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Theorems · Theorem · general topology

insert_mem_nhdsWithin_insert

∀ {α : Type u_1} [inst : TopologicalSpace α] {a : α} {s t : Set α},
  t ∈ nhdsWithin a s → insert a t ∈ nhdsWithin a (insert a s)
Defined in
Mathlib.Topology.NhdsWithin
Cited by
1 results in Mathlib
Foundations
Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpace
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

ContDiffWithinAt.mono_of_mem_nhdsWithin · cited by 13ContDiffWithinAt.mono_of_…Set · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceFilter · cited by 8121FilternhdsWithin · cited by 1912nhdsWithinFilter.mem_of_superset · cited by 308Filter.mem_of_supersetnhdsWithin_insert · cited by 13nhdsWithin_insertinsert_mem_nhdsWithin_insertCITED BYCITES

Cites6

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Cited by1

Results whose statement or proof uses this declaration.