reserve x, y, z, s for ExtReal;
reserve i, j for Integer;
reserve n, m for Nat;

theorem Th7:
  x in REAL & y in REAL or z in REAL implies
  (x + y) / z = x/z + y/z
  proof
    assume
A1: x in REAL & y in REAL or z in REAL;
    per cases by A1;
    suppose x in REAL & y in REAL;
      then reconsider x1 = x, y1 = y as Real;
      per cases by XXREAL_0:14;
      suppose z in REAL;
        hence thesis by XXREAL_3:95;
      end;
      suppose
A2:     z = +infty or z = -infty;
        thus (x + y) / z = 0+0 by A2
        .= x/z + y/z by A2;
      end;
    end;
    suppose z in REAL;
      hence thesis by XXREAL_3:95;
    end;
  end;
