theorem
  X "\/" Y = (X \+\ Y) "\/" (X "/\" Y)
proof
  thus X "\/" Y = (Y \ X) "\/" X by Th35
    .= (Y \ X) "\/" ((X \ Y) "\/" (X "/\" Y)) by Th36
    .= (X \+\ Y) "\/" (X "/\" Y) by LATTICES:def 5;
end;
