))):(((eq fofType) (g (x0 (g x1)))) (g (x0 (g x1))))
% Found (eq_ref0 (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found ((eq_ref fofType) (g (x0 (g x1)))) as proof of (((eq fofType) (g (x0 (g x1)))) (g (b x1)))
% Found (eq_sym100 ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g (b x1))) (g (x0 (g x1))))
% Found ((eq_sym10 (g (b x1))) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g (b x1))) (g (x0 (g x1))))
% Found (((eq_sym1 (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g (b x1))) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g (b x1))) (g (x0 (g x1))))
% Found ((((eq_sym fofType) (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1))))) as proof of (((eq fofType) (g (b x1))) (g (x0 (g x1))))
% Found (x20 ((((eq_sym fofType) (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found ((x2 (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found (((x (b x1)) (x0 (g x1))) ((((eq_sym fofType) (g (x0 (g x1)))) (g (b x1))) ((eq_ref fofType) (g (x0 (g x1)))))) as proof of (((eq fofType) (b x1)) (x0 (g x1)))
% Found eq_ref000:=(eq_ref00 P):((P (b x1))->(P (b x1)))
% Found (eq_ref00 P) as proof of (P0 (b x1))
% Found ((eq_ref0 (b x1)) P) as proof of (P0 (b x1))
% Found (((eq_ref fofType) (b x1)) P) as proof of (P0 (b x1))
% Found (((eq_ref fofType) (b x1)) P) as proof of (P0 (b x1))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_sym1000 ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) (b x1)) P)) as proof of ((P (b x1))->(P (x0 (g x1))))
% Found ((eq_sym1000 ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) (b x1)) P)) as proof of ((P (b x1))->(P (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) (b x1)))=> ((eq_sym100 x2) (fun (x4:fofType)=> ((P (b x1))->(P x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) (b x1)) P)) as proof of ((P (b x1))->(P (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) (b x1)))=> (((eq_sym10 (b x1)) x2) (fun (x4:fofType)=> ((P (b x1))->(P x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) (b x1)) P)) as proof of ((P (b x1))->(P (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) (b x1)))=> ((((eq_sym1 (x0 (g x1))) (b x1)) x2) (fun (x4:fofType)=> ((P (b x1))->(P x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) (b x1)) P)) as proof of ((P (b x1))->(P (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) (b x1)))=> (((((eq_sym fofType) (x0 (g x1))) (b x1)) x2) (fun (x4:fofType)=> ((P (b x1))->(P x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) (b x1)) P)) as proof of ((P (b x1))->(P (x0 (g x1))))
% Found (fun (P:(fofType->Prop))=> (((fun (x2:(((eq fofType) (x0 (g x1))) (b x1)))=> (((((eq_sym fofType) (x0 (g x1))) (b x1)) x2) (fun (x4:fofType)=> ((P (b x1))->(P x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) (b x1)) P))) as proof of ((P (b x1))->(P (x0 (g x1))))
% Found eq_ref000:=(eq_ref00 P):((P (b x1))->(P (b x1)))
% Found (eq_ref00 P) as proof of (P0 (b x1))
% Found ((eq_ref0 (b x1)) P) as proof of (P0 (b x1))
% Found (((eq_ref fofType) (b x1)) P) as proof of (P0 (b x1))
% Found (((eq_ref fofType) (b x1)) P) as proof of (P0 (b x1))
% Found eq_ref00:=(eq_ref0 (x0 (g x1))):(((eq fofType) (x0 (g x1))) (x0 (g x1)))
% Found (eq_ref0 (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_ref fofType) (x0 (g x1))) as proof of (((eq fofType) (x0 (g x1))) (b x1))
% Found ((eq_sym1000 ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) (b x1)) P)) as proof of ((P (b x1))->(P (x0 (g x1))))
% Found ((eq_sym1000 ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) (b x1)) P)) as proof of ((P (b x1))->(P (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) (b x1)))=> ((eq_sym100 x2) (fun (x4:fofType)=> ((P (b x1))->(P x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) (b x1)) P)) as proof of ((P (b x1))->(P (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) (b x1)))=> (((eq_sym10 (b x1)) x2) (fun (x4:fofType)=> ((P (b x1))->(P x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) (b x1)) P)) as proof of ((P (b x1))->(P (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) (b x1)))=> ((((eq_sym1 (x0 (g x1))) (b x1)) x2) (fun (x4:fofType)=> ((P (b x1))->(P x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) (b x1)) P)) as proof of ((P (b x1))->(P (x0 (g x1))))
% Found (((fun (x2:(((eq fofType) (x0 (g x1))) (b x1)))=> (((((eq_sym fofType) (x0 (g x1))) (b x1)) x2) (fun (x4:fofType)=> ((P (b x1))->(P x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) (b x1)) P)) as proof of ((P (b x1))->(P (x0 (g x1))))
% Found (fun (P:(fofType->Prop))=> (((fun (x2:(((eq fofType) (x0 (g x1))) (b x1)))=> (((((eq_sym fofType) (x0 (g x1))) (b x1)) x2) (fun (x4:fofType)=> ((P (b x1))->(P x4))))) ((eq_ref fofType) (x0 (g x1)))) (((eq_ref fofType) (b x1)) P))) as proof of ((P (b x1))->(P (x0 (g x1))))
% Found eq_ref000:=(eq_ref00 P):((P x1)->(P x1))
% Found (eq_ref00 P) as proof o
% EOF
%------------------------------------------------------------------------------