English
The neighborhood at a for the infimum over a set of topologies sInf s is the infimum over t in s of nhds in t.
Русский
Окрестность в a для топологии sInf s равна наименьшему общему окрестностям по всем t ∈ s.
LaTeX
$$theorem nhds_sInf {s : Set (TopologicalSpace α)} {a : α} : @nhds α (sInf s) a = ⨅ t ∈ s, @nhds α t a$$
Lean4
theorem nhds_sInf {s : Set (TopologicalSpace α)} {a : α} : @nhds α (sInf s) a = ⨅ t ∈ s, @nhds α t a :=
(gc_nhds a).u_sInf