proposition: Lemma maxr_cvg_0_cvg_0 u r : r < 0 -> (forall k, u k <= 0) -> maxr (u n) r @[n --> \oo] --> 0 -> u n @[n --> \oo] --> 0.
proof: Proof. rewrite -[in r < _]oppr0 ltrNr => r0 u0. under eq_fun do rewrite -(opprK (u _)) -[in maxr _ _](opprK r) -oppr_min. rewrite -[in _ --> _]oppr0 => /cvgNP/minr_cvg_0_cvg_0-/(_ r0). have Nu0 k : 0 <= - u k by rewrite lerNr oppr0. by move=> /(_ Nu0)/(cvgNP _ _).2; rewrite opprK oppr0. Qed.
imports: mathcomp(all_ssreflect ssralg ssrint ssrnum matrix) mathcomp(interval rat) mathcomp(mathcomp_extra boolp classical_sets functions) mathcomp(set_interval) reals ereal signed topology normedtype landau