precoverage_inf — Mathlib

English

The precoverage of the infimum P ⊓ Q equals the infimum of precoverages: precoverage (P ⊓ Q) = precoverage P ⊓ precoverage Q.

Русский

Покрытие равняется пересечению: precoverage (P ⊓ Q) = precoverage P ⊓ precoverage Q.

LaTeX

$$precoverage (P ⊓ Q) = precoverage P ⊓ precoverage Q$$

Lean4

theorem precoverage_inf : precoverage (P ⊓ Q) = precoverage P ⊓ precoverage Q :=
  by
  ext X R
  exact ⟨fun hS ↦ ⟨fun _ _ hf ↦ (hS hf).left, fun _ _ hf ↦ (hS hf).right⟩, fun h ↦ fun _ _ hf ↦ ⟨h.left hf, h.right hf⟩⟩

Похожие утверждения