theorem Th32:
  "\/"({a"/\"b: b in X}, C) [= a"/\""\/"(X,C)
proof
  set Y = {a"/\"b: b in X};
  Y is_less_than a"/\""\/"(X,C)
  proof
    let c;
    assume c in Y;
    then consider b such that
A1: c = a"/\"b and
A2: b in X;
    X is_less_than "\/"(X,C) by Def21;
    then b [= "\/"(X,C) by A2;
    hence thesis by A1,LATTICES:9;
  end;
  hence thesis by Def21;
end;
