 reserve L for AD_Lattice;
 reserve x,y,z for Element of L;
 reserve L for GAD_Lattice;
 reserve x,y,z for Element of L;

theorem   :: Theorem 3.13. (1) => (2)
  (for a,b,c being Element of L holds
    (a "\/" b) "/\" c = (a "/\" c) "\/" (b "/\" c)) implies
    for a,b being Element of L holds (a "\/" b) "/\" b = b
  proof
    assume
A1: for a,b,c being Element of L holds
    (a "\/" b) "/\" c = (a "/\" c) "\/" (b "/\" c);
    let a,b be Element of L;
    (a "\/" b) "/\" b = (a "/\" b) "\/" (b "/\" b) by A1
                     .= (a "/\" b) "\/" b by IMeet
                     .= b by LATTICES:def 8;
    hence thesis;
  end;
