toIcoMod_eventuallyEq_toIocMod — Mathlib

English

Same eventual equality principle as earlier; repeated for compatibility in the library.

Русский

Та же принципиальная идея eventual equality; повторение для совместимости библиотеки.

LaTeX

$$toIcoMod_eventuallyEq_toIocMod hp a (hx) : toIcoMod hp a =ᶠ[nhds x] toIocMod hp a$$

Lean4

theorem toIcoMod_eventuallyEq_toIocMod (hx : (x : 𝕜 ⧸ zmultiples p) ≠ a) : toIcoMod hp a =ᶠ[𝓝 x] toIocMod hp a :=
  IsOpen.mem_nhds
      (by
        rw [Ico_eq_locus_Ioc_eq_iUnion_Ioo]
        exact isOpen_iUnion fun i => isOpen_Ioo) <|
    (not_modEq_iff_toIcoMod_eq_toIocMod hp).1 <| not_modEq_iff_ne_mod_zmultiples.2 hx.symm

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