
theorem Th7:
  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 Def5
    .= (x "\/" x) "/\" (x "\/" y) "/\" (x "\/" z) by Def5
    .= x "/\" (x "\/" y) "/\" (x "\/" z)
    .= x "/\" (x "\/" z) by LATTICES:def 9
    .= x by LATTICES:def 9;
  hence thesis;
end;
