Definition mulr_cp1 := (mulr_ilte1, mulr_egte1).
(* ler and ^-1 *)

Lemma exprn_ilt1 n x : 0 <= x -> x < 1 -> x ^+ n < 1 = (n != 0%N).
Definition exprn_ilte1 := (exprn_ile1, exprn_ilt1).