 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 Th38: :: (2.41)
  a < b implies b => c < a => c & c => a < c => b
  proof
    assume
A1: a < b;
    (Top L) => (a => c) = (a => c) by Th23; then
A2: (a => (b => c)) < (a => c) by A1,Th25;
    (a "/\" (b => c)) < (b => c) by Th6; then
A3: (b => c) < (a => (b => c)) by Def4;
A4: c => Top L = Top L by Th21;
    (c => (a => b)) => ((c => a) => (c => b)) = Top L by Th25;
    hence thesis by A1,A2,A3,A4,Th23,Def3;
  end;
