map_fst_nhds — Mathlib

English

A collection of simp lemmas about the fst projection and nhdsWithin on product sets.

Русский

Список упрощений для проекции fst и nhdsWithin на произведениях множеств.

LaTeX

$$$$\text{(simp lemmas for }\mathrm{map\_fst\_nhdsWithin}\text{).}$$$$

Lean4

@[simp]
theorem map_fst_nhds (x : X × Y) : map Prod.fst (𝓝 x) = 𝓝 x.1 :=
  le_antisymm continuousAt_fst <| (map_fst_nhdsWithin x).symm.trans_le (map_mono inf_le_left)

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