Definition exprn_cp1 := (exprn_ilte1, exprn_egte1).

(* Specifications: *)
Lemma ler_iexpr x n : (0 < n)%N -> 0 <= x -> x <= 1 -> x ^+ n <= x.
Definition lter_iexpr := (ler_iexpr, ltr_iexpr).
Lemma ler_eexpr x n : (0 < n)%N -> 1 <= x -> x <= x ^+ n.
Lemma ltr_eexpr x n : 1 < x -> (x < x ^+ n) = (1 < n)%N.
Definition lter_eexpr := (ler_eexpr, ltr_eexpr).