helm/software/matita/contribs/dama/dama/models/nat_lebesgue.ma

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  14
  15 include "lebesgue.ma".
  16 include "models/nat_order_continuous.ma".
  17
  18 alias symbol "pair" = "dependent pair".
  19 theorem nat_lebesgue_oc:
  20    ∀a:sequence ℕ.∀l,u:ℕ.∀H:∀i:nat.a i ∈ [l,u].
  21      ∀x:ℕ.a order_converges x →
  22       x ∈ [l,u] ∧
  23       ∀h:x ∈ [l,u].
  24        uniform_converge {[l,u]} ⌊n,〈a n,H n〉⌋ 〈x,h〉.
  25 intros; apply lebesgue_oc; [apply nat_us_is_oc] assumption;
  26 qed.
  27