theorem GL:
  for a,b be non zero Nat holds
    a/(a gcd b) = (a lcm b)/b
  proof
    let a,b be non zero Nat;
    a/(a gcd b) = (a*b)/(b*(a gcd b)) by XCMPLX_1:91
    .= ((a gcd b)*(a lcm b))/(b*(a gcd b)) by NAT_D:29
    .= (a lcm b)/b by XCMPLX_1:91;
    hence thesis;
  end;
