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

Lemma col_2D' a b c : (bet a b c \/ bet b c a \/ bet c a b) ->
(a 0 0 - b 0 0) * (b 0 1 - c 0 1) == (a 0 1 - b 0 1) * (b 0 0 - c 0 0).