reserve L for D_Lattice;
reserve a, b, c for Element of L;
reserve L for B_Lattice;
reserve a, b for Element of L;

theorem Th21:
  ( a"/\"b )` = a`"\/" b`
proof
A1: (a`"\/"b`)"/\"(a"/\"b) = (a"/\"b)"/\"(a`"\/"b`) &
    (a`"\/"b`)"\/"(a"/\"b) = (a"/\"b)"\/"(a`"\/"b`);
A2: (a`"\/"b`)"/\"(a"/\"b) = ((a`"\/"b`)"/\"a)"/\"b by Def7
    .= ((a`"/\"a)"\/"(b`"/\"a))"/\"b by Def11
    .= (Bottom L"\/"(b`"/\"a))"/\"b by Th18
    .= (b"/\"b`)"/\"a by Def7
    .= Bottom L"/\"a by Th18
    .= Bottom L;
  (a`"\/"b`)"\/"(a"/\"b) = a`"\/"(b`"\/"(a"/\"b)) by Def5
    .= a`"\/"((b`"\/"a)"/\"(b`"\/"b)) by Th9
    .= a`"\/"((b`"\/"a)"/\"Top L) by Th19
    .= b`"\/"(a"\/"a`) by Def5
    .= b`"\/"Top L by Th19
    .= Top L;
  then a`"\/"b` is_a_complement_of a"/\"b by A1,A2;
  hence thesis by Def21;
end;
