isOpen_of_openSubgroup — Mathlib

English

OpenSubgroup G forms a meet-semilattice with meet given by intersection.

Русский

OpenSubgroup G образует полузадачу (meet) с наименьшей верхой через пересечение.

LaTeX

$$$$ \\text{SemilatticeInf}(\\mathrm{OpenSubgroup}(G)) \\ni U,V \\mapsto U \\cap V. $$$$

Lean4

@[to_additive]
theorem isOpen_of_openSubgroup [ContinuousMul G] (H : Subgroup G) {U : OpenSubgroup G} (h : ↑U ≤ H) :
    IsOpen (H : Set G) :=
  isOpen_mono h U.isOpen

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