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 :: SETFAM_1:6
  sf <> {} & (for Z1 be set st Z1 in sf holds G c= Z1) implies G c=
  Intersect sf
proof
  assume that
A1: sf <> {} and
A2: for Z1 be set st Z1 in sf holds G c= Z1;
  Intersect sf = meet sf by A1,SETFAM_1:def 9;
  hence thesis by A1,A2,SETFAM_1:5;
end;
