reserve L for Boolean non empty RelStr;
reserve a,b,c,d for Element of L;

theorem
  a\(b"\/"c) = (a\b)"/\"(a\c)
proof
  thus a\(b"\/"c) = a"/\"('not' b"/\"'not' c) by Th36
    .= (a"/\"a)"/\"('not' b"/\"'not' c) by Th2
    .= ((a"/\"a)"/\"'not' b)"/\"'not' c by LATTICE3:16
    .= (a"/\"(a"/\"'not' b))"/\"'not' c by LATTICE3:16
    .= (a\b)"/\" (a\c) by LATTICE3:16;
end;
