reserve a,b,c,d,x,j,k,l,m,n,o,xi,xj for Nat,
  p,q,t,z,u,v for Integer,
  a1,b1,c1,d1 for Complex;

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;
