reserve L for Ortholattice,
  a, b, c for Element of L;

theorem Th2:
  a "\/" a` = Top L & a "/\" a` = Bottom L
proof
A1: (a "\/" a`) "\/" b = a "\/" a`
  proof
    thus (a "\/" a`) "\/" b = (b "\/" b`) "\/" b by ROBBINS3:def 7
      .= b` "\/" (b "\/" b) by LATTICES:def 5
      .= b` "\/" b
      .= a "\/" a` by ROBBINS3:def 7;
  end;
  then b "\/" (a "\/" a`) = a "\/" a`;
  hence a "\/" a` = Top L by A1,LATTICES:def 17;
A2: (a "/\" a`) "/\" b = a "/\" a`
  proof
    thus (a "/\" a`) "/\" b = (a` "\/" a``)` "/\" b by ROBBINS1:def 23
      .= (b` "\/" b``)` "/\" b by ROBBINS3:def 7
      .= (b "/\" b`) "/\" b by ROBBINS1:def 23
      .= b` "/\" (b "/\" b) by LATTICES:def 7
      .= b` "/\" b
      .= (b`` "\/" b`)` by ROBBINS1:def 23
      .= (a`` "\/" a`)` by ROBBINS3:def 7
      .= a "/\" a` by ROBBINS1:def 23;
  end;
  then b "/\" (a "/\" a`) = a "/\" a`;
  hence thesis by A2,LATTICES:def 16;
end;
