
theorem CDN:
  for a,b,c be Nat st a,b are_coprime holds
    c divides a*b implies (a gcd c)*(b gcd c) = c
  proof
    let a,b,c be Nat such that
    A1: a,b are_coprime;
    assume
    A2: c divides a*b;
    |.c.| = c gcd (a*b) by A2
    .= (c gcd a)*(c gcd b) by A1,NEWTON03:35;
    hence thesis;
  end;
