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Theorems · Theorem · general topology

Filter.image_mem_map_iff

∀ {α : Type u_1} {β : Type u_2} {f : Filter α} {m : α → β} {s : Set α},
  Function.Injective m → (m '' s ∈ Filter.map m f ↔ s ∈ f)
Defined in
Mathlib.Order.Filter.Map
Cited by
3 results in Mathlib
Foundations
Depth 11 from the axioms · uses propext, Quot.sound
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Around this declaration

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

Filter.mem_comap_iff · cited by 1Filter.mem_comap_iffmem_nhds_subtype_iff_nhdsWithin · cited by 0mem_nhds_subtype_iff_nhds…mem_nhdsSet_subtype_iff_nhdsSetWithin · cited by 0mem_nhdsSet_subtype_iff_n…Set · cited by 53352SetFilter · cited by 8121FilterSet.image · cited by 5609Set.imageFilter.map · cited by 819Filter.mapSet.preimage_image_eq · cited by 87Set.preimage_image_eqFilter.image_mem_map · cited by 39Filter.image_mem_mapFilter.image_mem_map_iffCITED BYCITES

Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by3

Results whose statement or proof uses this declaration.