
theorem for a,b be Integer holds parity (a*b) = (parity a)*(parity b)
  proof
    let a,b be Integer;
    per cases;
    suppose a is even; then
      parity a = 0 & parity (a*b) = 0;
      hence thesis;
    end;
    suppose a is odd; then
      parity a = 1 & (b is even iff a*b is even);
      hence thesis;
    end;
  end;
