
theorem Th6:
  for L being join-commutative meet-absorbing meet-commutative
  join-absorbing join-idempotent distributive non empty LattStr for x, y, z
  being Element of L holds ((x "\/" y) "\/" z) "/\" x = x
proof
  let L be join-commutative meet-absorbing meet-commutative join-absorbing
  join-idempotent distributive non empty LattStr;
  let x, y, z be Element of L;
  ((x "\/" y) "\/" z) "/\" x = (x "/\" (x "\/" y)) "\/" (x "/\" z) by
LATTICES:def 11
    .= (x "/\" x) "\/" (x "/\" y) "\/" (x "/\" z) by LATTICES:def 11
    .= x "\/" (x "/\" y) "\/" (x "/\" z)
    .= x "\/" (x "/\" z) by LATTICES:def 8
    .= x by LATTICES:def 8;
  hence thesis;
end;
