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 :: SETFAM_1:11
  SF = {V} implies meet SF = V
proof
  assume
A1: SF = {V};
  now
    let i be object;
    assume
A2: i in I;
    then consider Q be Subset-Family of (M.i) such that
A3: Q = SF.i and
A4: (meet SF).i = Intersect Q by Def1;
    thus (meet SF).i = meet Q by A1,A2,A3,A4,SETFAM_1:def 9
      .= meet {V.i} by A1,A2,A3,PZFMISC1:def 1
      .= V.i by SETFAM_1:10;
  end;
  hence thesis;
end;
