for r, s being Real
for V being RealLinearSpace
for v, u being VECTOR of V
for I being affinely-independent Subset of V
for p1, p2, w1, w2 being Element of V st v in conv I & u in conv I & not u in conv (I \ {p1}) & not u in conv (I \ {p2}) & w1 in conv (I \ {p1}) & w2 in conv (I \ {p2}) & (r * u) + ((1 - r) * w1) = v & (s * u) + ((1 - s) * w2) = v & r < 1 & s < 1 holds
( w1 = w2 & r = s )