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

Lemma ratio_cp (a b c : R) :
a - b != 0 ->  b - c != 0 -> c - a != 0 ->
0 < (b-a) / (c-a) < 1 \/ 0 < (c-b) / (a-b) < 1 \/ 0 < (a-c) / (b-c) < 1.