theorem Th55:
  i => j [= i => (j"\/"k) & i => j [= (i"/\"k) => j & i => j [= i
  => (k"\/"j) & i => j [= (k"/\"i) => j
proof
A1: i"/\"(i=>j) [= j by FILTER_0:def 7;
  (i"/\"k)"/\"(i=>j) [= i"/\" (i=>j) by LATTICES:6,9;
  then
A2: (i"/\"k)"/\"(i=>j) [= j by A1,LATTICES:7;
  j [= j"\/"k by LATTICES:5;
  then i"/\"(i=>j) [= j"\/"k by A1,LATTICES:7;
  hence thesis by A2,FILTER_0:def 7;
end;
