
theorem
  for V being RealLinearSpace, v being VECTOR of V, L being
  Linear_Combination of {v} st L is convex holds L.v = 1 & Sum(L) = L.v * v
proof
  let V be RealLinearSpace;
  let v be VECTOR of V;
  let L be Linear_Combination of {v};
  Carrier(L) c= {v} by RLVECT_2:def 6;
  then
A1: Carrier(L) = {} or Carrier(L) = {v} by ZFMISC_1:33;
  assume L is convex;
  hence thesis by A1,Lm11,Th21;
end;
