
theorem Th10:
  for T being reflexive transitive antisymmetric with_suprema
TA-structure st T is adj-structured for t1,t2 being type of T st t1 <= t2 holds
  adjs t2 c= adjs t1
proof
  let T be reflexive transitive antisymmetric with_suprema TA-structure such
  that
A1: for t1,t2 being type of T holds adjs(t1"\/"t2) = (adjs t1) /\ (adjs t2);
  let t1,t2 be type of T;
  assume t1 <= t2;
  then t1"\/"t2 = t2 by YELLOW_0:24;
  then adjs t2 = (adjs t1)/\(adjs t2) by A1;
  hence thesis by XBOOLE_1:17;
end;
