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 :: FINSET_1:26
  doms F is finite-yielding implies rngs F is finite-yielding
proof
  assume
A1: doms F is finite-yielding;
  let i be object such that
A2: i in I;
  reconsider f = F.i as Function;
  (doms F).i is finite by A1;
  then dom f is finite by A2,Th14;
  then rng f is finite by FINSET_1:8;
  hence thesis by A2,Th13;
end;
