reserve f,g,h for Function,
  A for set;
reserve F for Function,
  B,x,y,y1,y2,z for set;
reserve x,z for object;

theorem Th13:
  dom (A --> x) = A & rng (A --> x) c= {x}
proof
  now
    per cases;
    suppose
A1:   A = {};
      thus thesis by A1;
    end;
    suppose
      A <> {};
      hence thesis by RELAT_1:160;
    end;
  end;
  hence thesis;
end;
