 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 Th31: :: (2.32)
  (a => b) => ((a => c) => (a => (b "/\" c))) = Top L
  proof
A1: a "/\" (a => c) < c by Th17;
A2: a "/\" (a => b) < b by Th17;
    (a "/\" (a => c)) "/\" (a "/\" (a => b)) < c "/\" b by Lm2,A1,A2; then
    ((a => c) "/\" a) "/\" a "/\" ((a => b)) < c "/\" b
      by LATTICES:def 7; then
    (a => c) "/\" (a "/\" a) "/\" ((a => b)) < c "/\" b
      by LATTICES:def 7; then
    a "/\" ((a => c) "/\" (a => b)) <  b "/\" c by LATTICES:def 7; then
    ((a => c) "/\" (a => b)) < (a => (b "/\" c)) by Def4; then
    (a => b) < ((a => c) => (a => (b "/\" c))) by Def4;
    hence thesis;
  end;
