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;
reserve X, Y, Z for ManySortedSet of I;
reserve SF, SG, SH for MSSubsetFamily of M,
  SFe for non-empty MSSubsetFamily of M,
  V, W for ManySortedSubset of M;

theorem Th36:
  SF (\) A is MSSubsetFamily of M
proof
  SF c= bool M by PBOOLE:def 18;
  then
A1: SF (\) A c= (bool M) (\) A by PBOOLE:53;
  (bool M) (\) A c= bool M by PBOOLE:56;
  then SF (\) A c= bool M by A1,PBOOLE:13;
  hence thesis by PBOOLE:def 18;
end;
