
theorem
  for a,b be non zero Integer holds Parity a > Parity b implies
  a div (Parity b) is even
  proof
    let a,b be non zero Integer;
    assume Parity a > Parity b; then
    A0: 2*(Parity b) divides Parity a by P2P;
    Parity a divides a by Th3; then
    2*(Parity b) divides a by INT_2:9,A0; then
    consider c be Integer such that
    A1: a = 2*(Parity b)*c;
    (0 + (2*c)*(Parity b)) div (Parity b) = (0 div (Parity b)) + 2*c
      by NAT_D:61;
    hence thesis by A1;
  end;
