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 LCM1:
  for a,b be Integer holds
    a divides b iff a lcm b = |.b.|
  proof
    let a,b be Integer;
    thus a divides b implies a lcm b= |.b.|
    proof
      assume a divides b; then
      |.b.| = |.a.| lcm |.b.| by INT_2:16, NEWTON:44;
      hence thesis by Def2;
    end;
    assume a lcm b = |.b.|; then
    |.a.| lcm |.b.| = |.b.| by Def2;
    hence thesis by NEWTON:44,INT_2:16;
  end;
