theorem Th50:
  a <=> b = (a"/\"b)"\/"(a`"/\"b`)
proof
  thus a <=> b = (a`"\/"b)"/\"(b => a) by FILTER_0:42
    .= (a`"\/"b)"/\"(b`"\/"a) by FILTER_0:42
    .= (a`"/\"(b`"\/"a))"\/"(b"/\"(b`"\/"a)) by LATTICES:def 11
    .= ((a`"/\"b`)"\/"(a`"/\"a))"\/"(b"/\"(b`"\/"a)) by LATTICES:def 11
    .= ((a`"/\"b`)"\/"(a`"/\"a))"\/"((b"/\"b`)"\/"(b"/\" a)) by LATTICES:def 11
    .= ((a`"/\"b`)"\/"Bottom B)"\/"((b"/\"b`)"\/"(b"/\"a)) by LATTICES:20
    .= ((a`"/\"b`)"\/"Bottom B)"\/"(Bottom B"\/"(b"/\"a)) by LATTICES:20
    .= (a`"/\"b`)"\/"(Bottom B"\/"(b"/\"a))
    .= (a"/\"b)"\/"(a`"/\"b`);
end;
