reserve L for Lattice,
  p,p1,q,q1,r,r1 for Element of L;
reserve x,y,z,X,Y,Z,X1,X2 for set;

theorem Th5:
  for L being meet-absorbing meet-commutative join-absorbing
meet-associative non empty LattStr, a, b, c, d being Element of L st a [= b &
  c [= d holds a "/\" c [= b "/\" d
proof
  let L be meet-absorbing meet-commutative meet-associative join-absorbing
  non empty LattStr, a, b, c, d be Element of L;
  assume a [= b;
  then
A1: a "/\" b = a by LATTICES:4;
  assume c [= d;
  then a "/\" c = (a "/\" b) "/\" (c "/\" d) by A1,LATTICES:4
    .= ((a "/\" b) "/\" c) "/\" d by LATTICES:def 7
    .= (b "/\" (a "/\" c)) "/\" d by LATTICES:def 7
    .= (a "/\" c) "/\" (b "/\" d) by LATTICES:def 7;
  hence thesis by LATTICES:4;
end;
