proposition: Lemma expr_lt1 n x : (0 < n)%N -> 0 <= x -> (x ^+ n < 1) = (x < 1).
proof: Proof. by move=> ngt0 xge0; rewrite -{1}[1](expr1n _ n) ltr_pXn2r // [_ \in _]ler01. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(ssrAC div fintype path bigop order finset fingroup) mathcomp(ssralg poly)