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

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