%--------------------------------------------------------------------------
% File     : SET755+4 : TPTP v9.0.0. Bugfixed v2.2.1.
% Domain   : Set Theory (Mappings)
% Problem  : If X is a subset of Y, then f-1(X) is a subset of f-1(Y)
% Version  : [Pas99] axioms.
% English  :

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

% Status   : Theorem
% Rating   : 0.42 v9.0.0, 0.36 v8.2.0, 0.42 v8.1.0, 0.44 v7.4.0, 0.40 v7.3.0, 0.34 v7.2.0, 0.31 v7.1.0, 0.30 v7.0.0, 0.40 v6.4.0, 0.42 v6.2.0, 0.48 v6.1.0, 0.57 v5.5.0, 0.63 v5.4.0, 0.64 v5.3.0, 0.70 v5.2.0, 0.60 v5.1.0, 0.62 v4.1.0, 0.61 v4.0.1, 0.70 v4.0.0, 0.67 v3.7.0, 0.60 v3.5.0, 0.58 v3.4.0, 0.74 v3.3.0, 0.64 v3.2.0, 0.73 v3.1.0, 0.78 v2.7.0, 0.83 v2.6.0, 0.86 v2.5.0, 0.88 v2.4.0, 0.50 v2.3.0, 0.33 v2.2.1
% Syntax   : Number of formulae    :   29 (   1 unt;   0 def)
%            Number of atoms       :  133 (   6 equ)
%            Maximal formula atoms :   11 (   4 avg)
%            Number of connectives :  106 (   2   ~;   2   |;  53   &)
%                                         (  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(thIIa05,conjecture,
    ! [F,A,B,X,Y] :
      ( ( maps(F,A,B)
        & subset(X,B)
        & subset(Y,B)
        & subset(X,Y) )
     => subset(inverse_image2(F,X),inverse_image2(F,Y)) ) ).

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