Theorems · Theorem · general topology
Ultrafilter.comap_pure
∀ {α : Type u} {β : Type v} {m : α → β} (a : α) (inj : Function.Injective m) (large : Set.range m ∈ pure (m a)),
(pure (m a)).comap inj large = pure a- Defined in
- Mathlib.Order.Filter.Ultrafilter.Defs
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Filterproof · cited by 8,121
- Set.preimageproof · cited by 4,946
- Set.rangestatement and proof · cited by 4,705
- Filter.principalproof · cited by 740
- Ultrafilterstatement · cited by 193
- Set.image_singletonproof · cited by 174
- Set.preimage_image_eqproof · cited by 87
- Filter.principal_singletonproof · cited by 31
- Ultrafilter.coe_injectiveproof · cited by 8
- Ultrafilter.comapstatement and proof · cited by 5
- Filter.comap_pureproof · cited by 3
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