isCoboundedUnder_ge_of_isCobounded

English

If g is antitone and the filter F is cobounded, then the induced coboundedness under g in the opposite order holds.

Русский

Если g антитонна, и фильтр F кобounded, то переход к обратному порядку сохраняет кобoundedность.

LaTeX

$$Antitone.isCoboundedUnder_ge_of_isCobounded$$

Lean4

theorem isCoboundedUnder_ge_of_isCobounded {f : R → S} (f_decr : Antitone f) [NeBot F] (cobdd : IsCobounded (· ≤ ·) F) :
    F.IsCoboundedUnder (· ≥ ·) f :=
  Monotone.isCoboundedUnder_le_of_isCobounded (S := Sᵒᵈ) f_decr cobdd

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