 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  :: (2.43)
  (a => b) => ((c => d) => ((a "\/" c) => (b "\/" d))) = Top L
  proof
    ((c => d) "/\" (a => b)) < (a => b) by Th6; then
A1: (((c => d) "/\" (a => b)) "/\" a) < b by Def4;
    ((c => d) "/\" (a => b)) < (c => d) by Th6; then
    (c "/\" ((c => d) "/\" (a => b))) < d by Def4; then
    (((c => d) "/\" (a => b)) "/\" a) "\/" (((c => d) "/\" (a => b)) "/\" c) <
      (b "\/" d) by Lm2,A1; then
    ((c => d) "/\" (a => b)) "/\" (a "\/" c) < (b "\/" d)
      by LATTICES:def 11; then
    (c => d) "/\" (a => b) < ((a "\/" c) => (b "\/" d)) by Def4; then
    (a => b)< ((c => d) => ((a "\/" c) => (b "\/" d))) by Def4;
    hence thesis;
  end;
