
theorem
  for V being RealLinearSpace, v1,v2,v3 being VECTOR of V, L being
  Linear_Combination of V st L is convex & Carrier(L) = {v1,v2,v3} & v1 <> v2 &
v2 <> v3 & v3 <> v1 holds L.v1 + L.v2 + L.v3 = 1 & L.v1 >= 0 & L.v2 >= 0 & L.v3
  >= 0 & Sum(L) = L.v1 * v1 + L.v2 * v2 + L.v3 * v3 by Lm15;
