 reserve L for Quasi-Boolean_Algebra,
         x, y, z for Element of L;
 reserve L for Nelson_Algebra,
         a, b, c, d, x, y, z for Element of L;

theorem
  (a "/\" -a) "/\" (b "\/" -b) = a "/\" -a
  proof
    ((-b) "/\" (--b)) < ((-a) "\/" a) by Def13; then
    -(b "\/" (-b)) < ((-a) "\/" a) by Th1; then
    -(b "\/" (-b)) < ((-a) "\/"(--a)) by ROBBINS3:def 6; then
    -(b "\/" (-b)) < -(a "/\"(-a)) by Th8; then
    (a "/\" -a) <= (b "\/" -b) by Th5,Def13;
    hence thesis;
  end;
