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

Lemma ratio_cp' (a b c : R) :
b - a != 0 -> c - a != 0 -> b - c != 0 ->
[|| 0 < (b-a) / (c-a) < 1, 0 < (c-b) / (a-b) < 1 | 0 < (a-c) / (b-c) < 1].