
theorem Th9:
  for V being RealLinearSpace, M1,M2 being Subset of V st M1 c= M2
  holds Circled-Family M2 c= Circled-Family M1
proof
  let V be RealLinearSpace, M1,M2 be Subset of V such that
A1: M1 c= M2;
  let M be object;
  assume
A2: M in Circled-Family M2;
  then reconsider M as Subset of V;
  M2 c= M by A2,Def2;
  then
A3: M1 c= M by A1;
  M is circled by A2,Def2;
  hence thesis by A3,Def2;
end;
