reserve T for 1-sorted;

theorem Th1:
  for A,B being Subset of T holds A \/ B = [#] T iff A` c= B
proof
  let A,B be Subset of T;
  hereby
    assume A \/ B = [#] T;
    then [#] T \ A = B \ A by XBOOLE_1:40;
    hence A` c= B by XBOOLE_1:36;
  end;
    assume A` c= B;
    then A \/ A` c= A \/ B by XBOOLE_1:9;
    then [#] T c= A \/ B by PRE_TOPC:2;
    hence A \/ B = [#] T;
end;
