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

Lemma upper_dim_dgc1 (a b c p q : 'rV[R]_(2)) (m := (1 / (1 + 1)) *: (p + q)) :
p 0 0 - m 0 0 == 0 -> p <> q ->
cong a p a q -> cong b p b q -> cong c p c q ->
(a 0 0 - b 0 0) * (b 0 1 - c 0 1) == (a 0 1 - b 0 1) * (b 0 0 - c 0 0).