Definition contraction a b k := k *: (b - a) + a.

Lemma upper_dim_aux (a b m : 'rV[R]_(2)) (c0 c1: R) :
c0 * (m 0 0 - a 0 0) + c1 * (m 0 1 - a 0 1) = 0 ->
c0 * (m 0 0 - b 0 0) + c1 * (m 0 1 - b 0 1) = 0 ->
c0 * (b 0 0 - a 0 0) = - c1 * (b 0 1 - a 0 1).