proposition: Lemma ltr_creal (e : F) (i : nat) (x : creal) (j : nat) (a : F) : 0 < e -> (cauchymod x e <= i)%N -> (cauchymod x e <= j)%N -> x i <= a - e -> x j < a.
proof: Proof. move=> e_gt0 hi hj ha; have := cauchymodP e_gt0 hj hi. rewrite ltr_distl=> /andP[_ /lt_le_trans-> //]. by rewrite -(ler_add2r (- e)) addrK. Qed.
imports: mathcomp.ssreflect.ssreflect mathcomp(ssrfun ssrbool eqtype ssrnat seq choice fintype) mathcomp(bigop order ssralg ssrnum ssrint rat poly polydiv polyorder) mathcomp(perm matrix mxpoly polyXY binomial bigenough)