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_1:9
  G in sf & G misses H implies Intersect sf misses H
proof
  assume that
A1: G in sf and
A2: G misses H;
  Intersect sf = meet sf by A1,SETFAM_1:def 9;
  hence thesis by A1,A2,SETFAM_1:8;
end;
