reserve a,b,p,x,x9,x1,x19,x2,y,y9,y1,y19,y2,z,z9,z1,z2 for object,
   X,X9,Y,Y9,Z,Z9 for set;
reserve A,D,D9 for non empty set;
reserve f,g,h for Function;

theorem Th15:
  f tolerates g & x in dom f implies (f+*g).x = f.x
proof
  assume that
A1: f tolerates g and
A2: x in dom f;
  now
    per cases;
    suppose
      x in dom g;
      then x in dom f /\ dom g & (f+*g).x = g.x by A2,Th13,XBOOLE_0:def 4;
      hence thesis by A1;
    end;
    suppose
      not x in dom g;
      hence thesis by Th11;
    end;
  end;
  hence thesis;
end;
