
theorem Th11:
  for V being RealLinearSpace, M being Subset of V holds M c= Cir( M)
proof
  let V be RealLinearSpace, M be Subset of V, u be object;
  assume
A1: u in M;
  for Y being set holds Y in Circled-Family M implies u in Y
  proof
    let Y be set;
    assume
A2: Y in Circled-Family M;
    then reconsider Y as Subset of V;
    M c= Y by A2,Def2;
    hence thesis by A1;
  end;
  hence thesis by SETFAM_1:def 1;
end;
