proposition: Lemma ltr_distr_creal (e : F) (i : nat) (x : creal) (j : nat) (a b : F) : 0 < e -> (cauchymod x e <= i)%N -> (cauchymod x e <= j)%N -> a + e <= `| x i - b | -> a < `| x j - b |.
proof: Proof. move=> e_gt0 hi hj hb; apply: contraLR hb; rewrite -ltNge -leNgt. by move=> ha; rewrite (@ltr_distl_creal e j) // 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)