reserve I, G, H for set, i, x for object,
  A, B, M for ManySortedSet of I,
  sf, sg, sh for Subset-Family of I,
  v, w for Subset of I,
  F for ManySortedFunction of I;

theorem Th18:
  A c= B & B is finite-yielding implies A is finite-yielding
proof
  assume
A1: A c= B & B is finite-yielding;
  let i be object;
  assume i in I;
  then A.i c= B.i & B.i is finite by A1;
  hence thesis;
end;
