for r being Real
for V being RealLinearSpace
for v1, v2 being VECTOR of V
for I being affinely-independent Subset of V st v1 in Affin I & v2 in Affin I holds
(((1 - r) * v1) + (r * v2)) |-- I = ((1 - r) * (v1 |-- I)) + (r * (v2 |-- I))