 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 Th28: :: (2.29)
  (a => c) => ((b => c) => ((a "\/" b) => c)) = Top L
  proof
A1: a "/\" (a => c) < c by Th17;
A2: b "/\" (b => c) < c by Th17;
    (a "/\" (a => c)) "/\" (b => c) < (a "/\" (a => c)) by Th6; then
A3: (a "/\" (a => c)) "/\" (b => c) < c by A1,Def3;
    (b "/\" (b => c)) "/\" (a => c) < (b "/\" (b => c)) by Th6; then
    (b "/\" (b => c)) "/\" (a => c) < c by A2,Def3; then
    (a "/\" (a => c) "/\" (b => c)) "\/" (b "/\" (b => c)"/\" (a => c)) < c
      by Def7,A3; then
    (a "/\" ((a => c) "/\" (b => c))) "\/" (b "/\" (b => c) "/\" (a => c)) < c
      by LATTICES:def 7; then
    (a "/\" ((a => c) "/\" (b => c))) "\/" ( b "/\" ((b => c)"/\" (a => c)))
      < c by LATTICES:def 7; then
    ((b => c) "/\" (a => c)) "/\" (a "\/" b) < c by LATTICES:def 11; then
    ((b => c) "/\" (a => c)) < (a "\/" b) => c by Def4; then
    (a => c) < (b => c) => ((a "\/" b) => c) by Def4;
    hence thesis;
  end;
