bliminf_or_eq_inf — Mathlib

English

The sup with not p and p corresponds to limsup of p: blimsup u f p ⊔ blimsup u f (¬p ·) = limsup u f.

Русский

Суп с не p и p соответствует limsup: blimsup u f p ⊔ blimsup u f (¬p ·) = limsup u f.

LaTeX

$$$\\operatorname{blimsup}(u,f,p) \\sqcup \\operatorname{blimsup}(u,f(\\lnot p \\cdot)) = \\operatorname{limsup} u f$$$

Lean4

@[simp]
theorem bliminf_or_eq_inf : (bliminf u f fun x => p x ∨ q x) = bliminf u f p ⊓ bliminf u f q :=
  blimsup_or_eq_sup (α := αᵒᵈ)

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