proposition: Lemma nonincreasing_cvgn (u_ : R ^nat) : nonincreasing_seq u_ -> has_lbound (range u_) -> u_ @ \oo --> inf (u_ @` setT).
proof: Proof. rewrite -nondecreasing_opp => u_nd u_lb; rewrite -[X in X @ _ --> _](opprK u_). apply: cvgN; rewrite image_comp; apply: nondecreasing_cvgn => //. by move/has_lb_ubN : u_lb; rewrite image_comp. 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