Definition andb_assoc := Bool.andb_assoc.Implicit Types (v : (@Vector R n)).

Lemma bet_lt1 (k1 k2 k3 : R) : 0 < k1 -> 0 < k2 -> k1 < 1 -> 0 < k3 -> k3 < k1+k2-k1*k2 -> ((k1+k2-k1*k2)/k3)^-1 < 1.