bind_inf_principal — Mathlib

English

Another formulation about bind with infimum and principal operations: (f ⊔ 𝓟 s) bind g equals f.bind g ⊔ 𝓟 s.

Русский

Другая формулировка связывания с Inf и принципиалом: (f ⊔ 𝓟 s) bind g равно f.bind g ⊔ 𝓟 s.

LaTeX

$$$(f \\sqcup \\mathcal{P} s) \\!\\mathrm{bind}\\ g = f \\mathrm{bind}\\ g \\sqcup \\mathcal{P} s$$

Lean4

theorem bind_inf_principal {f : Filter α} {g : α → Filter β} {s : Set β} :
    (f.bind fun x => g x ⊓ 𝓟 s) = f.bind g ⊓ 𝓟 s :=
  Filter.ext fun s => by simp only [mem_bind, mem_inf_principal]

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