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nat model ported to the dualized version, but not itself dualized dedekind-sig-compl...
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14
15 include "lebesgue.ma".
16 include "models/nat_order_continuous.ma".
17
18 theorem nat_lebesgue_oc:
19    ∀a:sequence ℕ.∀l,u:ℕ.∀H:∀i:nat.a i ∈ [l,u]. 
20      ∀x:ℕ.a order_converges x → 
21       x ∈ [l,u] ∧ 
22       ∀h:x ∈ [l,u].
23        uniform_converge {[l,u]} ⌊n,≪a n,H n≫⌋ ≪x,h≫.
24 intros; apply lebesgue_oc; [apply nat_us_is_oc] assumption;
25 qed.
26