Section Ratio.
Variable R : realFieldType.
Variable n : nat.
Implicit Types (v : (@Vector R n)).
Definition ratio v1 v2 :=
if [pick k : 'I_(n.+1) | v2 0 k != 0] is Some k
then v1 0 k / v2 0 k else 0.

Lemma ratio_bet'' v1 v2 k1 :
0 < k1 -> v1 != v2 -> k1^-1 = ratio (v2 - v1) (k1 *: (v2 - v1)).