preStoneCechCompat — Mathlib

English

Same as 200125 with the simplified simp-based presentation.

Русский

То же, что и в 200125, упрощённо через simp.

LaTeX

$$preStoneCech_hom_ext$$

Lean4

theorem preStoneCechCompat {F G : Ultrafilter α} {x : α} (hF : ↑F ≤ 𝓝 x) (hG : ↑G ≤ 𝓝 x) :
    Ultrafilter.extend g F = Ultrafilter.extend g G :=
  by
  replace hF := (map_mono hF).trans hg.continuousAt
  replace hG := (map_mono hG).trans hg.continuousAt
  rwa [show Ultrafilter.extend g G = g x by rwa [ultrafilter_extend_eq_iff, G.coe_map], ultrafilter_extend_eq_iff,
    F.coe_map]

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