
theorem Th17:
  for L be LATTICE st L is distributive for a,b,c be Element of L
  holds a"\/"(b"/\"c) = (a"\/"b) "/\" (a"\/"c)
proof
  let L be LATTICE such that
A1: L is distributive;
  let a,b,c be Element of L;
  (a"\/"b) "/\" (a"\/"c) = ((a"\/"b) "/\" a) "\/"((a"\/"b) "/\" c) by A1,
WAYBEL_1:def 3
    .= a "\/" ((a"\/"b) "/\" c) by LATTICE3:18
    .= a "\/" ((c"/\"a) "\/" (c"/\"b)) by A1,WAYBEL_1:def 3
    .= (a "\/" (c"/\"a)) "\/" (c"/\"b) by LATTICE3:14
    .= a "\/" (c"/\"b) by LATTICE3:17;
  hence thesis;
end;
