
theorem
  for V be RealLinearSpace, M1,M2,M3 being Subset of V, r1,r2,r3 being
Real st M1 is circled & M2 is circled & M3 is circled holds r1*M1 + r2*M2 + r3*
  M3 is circled
proof
  let V be RealLinearSpace, M1,M2,M3 be Subset of V, r1,r2,r3 be Real;
  assume that
A1: M1 is circled & M2 is circled and
A2: M3 is circled;
  r1*M1 + r2*M2 is circled by A1,Th3;
  then 1*(r1*M1 + r2*M2) + r3*M3 is circled by A2,Th3;
  hence thesis by CONVEX1:32;
end;
