Theorems · Theorem · general topology
TopologicalSpace.Closeds.coe_finset_inf
∀ {ι : Type u_1} {α : Type u_2} [inst : TopologicalSpace α] (f : ι → TopologicalSpace.Closeds α) (s : Finset ι),
↑(s.inf f) = s.inf (SetLike.coe ∘ f)- Defined in
- Mathlib.Topology.Sets.Closeds
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Finsetstatement and proof · cited by 13,712
- SetLike.coestatement and proof · cited by 8,199
- Finset.infstatement · cited by 219
- TopologicalSpace.Closedsstatement and proof · cited by 168
- map_finset_infproof · cited by 10
- TopologicalSpace.Closeds.coe_topproof · cited by 2
- TopologicalSpace.Closeds.coe_infproof · cited by 1
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