 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 Th11:
  (-a) "\/" b <= a => b
  proof
    a < -!a by Def11; then
    (a "/\" (-b)) < ((-!a) "/\" (-b)) by Lm1; then
A1: (a "/\" -b) < -((!a) "\/" b) by Th1;
    -(a => b) < (a "/\" -b) by Def10; then
A2: -(a => b) < -((!a) "\/" b) by A1,Def3;
    (a => (Bottom L)) < a => Bottom L by Def2; then
    ((a => (Bottom L)) "/\" a) < Bottom L by Def4; then
    (a "/\" (a => (Top L)`)) < Bottom L by Th2; then
A3: a "/\" (!a) < (Bottom L) by Def14;
    Bottom L <= b; then
    Bottom L < b by Th5; then
    a "/\" (!a) < b by A3,Def3; then
A4: (!a) < (a => b) by Def4;
    b "/\" a < b by Th6; then
    b < (a => b) by Def4; then
A5: (!a) "\/" b <= (a => b) by A2,Th5,A4,Def7;
    (a "/\" (-a)) < Bottom L by Def13; then
A6: (-a) < (a => (Bottom L)) by Def4;
    (a => (Top L)`) = (!a) by Def14; then
A7: (-a) < (!a) by A6,Th2;
A8: (-!a) < a by Def12;
    a = (--a) by ROBBINS3:def 6; then
    -a <= (!a) by A8,A7,Th5; then
    b "\/" (-a) <= b "\/" (!a) by Th10;
    hence thesis by A5,Th9;
  end;
