%--------------------------------------------------------------------------
% File     : SET735+4 : TPTP v8.2.0. Bugfixed v2.2.1.
% Domain   : Set Theory (Mappings)
% Problem  : Property of mappings
% Version  : [Pas99] axioms.
% English  : If GoF1 and GoF2 are identities,and the images of A by F1
%            and F2 are equal, then F1 and F2 are equal.

% Refs     : [Pas99] Pastre (1999), Email to G. Sutcliffe
% Source   : [Pas99]
% Names    :

% Status   : Theorem
% Rating   : 0.86 v8.2.0, 0.89 v7.5.0, 0.91 v7.4.0, 0.83 v7.1.0, 0.78 v7.0.0, 0.87 v6.4.0, 0.85 v6.3.0, 0.83 v6.2.0, 0.92 v6.1.0, 0.97 v6.0.0, 0.96 v5.2.0, 0.95 v5.0.0, 0.96 v3.7.0, 0.95 v3.3.0, 0.93 v3.2.0, 0.91 v3.1.0, 0.89 v2.7.0, 0.67 v2.6.0, 0.71 v2.5.0, 0.88 v2.4.0, 0.75 v2.3.0, 0.67 v2.2.1
% Syntax   : Number of formulae    :   29 (   1 unt;   0 def)
%            Number of atoms       :  135 (   6 equ)
%            Maximal formula atoms :   11 (   4 avg)
%            Number of connectives :  108 (   2   ~;   2   |;  55   &)
%                                         (  30 <=>;  19  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   19 (   9 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   16 (  15 usr;   0 prp; 2-6 aty)
%            Number of functors    :   15 (  15 usr;   1 con; 0-5 aty)
%            Number of variables   :  138 ( 129   !;   9   ?)
% SPC      : FOF_THM_RFO_SEQ

% Comments :
% Bugfixes : v2.2.1 - Bugfixes in SET006+1.ax.
%--------------------------------------------------------------------------
%----Include set theory definitions
include('Axioms/SET006+0.ax').
%----Include mappings axioms
include('Axioms/SET006+1.ax').
%--------------------------------------------------------------------------
fof(thII26,conjecture,
    ! [F1,F2,G,A,B] :
      ( ( maps(F1,A,B)
        & maps(F2,A,B)
        & maps(G,B,A)
        & identity(compose_function(G,F1,A,B,A),A)
        & identity(compose_function(G,F2,A,B,A),A)
        & equal_set(image3(F1,A,B),image3(F2,A,B)) )
     => equal_maps(F1,F2,A,B) ) ).

%--------------------------------------------------------------------------