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

Lemma upper_dim_dgc_aux1 (p q : 'rV[R]_(2)) (m := (1 / (1 + 1)) *: (p + q)) :
p 0 1 - m 0 1 == 0 -> p <> q ->
(m 0 1 - p 0 1 == 0) && (m 0 0 - p 0 0 != 0).