
theorem for a,b be Integer holds parity (a lcm b) = parity (a*b)
  proof
    let a,b be Integer;
    per cases;
    suppose
      A1: a*b is odd; then
      a is odd & b is odd; then
      a lcm b is odd;
      hence thesis by A1;
    end;
    suppose
      A1: a*b is even;
      then a is even or b is even; then
      a lcm b is even;
      hence thesis by A1;
    end;
  end;
