TSTP Solution File: ALG274^5 by cocATP---0.2.0

%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : ALG274^5 : TPTP v6.1.0. Bugfixed v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n107.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 13:18:22 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  : ALG274^5 : TPTP v6.1.0. Bugfixed v5.3.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n107.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 09:04:26 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 0x1a466c8>, <kernel.Type object at 0x19e7cf8>) of role type named g_type
% Using role type
% Declaring g:Type
% FOF formula (<kernel.Constant object at 0x14d77e8>, <kernel.DependentProduct object at 0x19e7b48>) of role type named cGROUP3_type
% Using role type
% Declaring cGROUP3:((g->(g->g))->(g->Prop))
% FOF formula (<kernel.Constant object at 0x1a466c8>, <kernel.DependentProduct object at 0x19e7dd0>) of role type named cGROUP4_type
% Using role type
% Declaring cGROUP4:((g->(g->g))->Prop)
% FOF formula (<kernel.Constant object at 0x1a46908>, <kernel.DependentProduct object at 0x19e7b48>) of role type named cGRP_ASSOC_type
% Using role type
% Declaring cGRP_ASSOC:((g->(g->g))->Prop)
% FOF formula (<kernel.Constant object at 0x1a46908>, <kernel.DependentProduct object at 0x19e7dd0>) of role type named cGRP_DIVISORS_type
% Using role type
% Declaring cGRP_DIVISORS:((g->(g->g))->Prop)
% FOF formula (<kernel.Constant object at 0x19e7d88>, <kernel.DependentProduct object at 0x19e7c68>) of role type named cGRP_RIGHT_INVERSE_type
% Using role type
% Declaring cGRP_RIGHT_INVERSE:((g->(g->g))->(g->Prop))
% FOF formula (<kernel.Constant object at 0x19e7cb0>, <kernel.DependentProduct object at 0x19e77e8>) of role type named cGRP_RIGHT_UNIT_type
% Using role type
% Declaring cGRP_RIGHT_UNIT:((g->(g->g))->(g->Prop))
% FOF formula (((eq ((g->(g->g))->Prop)) cGRP_ASSOC) (fun (Xf:(g->(g->g)))=> (forall (Xa:g) (Xb:g) (Xc:g), (((eq g) ((Xf ((Xf Xa) Xb)) Xc)) ((Xf Xa) ((Xf Xb) Xc)))))) of role definition named cGRP_ASSOC_def
% A new definition: (((eq ((g->(g->g))->Prop)) cGRP_ASSOC) (fun (Xf:(g->(g->g)))=> (forall (Xa:g) (Xb:g) (Xc:g), (((eq g) ((Xf ((Xf Xa) Xb)) Xc)) ((Xf Xa) ((Xf Xb) Xc))))))
% Defined: cGRP_ASSOC:=(fun (Xf:(g->(g->g)))=> (forall (Xa:g) (Xb:g) (Xc:g), (((eq g) ((Xf ((Xf Xa) Xb)) Xc)) ((Xf Xa) ((Xf Xb) Xc)))))
% FOF formula (((eq ((g->(g->g))->Prop)) cGRP_DIVISORS) (fun (Xf:(g->(g->g)))=> (forall (Xa:g) (Xb:g), ((and ((ex g) (fun (Xx:g)=> (((eq g) ((Xf Xa) Xx)) Xb)))) ((ex g) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb))))))) of role definition named cGRP_DIVISORS_def
% A new definition: (((eq ((g->(g->g))->Prop)) cGRP_DIVISORS) (fun (Xf:(g->(g->g)))=> (forall (Xa:g) (Xb:g), ((and ((ex g) (fun (Xx:g)=> (((eq g) ((Xf Xa) Xx)) Xb)))) ((ex g) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb)))))))
% Defined: cGRP_DIVISORS:=(fun (Xf:(g->(g->g)))=> (forall (Xa:g) (Xb:g), ((and ((ex g) (fun (Xx:g)=> (((eq g) ((Xf Xa) Xx)) Xb)))) ((ex g) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb))))))
% FOF formula (((eq ((g->(g->g))->(g->Prop))) cGRP_RIGHT_INVERSE) (fun (Xf:(g->(g->g))) (Xe:g)=> (forall (Xa:g), ((ex g) (fun (Xb:g)=> (((eq g) ((Xf Xa) Xb)) Xe)))))) of role definition named cGRP_RIGHT_INVERSE_def
% A new definition: (((eq ((g->(g->g))->(g->Prop))) cGRP_RIGHT_INVERSE) (fun (Xf:(g->(g->g))) (Xe:g)=> (forall (Xa:g), ((ex g) (fun (Xb:g)=> (((eq g) ((Xf Xa) Xb)) Xe))))))
% Defined: cGRP_RIGHT_INVERSE:=(fun (Xf:(g->(g->g))) (Xe:g)=> (forall (Xa:g), ((ex g) (fun (Xb:g)=> (((eq g) ((Xf Xa) Xb)) Xe)))))
% FOF formula (((eq ((g->(g->g))->(g->Prop))) cGRP_RIGHT_UNIT) (fun (Xf:(g->(g->g))) (Xe:g)=> (forall (Xa:g), (((eq g) ((Xf Xa) Xe)) Xa)))) of role definition named cGRP_RIGHT_UNIT_def
% A new definition: (((eq ((g->(g->g))->(g->Prop))) cGRP_RIGHT_UNIT) (fun (Xf:(g->(g->g))) (Xe:g)=> (forall (Xa:g), (((eq g) ((Xf Xa) Xe)) Xa))))
% Defined: cGRP_RIGHT_UNIT:=(fun (Xf:(g->(g->g))) (Xe:g)=> (forall (Xa:g), (((eq g) ((Xf Xa) Xe)) Xa)))
% FOF formula (((eq ((g->(g->g))->(g->Prop))) cGROUP3) (fun (Xf:(g->(g->g))) (Xe:g)=> ((and ((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) Xe))) ((cGRP_RIGHT_INVERSE Xf) Xe)))) of role definition named cGROUP3_def
% A new definition: (((eq ((g->(g->g))->(g->Prop))) cGROUP3) (fun (Xf:(g->(g->g))) (Xe:g)=> ((and ((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) Xe))) ((cGRP_RIGHT_INVERSE Xf) Xe))))
% Defined: cGROUP3:=(fun (Xf:(g->(g->g))) (Xe:g)=> ((and ((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) Xe))) ((cGRP_RIGHT_INVERSE Xf) Xe)))
% FOF formula (((eq ((g->(g->g))->Prop)) cGROUP4) (fun (Xf:(g->(g->g)))=> ((and (cGRP_ASSOC Xf)) (cGRP_DIVISORS Xf)))) of role definition named cGROUP4_def
% A new definition: (((eq ((g->(g->g))->Prop)) cGROUP4) (fun (Xf:(g->(g->g)))=> ((and (cGRP_ASSOC Xf)) (cGRP_DIVISORS Xf))))
% Defined: cGROUP4:=(fun (Xf:(g->(g->g)))=> ((and (cGRP_ASSOC Xf)) (cGRP_DIVISORS Xf)))
% FOF formula (forall (Xf:(g->(g->g))), ((iff ((ex g) (fun (Xe:g)=> ((cGROUP3 Xf) Xe)))) (cGROUP4 Xf))) of role conjecture named cEQUIV_03_04
% Conjecture to prove = (forall (Xf:(g->(g->g))), ((iff ((ex g) (fun (Xe:g)=> ((cGROUP3 Xf) Xe)))) (cGROUP4 Xf))):Prop
% Parameter g_DUMMY:g.
% We need to prove ['(forall (Xf:(g->(g->g))), ((iff ((ex g) (fun (Xe:g)=> ((cGROUP3 Xf) Xe)))) (cGROUP4 Xf)))']
% Parameter g:Type.
% Definition cGROUP3:=(fun (Xf:(g->(g->g))) (Xe:g)=> ((and ((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) Xe))) ((cGRP_RIGHT_INVERSE Xf) Xe))):((g->(g->g))->(g->Prop)).
% Definition cGROUP4:=(fun (Xf:(g->(g->g)))=> ((and (cGRP_ASSOC Xf)) (cGRP_DIVISORS Xf))):((g->(g->g))->Prop).
% Definition cGRP_ASSOC:=(fun (Xf:(g->(g->g)))=> (forall (Xa:g) (Xb:g) (Xc:g), (((eq g) ((Xf ((Xf Xa) Xb)) Xc)) ((Xf Xa) ((Xf Xb) Xc))))):((g->(g->g))->Prop).
% Definition cGRP_DIVISORS:=(fun (Xf:(g->(g->g)))=> (forall (Xa:g) (Xb:g), ((and ((ex g) (fun (Xx:g)=> (((eq g) ((Xf Xa) Xx)) Xb)))) ((ex g) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb)))))):((g->(g->g))->Prop).
% Definition cGRP_RIGHT_INVERSE:=(fun (Xf:(g->(g->g))) (Xe:g)=> (forall (Xa:g), ((ex g) (fun (Xb:g)=> (((eq g) ((Xf Xa) Xb)) Xe))))):((g->(g->g))->(g->Prop)).
% Definition cGRP_RIGHT_UNIT:=(fun (Xf:(g->(g->g))) (Xe:g)=> (forall (Xa:g), (((eq g) ((Xf Xa) Xe)) Xa))):((g->(g->g))->(g->Prop)).
% Trying to prove (forall (Xf:(g->(g->g))), ((iff ((ex g) (fun (Xe:g)=> ((cGROUP3 Xf) Xe)))) (cGROUP4 Xf)))
% Found x4:(cGRP_ASSOC Xf)
% Found x4 as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found x4 as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found x4 as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found (fun (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of (cGRP_ASSOC Xf)
% Found (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of (((cGRP_RIGHT_UNIT Xf) x0)->(cGRP_ASSOC Xf))
% Found (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of ((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->(cGRP_ASSOC Xf)))
% Found (and_rect10 (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found ((and_rect1 (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found x4 as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found (fun (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of (cGRP_ASSOC Xf)
% Found (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of (((cGRP_RIGHT_UNIT Xf) x0)->(cGRP_ASSOC Xf))
% Found (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of ((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->(cGRP_ASSOC Xf)))
% Found (and_rect10 (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found ((and_rect1 (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found (fun (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of (cGRP_ASSOC Xf)
% Found (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of (((cGRP_RIGHT_UNIT Xf) x0)->(cGRP_ASSOC Xf))
% Found (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of ((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->(cGRP_ASSOC Xf)))
% Found (and_rect10 (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found ((and_rect1 (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found (fun (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of (cGRP_ASSOC Xf)
% Found (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of (((cGRP_RIGHT_UNIT Xf) x0)->(cGRP_ASSOC Xf))
% Found (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of ((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->(cGRP_ASSOC Xf)))
% Found (and_rect10 (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found ((and_rect1 (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found x4 as proof of (cGRP_ASSOC Xf)
% Found x6:(cGRP_ASSOC Xf)
% Found x6 as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found x4 as proof of (cGRP_ASSOC Xf)
% Found x6:(cGRP_ASSOC Xf)
% Found x6 as proof of (cGRP_ASSOC Xf)
% Found x6:(cGRP_ASSOC Xf)
% Found (fun (x7:((cGRP_RIGHT_UNIT Xf) x0))=> x6) as proof of (cGRP_ASSOC Xf)
% Found (fun (x6:(cGRP_ASSOC Xf)) (x7:((cGRP_RIGHT_UNIT Xf) x0))=> x6) as proof of (((cGRP_RIGHT_UNIT Xf) x0)->(cGRP_ASSOC Xf))
% Found (fun (x6:(cGRP_ASSOC Xf)) (x7:((cGRP_RIGHT_UNIT Xf) x0))=> x6) as proof of ((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->(cGRP_ASSOC Xf)))
% Found (and_rect10 (fun (x6:(cGRP_ASSOC Xf)) (x7:((cGRP_RIGHT_UNIT Xf) x0))=> x6)) as proof of (cGRP_ASSOC Xf)
% Found ((and_rect1 (cGRP_ASSOC Xf)) (fun (x6:(cGRP_ASSOC Xf)) (x7:((cGRP_RIGHT_UNIT Xf) x0))=> x6)) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x6:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x6) x2)) (cGRP_ASSOC Xf)) (fun (x6:(cGRP_ASSOC Xf)) (x7:((cGRP_RIGHT_UNIT Xf) x0))=> x6)) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x6:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x6) x2)) (cGRP_ASSOC Xf)) (fun (x6:(cGRP_ASSOC Xf)) (x7:((cGRP_RIGHT_UNIT Xf) x0))=> x6)) as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found x4 as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found x4 as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found x4 as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found x4 as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found x4 as proof of (cGRP_ASSOC Xf)
% Found x6:(cGRP_ASSOC Xf)
% Found x6 as proof of (cGRP_ASSOC Xf)
% Found x6:(cGRP_ASSOC Xf)
% Found (fun (x7:((cGRP_RIGHT_UNIT Xf) x0))=> x6) as proof of (cGRP_ASSOC Xf)
% Found (fun (x6:(cGRP_ASSOC Xf)) (x7:((cGRP_RIGHT_UNIT Xf) x0))=> x6) as proof of (((cGRP_RIGHT_UNIT Xf) x0)->(cGRP_ASSOC Xf))
% Found (fun (x6:(cGRP_ASSOC Xf)) (x7:((cGRP_RIGHT_UNIT Xf) x0))=> x6) as proof of ((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->(cGRP_ASSOC Xf)))
% Found (and_rect10 (fun (x6:(cGRP_ASSOC Xf)) (x7:((cGRP_RIGHT_UNIT Xf) x0))=> x6)) as proof of (cGRP_ASSOC Xf)
% Found ((and_rect1 (cGRP_ASSOC Xf)) (fun (x6:(cGRP_ASSOC Xf)) (x7:((cGRP_RIGHT_UNIT Xf) x0))=> x6)) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x6:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x6) x2)) (cGRP_ASSOC Xf)) (fun (x6:(cGRP_ASSOC Xf)) (x7:((cGRP_RIGHT_UNIT Xf) x0))=> x6)) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x6:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x6) x2)) (cGRP_ASSOC Xf)) (fun (x6:(cGRP_ASSOC Xf)) (x7:((cGRP_RIGHT_UNIT Xf) x0))=> x6)) as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found x4 as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found x4 as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found x4 as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found x4 as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found x4 as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found x4 as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found (fun (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of (cGRP_ASSOC Xf)
% Found (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of (((cGRP_RIGHT_UNIT Xf) x0)->(cGRP_ASSOC Xf))
% Found (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of ((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->(cGRP_ASSOC Xf)))
% Found (and_rect10 (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found ((and_rect1 (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found (fun (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of (cGRP_ASSOC Xf)
% Found (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of (((cGRP_RIGHT_UNIT Xf) x0)->(cGRP_ASSOC Xf))
% Found (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of ((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->(cGRP_ASSOC Xf)))
% Found (and_rect10 (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found ((and_rect1 (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found (fun (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of (cGRP_ASSOC Xf)
% Found (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of (((cGRP_RIGHT_UNIT Xf) x0)->(cGRP_ASSOC Xf))
% Found (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of ((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->(cGRP_ASSOC Xf)))
% Found (and_rect10 (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found ((and_rect1 (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found x6:(cGRP_ASSOC Xf)
% Found x6 as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found x4 as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found x4 as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found x4 as proof of (cGRP_ASSOC Xf)
% Found x6:(cGRP_ASSOC Xf)
% Found (fun (x7:((cGRP_RIGHT_UNIT Xf) x0))=> x6) as proof of (cGRP_ASSOC Xf)
% Found (fun (x6:(cGRP_ASSOC Xf)) (x7:((cGRP_RIGHT_UNIT Xf) x0))=> x6) as proof of (((cGRP_RIGHT_UNIT Xf) x0)->(cGRP_ASSOC Xf))
% Found (fun (x6:(cGRP_ASSOC Xf)) (x7:((cGRP_RIGHT_UNIT Xf) x0))=> x6) as proof of ((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->(cGRP_ASSOC Xf)))
% Found (and_rect10 (fun (x6:(cGRP_ASSOC Xf)) (x7:((cGRP_RIGHT_UNIT Xf) x0))=> x6)) as proof of (cGRP_ASSOC Xf)
% Found ((and_rect1 (cGRP_ASSOC Xf)) (fun (x6:(cGRP_ASSOC Xf)) (x7:((cGRP_RIGHT_UNIT Xf) x0))=> x6)) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x6:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x6) x2)) (cGRP_ASSOC Xf)) (fun (x6:(cGRP_ASSOC Xf)) (x7:((cGRP_RIGHT_UNIT Xf) x0))=> x6)) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x6:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x6) x2)) (cGRP_ASSOC Xf)) (fun (x6:(cGRP_ASSOC Xf)) (x7:((cGRP_RIGHT_UNIT Xf) x0))=> x6)) as proof of (cGRP_ASSOC Xf)
% Found x0:(cGRP_ASSOC Xf)
% Found x0 as proof of (cGRP_ASSOC Xf)
% Found x1:(cGRP_ASSOC Xf)
% Found x1 as proof of (cGRP_ASSOC Xf)
% Found x1:(cGRP_ASSOC Xf)
% Found x1 as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found (fun (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of (cGRP_ASSOC Xf)
% Found (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of (((cGRP_RIGHT_UNIT Xf) x0)->(cGRP_ASSOC Xf))
% Found (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of ((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->(cGRP_ASSOC Xf)))
% Found (and_rect10 (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found ((and_rect1 (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found (fun (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4))) as proof of (cGRP_ASSOC Xf)
% Found (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4))) as proof of (((cGRP_RIGHT_INVERSE Xf) x0)->(cGRP_ASSOC Xf))
% Found (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4))) as proof of (((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))->(((cGRP_RIGHT_INVERSE Xf) x0)->(cGRP_ASSOC Xf)))
% Found (and_rect00 (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)))) as proof of (cGRP_ASSOC Xf)
% Found ((and_rect0 (cGRP_ASSOC Xf)) (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)))) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x2:(((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))->(((cGRP_RIGHT_INVERSE Xf) x0)->P)))=> (((((and_rect ((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) ((cGRP_RIGHT_INVERSE Xf) x0)) P) x2) x1)) (cGRP_ASSOC Xf)) (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)))) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x2:(((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))->(((cGRP_RIGHT_INVERSE Xf) x0)->P)))=> (((((and_rect ((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) ((cGRP_RIGHT_INVERSE Xf) x0)) P) x2) x1)) (cGRP_ASSOC Xf)) (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)))) as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found (fun (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of (cGRP_ASSOC Xf)
% Found (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of (((cGRP_RIGHT_UNIT Xf) x0)->(cGRP_ASSOC Xf))
% Found (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of ((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->(cGRP_ASSOC Xf)))
% Found (and_rect10 (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found ((and_rect1 (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found (fun (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4))) as proof of (cGRP_ASSOC Xf)
% Found (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4))) as proof of (((cGRP_RIGHT_INVERSE Xf) x0)->(cGRP_ASSOC Xf))
% Found (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4))) as proof of (((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))->(((cGRP_RIGHT_INVERSE Xf) x0)->(cGRP_ASSOC Xf)))
% Found (and_rect00 (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)))) as proof of (cGRP_ASSOC Xf)
% Found ((and_rect0 (cGRP_ASSOC Xf)) (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)))) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x2:(((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))->(((cGRP_RIGHT_INVERSE Xf) x0)->P)))=> (((((and_rect ((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) ((cGRP_RIGHT_INVERSE Xf) x0)) P) x2) x1)) (cGRP_ASSOC Xf)) (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)))) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x2:(((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))->(((cGRP_RIGHT_INVERSE Xf) x0)->P)))=> (((((and_rect ((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) ((cGRP_RIGHT_INVERSE Xf) x0)) P) x2) x1)) (cGRP_ASSOC Xf)) (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)))) as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found x4 as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found x4 as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found x4 as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found x4 as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found (fun (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of (cGRP_ASSOC Xf)
% Found (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of (((cGRP_RIGHT_UNIT Xf) x0)->(cGRP_ASSOC Xf))
% Found (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of ((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->(cGRP_ASSOC Xf)))
% Found (and_rect10 (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found ((and_rect1 (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found x4 as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found (fun (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of (cGRP_ASSOC Xf)
% Found (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of (((cGRP_RIGHT_UNIT Xf) x0)->(cGRP_ASSOC Xf))
% Found (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of ((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->(cGRP_ASSOC Xf)))
% Found (and_rect10 (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found ((and_rect1 (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found (fun (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of (cGRP_ASSOC Xf)
% Found (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of (((cGRP_RIGHT_UNIT Xf) x0)->(cGRP_ASSOC Xf))
% Found (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of ((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->(cGRP_ASSOC Xf)))
% Found (and_rect10 (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found ((and_rect1 (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found x6:(cGRP_ASSOC Xf)
% Found (fun (x7:((cGRP_RIGHT_UNIT Xf) x0))=> x6) as proof of (cGRP_ASSOC Xf)
% Found (fun (x6:(cGRP_ASSOC Xf)) (x7:((cGRP_RIGHT_UNIT Xf) x0))=> x6) as proof of (((cGRP_RIGHT_UNIT Xf) x0)->(cGRP_ASSOC Xf))
% Found (fun (x6:(cGRP_ASSOC Xf)) (x7:((cGRP_RIGHT_UNIT Xf) x0))=> x6) as proof of ((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->(cGRP_ASSOC Xf)))
% Found (and_rect10 (fun (x6:(cGRP_ASSOC Xf)) (x7:((cGRP_RIGHT_UNIT Xf) x0))=> x6)) as proof of (cGRP_ASSOC Xf)
% Found ((and_rect1 (cGRP_ASSOC Xf)) (fun (x6:(cGRP_ASSOC Xf)) (x7:((cGRP_RIGHT_UNIT Xf) x0))=> x6)) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x6:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x6) x2)) (cGRP_ASSOC Xf)) (fun (x6:(cGRP_ASSOC Xf)) (x7:((cGRP_RIGHT_UNIT Xf) x0))=> x6)) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x6:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x6) x2)) (cGRP_ASSOC Xf)) (fun (x6:(cGRP_ASSOC Xf)) (x7:((cGRP_RIGHT_UNIT Xf) x0))=> x6)) as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found (fun (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of (cGRP_ASSOC Xf)
% Found (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of (((cGRP_RIGHT_UNIT Xf) x0)->(cGRP_ASSOC Xf))
% Found (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of ((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->(cGRP_ASSOC Xf)))
% Found (and_rect10 (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found ((and_rect1 (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found (fun (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of (cGRP_ASSOC Xf)
% Found (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of (((cGRP_RIGHT_UNIT Xf) x0)->(cGRP_ASSOC Xf))
% Found (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of ((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->(cGRP_ASSOC Xf)))
% Found (and_rect10 (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found ((and_rect1 (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found (fun (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of (cGRP_ASSOC Xf)
% Found (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of (((cGRP_RIGHT_UNIT Xf) x0)->(cGRP_ASSOC Xf))
% Found (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of ((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->(cGRP_ASSOC Xf)))
% Found (and_rect10 (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found ((and_rect1 (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found x0:(cGRP_ASSOC Xf)
% Found x0 as proof of (cGRP_ASSOC Xf)
% Found eq_ref00:=(eq_ref0 ((ex g) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb)))):(((eq Prop) ((ex g) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb)))) ((ex g) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb))))
% Found (eq_ref0 ((ex g) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb)))) as proof of (((eq Prop) ((ex g) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb)))) b)
% Found ((eq_ref Prop) ((ex g) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb)))) as proof of (((eq Prop) ((ex g) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb)))) b)
% Found ((eq_ref Prop) ((ex g) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb)))) as proof of (((eq Prop) ((ex g) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb)))) b)
% Found ((eq_ref Prop) ((ex g) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb)))) as proof of (((eq Prop) ((ex g) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb)))) b)
% Found x:((ex g) (cGROUP3 Xf))
% Instantiate: b:=(cGROUP3 Xf):(g->Prop)
% Found x as proof of (P b)
% Found x:((ex g) (cGROUP3 Xf))
% Instantiate: b:=(cGROUP3 Xf):(g->Prop)
% Found x as proof of (P b)
% Found x0:(cGRP_ASSOC Xf)
% Found x0 as proof of (cGRP_ASSOC Xf)
% Found x1:(cGRP_ASSOC Xf)
% Found x1 as proof of (cGRP_ASSOC Xf)
% Found x1:(cGRP_ASSOC Xf)
% Found x1 as proof of (cGRP_ASSOC Xf)
% Found x1:(cGRP_ASSOC Xf)
% Found x1 as proof of (cGRP_ASSOC Xf)
% Found eq_ref00:=(eq_ref0 (fun (Xx:g)=> (((eq g) ((Xf Xa) Xx)) Xb))):(((eq (g->Prop)) (fun (Xx:g)=> (((eq g) ((Xf Xa) Xx)) Xb))) (fun (Xx:g)=> (((eq g) ((Xf Xa) Xx)) Xb)))
% Found (eq_ref0 (fun (Xx:g)=> (((eq g) ((Xf Xa) Xx)) Xb))) as proof of (((eq (g->Prop)) (fun (Xx:g)=> (((eq g) ((Xf Xa) Xx)) Xb))) b)
% Found ((eq_ref (g->Prop)) (fun (Xx:g)=> (((eq g) ((Xf Xa) Xx)) Xb))) as proof of (((eq (g->Prop)) (fun (Xx:g)=> (((eq g) ((Xf Xa) Xx)) Xb))) b)
% Found ((eq_ref (g->Prop)) (fun (Xx:g)=> (((eq g) ((Xf Xa) Xx)) Xb))) as proof of (((eq (g->Prop)) (fun (Xx:g)=> (((eq g) ((Xf Xa) Xx)) Xb))) b)
% Found ((eq_ref (g->Prop)) (fun (Xx:g)=> (((eq g) ((Xf Xa) Xx)) Xb))) as proof of (((eq (g->Prop)) (fun (Xx:g)=> (((eq g) ((Xf Xa) Xx)) Xb))) b)
% Found eq_ref00:=(eq_ref0 (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb))):(((eq (g->Prop)) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb))) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb)))
% Found (eq_ref0 (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb))) as proof of (((eq (g->Prop)) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb))) b)
% Found ((eq_ref (g->Prop)) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb))) as proof of (((eq (g->Prop)) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb))) b)
% Found ((eq_ref (g->Prop)) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb))) as proof of (((eq (g->Prop)) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb))) b)
% Found ((eq_ref (g->Prop)) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb))) as proof of (((eq (g->Prop)) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb))) b)
% Found x1:(cGRP_ASSOC Xf)
% Found x1 as proof of (cGRP_ASSOC Xf)
% Found x1:(cGRP_ASSOC Xf)
% Found x1 as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found (fun (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of (cGRP_ASSOC Xf)
% Found (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of (((cGRP_RIGHT_UNIT Xf) x0)->(cGRP_ASSOC Xf))
% Found (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of ((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->(cGRP_ASSOC Xf)))
% Found (and_rect10 (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found ((and_rect1 (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found (fun (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4))) as proof of (cGRP_ASSOC Xf)
% Found (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4))) as proof of (((cGRP_RIGHT_INVERSE Xf) x0)->(cGRP_ASSOC Xf))
% Found (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4))) as proof of (((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))->(((cGRP_RIGHT_INVERSE Xf) x0)->(cGRP_ASSOC Xf)))
% Found (and_rect00 (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)))) as proof of (cGRP_ASSOC Xf)
% Found ((and_rect0 (cGRP_ASSOC Xf)) (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)))) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x2:(((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))->(((cGRP_RIGHT_INVERSE Xf) x0)->P)))=> (((((and_rect ((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) ((cGRP_RIGHT_INVERSE Xf) x0)) P) x2) x1)) (cGRP_ASSOC Xf)) (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)))) as proof of (cGRP_ASSOC Xf)
% Found (fun (x1:((cGROUP3 Xf) x0))=> (((fun (P:Type) (x2:(((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))->(((cGRP_RIGHT_INVERSE Xf) x0)->P)))=> (((((and_rect ((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) ((cGRP_RIGHT_INVERSE Xf) x0)) P) x2) x1)) (cGRP_ASSOC Xf)) (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4))))) as proof of (cGRP_ASSOC Xf)
% Found (fun (x0:g) (x1:((cGROUP3 Xf) x0))=> (((fun (P:Type) (x2:(((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))->(((cGRP_RIGHT_INVERSE Xf) x0)->P)))=> (((((and_rect ((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) ((cGRP_RIGHT_INVERSE Xf) x0)) P) x2) x1)) (cGRP_ASSOC Xf)) (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4))))) as proof of (((cGROUP3 Xf) x0)->(cGRP_ASSOC Xf))
% Found (fun (x0:g) (x1:((cGROUP3 Xf) x0))=> (((fun (P:Type) (x2:(((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))->(((cGRP_RIGHT_INVERSE Xf) x0)->P)))=> (((((and_rect ((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) ((cGRP_RIGHT_INVERSE Xf) x0)) P) x2) x1)) (cGRP_ASSOC Xf)) (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4))))) as proof of (forall (x:g), (((cGROUP3 Xf) x)->(cGRP_ASSOC Xf)))
% Found (ex_ind00 (fun (x0:g) (x1:((cGROUP3 Xf) x0))=> (((fun (P:Type) (x2:(((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))->(((cGRP_RIGHT_INVERSE Xf) x0)->P)))=> (((((and_rect ((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) ((cGRP_RIGHT_INVERSE Xf) x0)) P) x2) x1)) (cGRP_ASSOC Xf)) (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)))))) as proof of (cGRP_ASSOC Xf)
% Found ((ex_ind0 (cGRP_ASSOC Xf)) (fun (x0:g) (x1:((cGROUP3 Xf) x0))=> (((fun (P:Type) (x2:(((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))->(((cGRP_RIGHT_INVERSE Xf) x0)->P)))=> (((((and_rect ((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) ((cGRP_RIGHT_INVERSE Xf) x0)) P) x2) x1)) (cGRP_ASSOC Xf)) (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)))))) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Prop) (x0:(forall (x:g), (((cGROUP3 Xf) x)->P)))=> (((((ex_ind g) (cGROUP3 Xf)) P) x0) x)) (cGRP_ASSOC Xf)) (fun (x0:g) (x1:((cGROUP3 Xf) x0))=> (((fun (P:Type) (x2:(((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))->(((cGRP_RIGHT_INVERSE Xf) x0)->P)))=> (((((and_rect ((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) ((cGRP_RIGHT_INVERSE Xf) x0)) P) x2) x1)) (cGRP_ASSOC Xf)) (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)))))) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Prop) (x0:(forall (x:g), (((cGROUP3 Xf) x)->P)))=> (((((ex_ind g) (cGROUP3 Xf)) P) x0) x)) (cGRP_ASSOC Xf)) (fun (x0:g) (x1:((cGROUP3 Xf) x0))=> (((fun (P:Type) (x2:(((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))->(((cGRP_RIGHT_INVERSE Xf) x0)->P)))=> (((((and_rect ((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) ((cGRP_RIGHT_INVERSE Xf) x0)) P) x2) x1)) (cGRP_ASSOC Xf)) (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)))))) as proof of (cGRP_ASSOC Xf)
% Found x:((ex g) (cGROUP3 Xf))
% Instantiate: f:=(cGROUP3 Xf):(g->Prop)
% Found x as proof of (P f)
% Found x:((ex g) (cGROUP3 Xf))
% Instantiate: f:=(cGROUP3 Xf):(g->Prop)
% Found x as proof of (P f)
% Found x:((ex g) (cGROUP3 Xf))
% Instantiate: f:=(cGROUP3 Xf):(g->Prop)
% Found x as proof of (P f)
% Found x:((ex g) (cGROUP3 Xf))
% Instantiate: f:=(cGROUP3 Xf):(g->Prop)
% Found x as proof of (P f)
% Found x4:(cGRP_ASSOC Xf)
% Found (fun (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of (cGRP_ASSOC Xf)
% Found (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of (((cGRP_RIGHT_UNIT Xf) x0)->(cGRP_ASSOC Xf))
% Found (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of ((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->(cGRP_ASSOC Xf)))
% Found (and_rect10 (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found ((and_rect1 (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found (fun (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4))) as proof of (cGRP_ASSOC Xf)
% Found (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4))) as proof of (((cGRP_RIGHT_INVERSE Xf) x0)->(cGRP_ASSOC Xf))
% Found (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4))) as proof of (((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))->(((cGRP_RIGHT_INVERSE Xf) x0)->(cGRP_ASSOC Xf)))
% Found (and_rect00 (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)))) as proof of (cGRP_ASSOC Xf)
% Found ((and_rect0 (cGRP_ASSOC Xf)) (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)))) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x2:(((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))->(((cGRP_RIGHT_INVERSE Xf) x0)->P)))=> (((((and_rect ((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) ((cGRP_RIGHT_INVERSE Xf) x0)) P) x2) x1)) (cGRP_ASSOC Xf)) (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)))) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x2:(((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))->(((cGRP_RIGHT_INVERSE Xf) x0)->P)))=> (((((and_rect ((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) ((cGRP_RIGHT_INVERSE Xf) x0)) P) x2) x1)) (cGRP_ASSOC Xf)) (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)))) as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found (fun (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of (cGRP_ASSOC Xf)
% Found (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of (((cGRP_RIGHT_UNIT Xf) x0)->(cGRP_ASSOC Xf))
% Found (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of ((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->(cGRP_ASSOC Xf)))
% Found (and_rect10 (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found ((and_rect1 (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found (fun (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4))) as proof of (cGRP_ASSOC Xf)
% Found (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4))) as proof of (((cGRP_RIGHT_INVERSE Xf) x0)->(cGRP_ASSOC Xf))
% Found (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4))) as proof of (((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))->(((cGRP_RIGHT_INVERSE Xf) x0)->(cGRP_ASSOC Xf)))
% Found (and_rect00 (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)))) as proof of (cGRP_ASSOC Xf)
% Found ((and_rect0 (cGRP_ASSOC Xf)) (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)))) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x2:(((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))->(((cGRP_RIGHT_INVERSE Xf) x0)->P)))=> (((((and_rect ((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) ((cGRP_RIGHT_INVERSE Xf) x0)) P) x2) x1)) (cGRP_ASSOC Xf)) (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)))) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x2:(((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))->(((cGRP_RIGHT_INVERSE Xf) x0)->P)))=> (((((and_rect ((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) ((cGRP_RIGHT_INVERSE Xf) x0)) P) x2) x1)) (cGRP_ASSOC Xf)) (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)))) as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found (fun (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of (cGRP_ASSOC Xf)
% Found (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of (((cGRP_RIGHT_UNIT Xf) x0)->(cGRP_ASSOC Xf))
% Found (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of ((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->(cGRP_ASSOC Xf)))
% Found (and_rect10 (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found ((and_rect1 (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found (fun (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of (cGRP_ASSOC Xf)
% Found (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of (((cGRP_RIGHT_UNIT Xf) x0)->(cGRP_ASSOC Xf))
% Found (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of ((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->(cGRP_ASSOC Xf)))
% Found (and_rect10 (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found ((and_rect1 (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found (fun (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4))) as proof of (cGRP_ASSOC Xf)
% Found (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4))) as proof of (((cGRP_RIGHT_INVERSE Xf) x0)->(cGRP_ASSOC Xf))
% Found (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4))) as proof of (((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))->(((cGRP_RIGHT_INVERSE Xf) x0)->(cGRP_ASSOC Xf)))
% Found (and_rect00 (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)))) as proof of (cGRP_ASSOC Xf)
% Found ((and_rect0 (cGRP_ASSOC Xf)) (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)))) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x2:(((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))->(((cGRP_RIGHT_INVERSE Xf) x0)->P)))=> (((((and_rect ((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) ((cGRP_RIGHT_INVERSE Xf) x0)) P) x2) x1)) (cGRP_ASSOC Xf)) (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)))) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x2:(((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))->(((cGRP_RIGHT_INVERSE Xf) x0)->P)))=> (((((and_rect ((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) ((cGRP_RIGHT_INVERSE Xf) x0)) P) x2) x1)) (cGRP_ASSOC Xf)) (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)))) as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found (fun (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of (cGRP_ASSOC Xf)
% Found (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of (((cGRP_RIGHT_UNIT Xf) x0)->(cGRP_ASSOC Xf))
% Found (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of ((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->(cGRP_ASSOC Xf)))
% Found (and_rect10 (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found ((and_rect1 (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found (fun (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4))) as proof of (cGRP_ASSOC Xf)
% Found (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4))) as proof of (((cGRP_RIGHT_INVERSE Xf) x0)->(cGRP_ASSOC Xf))
% Found (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4))) as proof of (((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))->(((cGRP_RIGHT_INVERSE Xf) x0)->(cGRP_ASSOC Xf)))
% Found (and_rect00 (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)))) as proof of (cGRP_ASSOC Xf)
% Found ((and_rect0 (cGRP_ASSOC Xf)) (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)))) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x2:(((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))->(((cGRP_RIGHT_INVERSE Xf) x0)->P)))=> (((((and_rect ((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) ((cGRP_RIGHT_INVERSE Xf) x0)) P) x2) x1)) (cGRP_ASSOC Xf)) (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)))) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x2:(((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))->(((cGRP_RIGHT_INVERSE Xf) x0)->P)))=> (((((and_rect ((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) ((cGRP_RIGHT_INVERSE Xf) x0)) P) x2) x1)) (cGRP_ASSOC Xf)) (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)))) as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found (fun (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of (cGRP_ASSOC Xf)
% Found (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of (((cGRP_RIGHT_UNIT Xf) x0)->(cGRP_ASSOC Xf))
% Found (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of ((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->(cGRP_ASSOC Xf)))
% Found (and_rect10 (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found ((and_rect1 (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found (fun (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of (cGRP_ASSOC Xf)
% Found (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of (((cGRP_RIGHT_UNIT Xf) x0)->(cGRP_ASSOC Xf))
% Found (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of ((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->(cGRP_ASSOC Xf)))
% Found (and_rect10 (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found ((and_rect1 (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found (fun (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of (cGRP_ASSOC Xf)
% Found (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of (((cGRP_RIGHT_UNIT Xf) x0)->(cGRP_ASSOC Xf))
% Found (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of ((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->(cGRP_ASSOC Xf)))
% Found (and_rect10 (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found ((and_rect1 (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found eq_ref00:=(eq_ref0 ((ex g) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb)))):(((eq Prop) ((ex g) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb)))) ((ex g) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb))))
% Found (eq_ref0 ((ex g) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb)))) as proof of (((eq Prop) ((ex g) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb)))) b)
% Found ((eq_ref Prop) ((ex g) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb)))) as proof of (((eq Prop) ((ex g) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb)))) b)
% Found ((eq_ref Prop) ((ex g) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb)))) as proof of (((eq Prop) ((ex g) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb)))) b)
% Found ((eq_ref Prop) ((ex g) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb)))) as proof of (((eq Prop) ((ex g) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb)))) b)
% Found x:((ex g) (fun (Xe:g)=> ((cGROUP3 Xf) Xe)))
% Instantiate: b:=(fun (Xe:g)=> ((cGROUP3 Xf) Xe)):(g->Prop)
% Found x as proof of (P b)
% Found x:((ex g) (fun (Xe:g)=> ((cGROUP3 Xf) Xe)))
% Instantiate: b:=(fun (Xe:g)=> ((cGROUP3 Xf) Xe)):(g->Prop)
% Found x as proof of (P b)
% Found x0:(cGRP_ASSOC Xf)
% Found x0 as proof of (cGRP_ASSOC Xf)
% Found eq_ref00:=(eq_ref0 a):(((eq (g->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (g->Prop)) a) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb)))
% Found ((eq_ref (g->Prop)) a) as proof of (((eq (g->Prop)) a) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb)))
% Found ((eq_ref (g->Prop)) a) as proof of (((eq (g->Prop)) a) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb)))
% Found ((eq_ref (g->Prop)) a) as proof of (((eq (g->Prop)) a) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb)))
% Found eq_ref00:=(eq_ref0 a):(((eq (g->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (g->Prop)) a) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb)))
% Found ((eq_ref (g->Prop)) a) as proof of (((eq (g->Prop)) a) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb)))
% Found ((eq_ref (g->Prop)) a) as proof of (((eq (g->Prop)) a) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb)))
% Found ((eq_ref (g->Prop)) a) as proof of (((eq (g->Prop)) a) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb)))
% Found eq_ref00:=(eq_ref0 ((ex g) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb)))):(((eq Prop) ((ex g) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb)))) ((ex g) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb))))
% Found (eq_ref0 ((ex g) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb)))) as proof of (((eq Prop) ((ex g) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb)))) b)
% Found ((eq_ref Prop) ((ex g) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb)))) as proof of (((eq Prop) ((ex g) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb)))) b)
% Found ((eq_ref Prop) ((ex g) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb)))) as proof of (((eq Prop) ((ex g) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb)))) b)
% Found ((eq_ref Prop) ((ex g) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb)))) as proof of (((eq Prop) ((ex g) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb)))) b)
% Found eq_ref00:=(eq_ref0 (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb))):(((eq (g->Prop)) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb))) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb)))
% Found (eq_ref0 (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb))) as proof of (((eq (g->Prop)) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb))) b)
% Found ((eq_ref (g->Prop)) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb))) as proof of (((eq (g->Prop)) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb))) b)
% Found ((eq_ref (g->Prop)) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb))) as proof of (((eq (g->Prop)) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb))) b)
% Found ((eq_ref (g->Prop)) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb))) as proof of (((eq (g->Prop)) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb))) b)
% Found eq_ref00:=(eq_ref0 (fun (Xx:g)=> (((eq g) ((Xf Xa) Xx)) Xb))):(((eq (g->Prop)) (fun (Xx:g)=> (((eq g) ((Xf Xa) Xx)) Xb))) (fun (Xx:g)=> (((eq g) ((Xf Xa) Xx)) Xb)))
% Found (eq_ref0 (fun (Xx:g)=> (((eq g) ((Xf Xa) Xx)) Xb))) as proof of (((eq (g->Prop)) (fun (Xx:g)=> (((eq g) ((Xf Xa) Xx)) Xb))) b)
% Found ((eq_ref (g->Prop)) (fun (Xx:g)=> (((eq g) ((Xf Xa) Xx)) Xb))) as proof of (((eq (g->Prop)) (fun (Xx:g)=> (((eq g) ((Xf Xa) Xx)) Xb))) b)
% Found ((eq_ref (g->Prop)) (fun (Xx:g)=> (((eq g) ((Xf Xa) Xx)) Xb))) as proof of (((eq (g->Prop)) (fun (Xx:g)=> (((eq g) ((Xf Xa) Xx)) Xb))) b)
% Found ((eq_ref (g->Prop)) (fun (Xx:g)=> (((eq g) ((Xf Xa) Xx)) Xb))) as proof of (((eq (g->Prop)) (fun (Xx:g)=> (((eq g) ((Xf Xa) Xx)) Xb))) b)
% Found x1:(cGRP_ASSOC Xf)
% Found x1 as proof of (cGRP_ASSOC Xf)
% Found x:((ex g) (cGROUP3 Xf))
% Instantiate: b:=(cGROUP3 Xf):(g->Prop)
% Found x as proof of (P b)
% Found x:((ex g) (cGROUP3 Xf))
% Instantiate: b:=(cGROUP3 Xf):(g->Prop)
% Found x as proof of (P b)
% Found x1:(cGRP_ASSOC Xf)
% Found x1 as proof of (cGRP_ASSOC Xf)
% Found classical_choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (b:B)=> ((fun (C:((forall (x:A), ((ex B) (fun (y:B)=> (((fun (x0:A) (y0:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y0))) x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((fun (x0:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y))) x) (f x)))))))=> (C (fun (x:A)=> ((fun (C0:((or ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))))=> ((((((or_ind ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) ((((ex_ind B) (fun (z:B)=> ((R x) z))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) (fun (y:B) (H:((R x) y))=> ((((ex_intro B) (fun (y0:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y0)))) y) (fun (_:((ex B) (fun (z:B)=> ((R x) z))))=> H))))) (fun (N:(not ((ex B) (fun (z:B)=> ((R x) z)))))=> ((((ex_intro B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))) b) (fun (H:((ex B) (fun (z:B)=> ((R x) z))))=> ((False_rect ((R x) b)) (N H)))))) C0)) (classic ((ex B) (fun (z:B)=> ((R x) z)))))))) (((choice A) B) (fun (x:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x))))))))
% Instantiate: b:=(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x)))))))):Prop
% Found classical_choice as proof of b
% Found eq_ref00:=(eq_ref0 ((ex g) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb)))):(((eq Prop) ((ex g) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb)))) ((ex g) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb))))
% Found (eq_ref0 ((ex g) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb)))) as proof of (((eq Prop) ((ex g) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb)))) b)
% Found ((eq_ref Prop) ((ex g) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb)))) as proof of (((eq Prop) ((ex g) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb)))) b)
% Found ((eq_ref Prop) ((ex g) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb)))) as proof of (((eq Prop) ((ex g) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb)))) b)
% Found ((eq_ref Prop) ((ex g) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb)))) as proof of (((eq Prop) ((ex g) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb)))) b)
% Found eq_ref00:=(eq_ref0 (f x4)):(((eq Prop) (f x4)) (f x4))
% Found (eq_ref0 (f x4)) as proof of (((eq Prop) (f x4)) (((eq g) ((Xf x4) Xa)) Xb))
% Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (((eq g) ((Xf x4) Xa)) Xb))
% Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (((eq g) ((Xf x4) Xa)) Xb))
% Found (fun (x4:g)=> ((eq_ref Prop) (f x4))) as proof of (((eq Prop) (f x4)) (((eq g) ((Xf x4) Xa)) Xb))
% Found (fun (x4:g)=> ((eq_ref Prop) (f x4))) as proof of (forall (x:g), (((eq Prop) (f x)) (((eq g) ((Xf x) Xa)) Xb)))
% Found eq_ref00:=(eq_ref0 (f x4)):(((eq Prop) (f x4)) (f x4))
% Found (eq_ref0 (f x4)) as proof of (((eq Prop) (f x4)) (((eq g) ((Xf Xa) x4)) Xb))
% Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (((eq g) ((Xf Xa) x4)) Xb))
% Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (((eq g) ((Xf Xa) x4)) Xb))
% Found (fun (x4:g)=> ((eq_ref Prop) (f x4))) as proof of (((eq Prop) (f x4)) (((eq g) ((Xf Xa) x4)) Xb))
% Found (fun (x4:g)=> ((eq_ref Prop) (f x4))) as proof of (forall (x:g), (((eq Prop) (f x)) (((eq g) ((Xf Xa) x)) Xb)))
% Found eq_ref00:=(eq_ref0 (f x4)):(((eq Prop) (f x4)) (f x4))
% Found (eq_ref0 (f x4)) as proof of (((eq Prop) (f x4)) (((eq g) ((Xf Xa) x4)) Xb))
% Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (((eq g) ((Xf Xa) x4)) Xb))
% Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (((eq g) ((Xf Xa) x4)) Xb))
% Found (fun (x4:g)=> ((eq_ref Prop) (f x4))) as proof of (((eq Prop) (f x4)) (((eq g) ((Xf Xa) x4)) Xb))
% Found (fun (x4:g)=> ((eq_ref Prop) (f x4))) as proof of (forall (x:g), (((eq Prop) (f x)) (((eq g) ((Xf Xa) x)) Xb)))
% Found eq_ref00:=(eq_ref0 (f x4)):(((eq Prop) (f x4)) (f x4))
% Found (eq_ref0 (f x4)) as proof of (((eq Prop) (f x4)) (((eq g) ((Xf x4) Xa)) Xb))
% Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (((eq g) ((Xf x4) Xa)) Xb))
% Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (((eq g) ((Xf x4) Xa)) Xb))
% Found (fun (x4:g)=> ((eq_ref Prop) (f x4))) as proof of (((eq Prop) (f x4)) (((eq g) ((Xf x4) Xa)) Xb))
% Found (fun (x4:g)=> ((eq_ref Prop) (f x4))) as proof of (forall (x:g), (((eq Prop) (f x)) (((eq g) ((Xf x) Xa)) Xb)))
% Found x1:(cGRP_ASSOC Xf)
% Found x1 as proof of (cGRP_ASSOC Xf)
% Found x1:(cGRP_ASSOC Xf)
% Found x1 as proof of (cGRP_ASSOC Xf)
% Found x1:(cGRP_ASSOC Xf)
% Found (fun (x2:(cGRP_DIVISORS Xf))=> x1) as proof of (cGRP_ASSOC Xf)
% Found (fun (x1:(cGRP_ASSOC Xf)) (x2:(cGRP_DIVISORS Xf))=> x1) as proof of ((cGRP_DIVISORS Xf)->(cGRP_ASSOC Xf))
% Found (fun (x1:(cGRP_ASSOC Xf)) (x2:(cGRP_DIVISORS Xf))=> x1) as proof of ((cGRP_ASSOC Xf)->((cGRP_DIVISORS Xf)->(cGRP_ASSOC Xf)))
% Found (and_rect00 (fun (x1:(cGRP_ASSOC Xf)) (x2:(cGRP_DIVISORS Xf))=> x1)) as proof of (cGRP_ASSOC Xf)
% Found ((and_rect0 (cGRP_ASSOC Xf)) (fun (x1:(cGRP_ASSOC Xf)) (x2:(cGRP_DIVISORS Xf))=> x1)) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x1:((cGRP_ASSOC Xf)->((cGRP_DIVISORS Xf)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) (cGRP_DIVISORS Xf)) P) x1) x)) (cGRP_ASSOC Xf)) (fun (x1:(cGRP_ASSOC Xf)) (x2:(cGRP_DIVISORS Xf))=> x1)) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x1:((cGRP_ASSOC Xf)->((cGRP_DIVISORS Xf)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) (cGRP_DIVISORS Xf)) P) x1) x)) (cGRP_ASSOC Xf)) (fun (x1:(cGRP_ASSOC Xf)) (x2:(cGRP_DIVISORS Xf))=> x1)) as proof of (cGRP_ASSOC Xf)
% Found x:((ex g) (fun (Xe:g)=> ((cGROUP3 Xf) Xe)))
% Instantiate: f:=(fun (Xe:g)=> ((cGROUP3 Xf) Xe)):(g->Prop)
% Found x as proof of (P f)
% Found x:((ex g) (fun (Xe:g)=> ((cGROUP3 Xf) Xe)))
% Instantiate: f:=(fun (Xe:g)=> ((cGROUP3 Xf) Xe)):(g->Prop)
% Found x as proof of (P f)
% Found x:((ex g) (fun (Xe:g)=> ((cGROUP3 Xf) Xe)))
% Instantiate: f:=(fun (Xe:g)=> ((cGROUP3 Xf) Xe)):(g->Prop)
% Found x as proof of (P f)
% Found x:((ex g) (fun (Xe:g)=> ((cGROUP3 Xf) Xe)))
% Instantiate: f:=(fun (Xe:g)=> ((cGROUP3 Xf) Xe)):(g->Prop)
% Found x as proof of (P f)
% Found x4:(cGRP_ASSOC Xf)
% Found (fun (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of (cGRP_ASSOC Xf)
% Found (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of (((cGRP_RIGHT_UNIT Xf) x0)->(cGRP_ASSOC Xf))
% Found (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of ((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->(cGRP_ASSOC Xf)))
% Found (and_rect10 (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found ((and_rect1 (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found (fun (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4))) as proof of (cGRP_ASSOC Xf)
% Found (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4))) as proof of (((cGRP_RIGHT_INVERSE Xf) x0)->(cGRP_ASSOC Xf))
% Found (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4))) as proof of (((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))->(((cGRP_RIGHT_INVERSE Xf) x0)->(cGRP_ASSOC Xf)))
% Found (and_rect00 (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)))) as proof of (cGRP_ASSOC Xf)
% Found ((and_rect0 (cGRP_ASSOC Xf)) (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)))) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x2:(((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))->(((cGRP_RIGHT_INVERSE Xf) x0)->P)))=> (((((and_rect ((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) ((cGRP_RIGHT_INVERSE Xf) x0)) P) x2) x1)) (cGRP_ASSOC Xf)) (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)))) as proof of (cGRP_ASSOC Xf)
% Found (fun (x1:((cGROUP3 Xf) x0))=> (((fun (P:Type) (x2:(((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))->(((cGRP_RIGHT_INVERSE Xf) x0)->P)))=> (((((and_rect ((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) ((cGRP_RIGHT_INVERSE Xf) x0)) P) x2) x1)) (cGRP_ASSOC Xf)) (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4))))) as proof of (cGRP_ASSOC Xf)
% Found (fun (x0:g) (x1:((cGROUP3 Xf) x0))=> (((fun (P:Type) (x2:(((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))->(((cGRP_RIGHT_INVERSE Xf) x0)->P)))=> (((((and_rect ((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) ((cGRP_RIGHT_INVERSE Xf) x0)) P) x2) x1)) (cGRP_ASSOC Xf)) (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4))))) as proof of (((cGROUP3 Xf) x0)->(cGRP_ASSOC Xf))
% Found (fun (x0:g) (x1:((cGROUP3 Xf) x0))=> (((fun (P:Type) (x2:(((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))->(((cGRP_RIGHT_INVERSE Xf) x0)->P)))=> (((((and_rect ((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) ((cGRP_RIGHT_INVERSE Xf) x0)) P) x2) x1)) (cGRP_ASSOC Xf)) (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4))))) as proof of (forall (x:g), (((cGROUP3 Xf) x)->(cGRP_ASSOC Xf)))
% Found (ex_ind00 (fun (x0:g) (x1:((cGROUP3 Xf) x0))=> (((fun (P:Type) (x2:(((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))->(((cGRP_RIGHT_INVERSE Xf) x0)->P)))=> (((((and_rect ((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) ((cGRP_RIGHT_INVERSE Xf) x0)) P) x2) x1)) (cGRP_ASSOC Xf)) (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)))))) as proof of (cGRP_ASSOC Xf)
% Found ((ex_ind0 (cGRP_ASSOC Xf)) (fun (x0:g) (x1:((cGROUP3 Xf) x0))=> (((fun (P:Type) (x2:(((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))->(((cGRP_RIGHT_INVERSE Xf) x0)->P)))=> (((((and_rect ((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) ((cGRP_RIGHT_INVERSE Xf) x0)) P) x2) x1)) (cGRP_ASSOC Xf)) (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)))))) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Prop) (x0:(forall (x:g), (((cGROUP3 Xf) x)->P)))=> (((((ex_ind g) (fun (Xe:g)=> ((cGROUP3 Xf) Xe))) P) x0) x)) (cGRP_ASSOC Xf)) (fun (x0:g) (x1:((cGROUP3 Xf) x0))=> (((fun (P:Type) (x2:(((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))->(((cGRP_RIGHT_INVERSE Xf) x0)->P)))=> (((((and_rect ((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) ((cGRP_RIGHT_INVERSE Xf) x0)) P) x2) x1)) (cGRP_ASSOC Xf)) (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)))))) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Prop) (x0:(forall (x:g), (((cGROUP3 Xf) x)->P)))=> (((((ex_ind g) (fun (Xe:g)=> ((cGROUP3 Xf) Xe))) P) x0) x)) (cGRP_ASSOC Xf)) (fun (x0:g) (x1:((cGROUP3 Xf) x0))=> (((fun (P:Type) (x2:(((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))->(((cGRP_RIGHT_INVERSE Xf) x0)->P)))=> (((((and_rect ((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) ((cGRP_RIGHT_INVERSE Xf) x0)) P) x2) x1)) (cGRP_ASSOC Xf)) (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)))))) as proof of (cGRP_ASSOC Xf)
% Found eq_ref00:=(eq_ref0 (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb))):(((eq (g->Prop)) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb))) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb)))
% Found (eq_ref0 (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb))) as proof of (((eq (g->Prop)) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb))) b)
% Found ((eq_ref (g->Prop)) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb))) as proof of (((eq (g->Prop)) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb))) b)
% Found ((eq_ref (g->Prop)) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb))) as proof of (((eq (g->Prop)) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb))) b)
% Found ((eq_ref (g->Prop)) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb))) as proof of (((eq (g->Prop)) (fun (Xy:g)=> (((eq g) ((Xf Xy) Xa)) Xb))) b)
% Found eq_ref00:=(eq_ref0 (fun (Xx:g)=> (((eq g) ((Xf Xa) Xx)) Xb))):(((eq (g->Prop)) (fun (Xx:g)=> (((eq g) ((Xf Xa) Xx)) Xb))) (fun (Xx:g)=> (((eq g) ((Xf Xa) Xx)) Xb)))
% Found (eq_ref0 (fun (Xx:g)=> (((eq g) ((Xf Xa) Xx)) Xb))) as proof of (((eq (g->Prop)) (fun (Xx:g)=> (((eq g) ((Xf Xa) Xx)) Xb))) b)
% Found ((eq_ref (g->Prop)) (fun (Xx:g)=> (((eq g) ((Xf Xa) Xx)) Xb))) as proof of (((eq (g->Prop)) (fun (Xx:g)=> (((eq g) ((Xf Xa) Xx)) Xb))) b)
% Found ((eq_ref (g->Prop)) (fun (Xx:g)=> (((eq g) ((Xf Xa) Xx)) Xb))) as proof of (((eq (g->Prop)) (fun (Xx:g)=> (((eq g) ((Xf Xa) Xx)) Xb))) b)
% Found ((eq_ref (g->Prop)) (fun (Xx:g)=> (((eq g) ((Xf Xa) Xx)) Xb))) as proof of (((eq (g->Prop)) (fun (Xx:g)=> (((eq g) ((Xf Xa) Xx)) Xb))) b)
% Found x4:(cGRP_ASSOC Xf)
% Found (fun (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of (cGRP_ASSOC Xf)
% Found (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of (((cGRP_RIGHT_UNIT Xf) x0)->(cGRP_ASSOC Xf))
% Found (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of ((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->(cGRP_ASSOC Xf)))
% Found (and_rect10 (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found ((and_rect1 (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found (fun (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4))) as proof of (cGRP_ASSOC Xf)
% Found (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4))) as proof of (((cGRP_RIGHT_INVERSE Xf) x0)->(cGRP_ASSOC Xf))
% Found (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4))) as proof of (((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))->(((cGRP_RIGHT_INVERSE Xf) x0)->(cGRP_ASSOC Xf)))
% Found (and_rect00 (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)))) as proof of (cGRP_ASSOC Xf)
% Found ((and_rect0 (cGRP_ASSOC Xf)) (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)))) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x2:(((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))->(((cGRP_RIGHT_INVERSE Xf) x0)->P)))=> (((((and_rect ((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) ((cGRP_RIGHT_INVERSE Xf) x0)) P) x2) x1)) (cGRP_ASSOC Xf)) (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)))) as proof of (cGRP_ASSOC Xf)
% Found (fun (x1:((cGROUP3 Xf) x0))=> (((fun (P:Type) (x2:(((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))->(((cGRP_RIGHT_INVERSE Xf) x0)->P)))=> (((((and_rect ((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) ((cGRP_RIGHT_INVERSE Xf) x0)) P) x2) x1)) (cGRP_ASSOC Xf)) (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4))))) as proof of (cGRP_ASSOC Xf)
% Found (fun (x0:g) (x1:((cGROUP3 Xf) x0))=> (((fun (P:Type) (x2:(((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))->(((cGRP_RIGHT_INVERSE Xf) x0)->P)))=> (((((and_rect ((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) ((cGRP_RIGHT_INVERSE Xf) x0)) P) x2) x1)) (cGRP_ASSOC Xf)) (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4))))) as proof of (((cGROUP3 Xf) x0)->(cGRP_ASSOC Xf))
% Found (fun (x0:g) (x1:((cGROUP3 Xf) x0))=> (((fun (P:Type) (x2:(((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))->(((cGRP_RIGHT_INVERSE Xf) x0)->P)))=> (((((and_rect ((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) ((cGRP_RIGHT_INVERSE Xf) x0)) P) x2) x1)) (cGRP_ASSOC Xf)) (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4))))) as proof of (forall (x:g), (((cGROUP3 Xf) x)->(cGRP_ASSOC Xf)))
% Found (ex_ind00 (fun (x0:g) (x1:((cGROUP3 Xf) x0))=> (((fun (P:Type) (x2:(((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))->(((cGRP_RIGHT_INVERSE Xf) x0)->P)))=> (((((and_rect ((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) ((cGRP_RIGHT_INVERSE Xf) x0)) P) x2) x1)) (cGRP_ASSOC Xf)) (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)))))) as proof of (cGRP_ASSOC Xf)
% Found ((ex_ind0 (cGRP_ASSOC Xf)) (fun (x0:g) (x1:((cGROUP3 Xf) x0))=> (((fun (P:Type) (x2:(((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))->(((cGRP_RIGHT_INVERSE Xf) x0)->P)))=> (((((and_rect ((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) ((cGRP_RIGHT_INVERSE Xf) x0)) P) x2) x1)) (cGRP_ASSOC Xf)) (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)))))) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Prop) (x0:(forall (x:g), (((cGROUP3 Xf) x)->P)))=> (((((ex_ind g) (cGROUP3 Xf)) P) x0) x)) (cGRP_ASSOC Xf)) (fun (x0:g) (x1:((cGROUP3 Xf) x0))=> (((fun (P:Type) (x2:(((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))->(((cGRP_RIGHT_INVERSE Xf) x0)->P)))=> (((((and_rect ((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) ((cGRP_RIGHT_INVERSE Xf) x0)) P) x2) x1)) (cGRP_ASSOC Xf)) (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)))))) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Prop) (x0:(forall (x:g), (((cGROUP3 Xf) x)->P)))=> (((((ex_ind g) (cGROUP3 Xf)) P) x0) x)) (cGRP_ASSOC Xf)) (fun (x0:g) (x1:((cGROUP3 Xf) x0))=> (((fun (P:Type) (x2:(((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))->(((cGRP_RIGHT_INVERSE Xf) x0)->P)))=> (((((and_rect ((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) ((cGRP_RIGHT_INVERSE Xf) x0)) P) x2) x1)) (cGRP_ASSOC Xf)) (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)))))) as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found (fun (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of (cGRP_ASSOC Xf)
% Found (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of (((cGRP_RIGHT_UNIT Xf) x0)->(cGRP_ASSOC Xf))
% Found (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of ((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->(cGRP_ASSOC Xf)))
% Found (and_rect10 (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found ((and_rect1 (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found (fun (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4))) as proof of (cGRP_ASSOC Xf)
% Found (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4))) as proof of (((cGRP_RIGHT_INVERSE Xf) x0)->(cGRP_ASSOC Xf))
% Found (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4))) as proof of (((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))->(((cGRP_RIGHT_INVERSE Xf) x0)->(cGRP_ASSOC Xf)))
% Found (and_rect00 (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)))) as proof of (cGRP_ASSOC Xf)
% Found ((and_rect0 (cGRP_ASSOC Xf)) (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)))) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x2:(((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))->(((cGRP_RIGHT_INVERSE Xf) x0)->P)))=> (((((and_rect ((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) ((cGRP_RIGHT_INVERSE Xf) x0)) P) x2) x1)) (cGRP_ASSOC Xf)) (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)))) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x2:(((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))->(((cGRP_RIGHT_INVERSE Xf) x0)->P)))=> (((((and_rect ((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) ((cGRP_RIGHT_INVERSE Xf) x0)) P) x2) x1)) (cGRP_ASSOC Xf)) (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)))) as proof of (cGRP_ASSOC Xf)
% Found x4:(cGRP_ASSOC Xf)
% Found (fun (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of (cGRP_ASSOC Xf)
% Found (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of (((cGRP_RIGHT_UNIT Xf) x0)->(cGRP_ASSOC Xf))
% Found (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4) as proof of ((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->(cGRP_ASSOC Xf)))
% Found (and_rect10 (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found ((and_rect1 (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)) as proof of (cGRP_ASSOC Xf)
% Found (fun (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4))) as proof of (cGRP_ASSOC Xf)
% Found (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4))) as proof of (((cGRP_RIGHT_INVERSE Xf) x0)->(cGRP_ASSOC Xf))
% Found (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4))) as proof of (((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))->(((cGRP_RIGHT_INVERSE Xf) x0)->(cGRP_ASSOC Xf)))
% Found (and_rect00 (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)))) as proof of (cGRP_ASSOC Xf)
% Found ((and_rect0 (cGRP_ASSOC Xf)) (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)))) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x2:(((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))->(((cGRP_RIGHT_INVERSE Xf) x0)->P)))=> (((((and_rect ((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) ((cGRP_RIGHT_INVERSE Xf) x0)) P) x2) x1)) (cGRP_ASSOC Xf)) (fun (x2:((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) (x3:((cGRP_RIGHT_INVERSE Xf) x0))=> (((fun (P:Type) (x4:((cGRP_ASSOC Xf)->(((cGRP_RIGHT_UNIT Xf) x0)->P)))=> (((((and_rect (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0)) P) x4) x2)) (cGRP_ASSOC Xf)) (fun (x4:(cGRP_ASSOC Xf)) (x5:((cGRP_RIGHT_UNIT Xf) x0))=> x4)))) as proof of (cGRP_ASSOC Xf)
% Found (((fun (P:Type) (x2:(((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))->(((cGRP_RIGHT_INVERSE Xf) x0)->P)))=> (((((and_rect ((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) x0))) ((cGRP_RIGHT_INVERSE Xf) x0)) P) x2) x1)) (cGRP_ASSOC Xf)) (fun 
% EOF
%------------------------------------------------------------------------------