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_1:3
  meet SFe c= union SFe
proof
  let i be object;
  assume
A1: i in I;
  then consider Q be Subset-Family of (M.i) such that
A2: Q = SFe.i and
A3: (meet SFe).i = Intersect Q by Def1;
  meet Q c= union Q & Intersect Q = meet Q by A1,A2,SETFAM_1:2,def 9;
  hence thesis by A1,A2,A3,MBOOLEAN:def 2;
end;
