%--------------------------------------------------------------------------
% File     : SET732+4 : TPTP v9.0.0. Bugfixed v2.2.1.
% Domain   : Set Theory (Mappings)
% Problem  : Property of restriction 3
% Version  : [Pas99] axioms.
% English  : If F is a mapping from A to B,and G equal to F on A and
%            C =image2(F,A) and F is injective, then G is one-to-one.

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

% Status   : Theorem
% Rating   : 0.61 v8.2.0, 0.69 v7.5.0, 0.75 v7.4.0, 0.63 v7.3.0, 0.62 v7.2.0, 0.59 v7.1.0, 0.52 v7.0.0, 0.67 v6.4.0, 0.69 v6.3.0, 0.67 v6.2.0, 0.76 v6.1.0, 0.77 v6.0.0, 0.78 v5.5.0, 0.85 v5.4.0, 0.86 v5.3.0, 0.89 v5.2.0, 0.85 v5.1.0, 0.86 v5.0.0, 0.88 v4.1.0, 0.91 v4.0.0, 0.92 v3.7.0, 0.95 v3.3.0, 0.93 v3.2.0, 0.91 v3.1.0, 0.89 v2.7.0, 0.83 v2.6.0, 0.86 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       :  137 (   7 equ)
%            Maximal formula atoms :   11 (   4 avg)
%            Number of connectives :  110 (   2   ~;   2   |;  55   &)
%                                         (  31 <=>;  20  =>;   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   :  140 ( 131   !;   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(thII23,conjecture,
    ! [F,G,A,B,C] :
      ( ( maps(F,A,B)
        & subset(C,B)
        & image2(F,A) = C
        & ! [X,Y] :
            ( ( member(X,A)
              & member(Y,C) )
           => ( apply(G,X,Y)
            <=> apply(F,X,Y) ) )
        & injective(F,A,B) )
     => one_to_one(G,A,C) ) ).

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