
theorem
  for V being RealLinearSpace, M1,M2 being Subset of V st M1 c= M2 holds
  Cir M1 c= Cir M2
proof
  let V be RealLinearSpace, M1,M2 be Subset of V;
  assume M1 c= M2;
  then Circled-Family M2 c= Circled-Family M1 by Th9;
  then
A1: meet Circled-Family M1 c= meet Circled-Family M2 by SETFAM_1:6;
  let x be object;
  assume x in Cir M1;
  hence thesis by A1;
end;
