Fact exp_app n m i v w : @exp (n+m) i (vec_app v w) = exp i v * exp (n+i) w.
Local Notation divides_mult_inv := prime_div_mult.

Lemma ps_exp n m (v : vec nat m) i : ~ divides (ps n) (exp i v).
Coercion tonat {n} := @pos2nat n.