theorem :: SETFAM_1:7 :: SETFAM_1:59
  SF c= SG implies meet SG c= meet SF
proof
  assume
A1: SF c= SG;
  let i be object;
  assume
A2: i in I;
  then consider Qf be Subset-Family of (M.i) such that
A3: Qf = SF.i and
A4: (meet SF).i = Intersect Qf by Def1;
  consider Qg be Subset-Family of (M.i) such that
A5: Qg = SG.i and
A6: (meet SG).i = Intersect Qg by A2,Def1;
  Qf c= Qg by A1,A2,A3,A5;
  hence thesis by A4,A6,SETFAM_1:44;
end;
