proposition: Lemma gtr_creal (e : F) (i : nat) (x : creal) (j : nat) (a : F) : 0 < e -> (cauchymod x e <= i)%N -> (cauchymod x e <= j)%N -> a + e <= x i-> a < x j.
proof: Proof. move=> e_gt0 hi hj ha; have := cauchymodP e_gt0 hj hi. rewrite ltr_distl=> /andP[/(le_lt_trans _)-> //]. by rewrite -(ler_add2r e) addrNK. 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)