Theorems · Theorem · logic and foundations
small_of_injective
∀ {α : Type v} {β : Type w} [Small.{u, w} β] {f : α → β}, Function.Injective f → Small.{u, v} α- Defined in
- Mathlib.Logic.Small.Basic
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Small
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Smallstatement and proof · cited by 369
- Equiv.ofInjectiveproof · cited by 64
- small_mapproof · cited by 3
Cited by15
Results whose statement or proof uses this declaration.
- small_of_surjectiveproof · cited by 11
- CategoryTheory.locallySmall_of_faithfulproof · cited by 5
- small_subsetproof · cited by 3
- Ordinal.sSup_add_one_lt_of_lt_cofproof · cited by 2
- CategoryTheory.essentiallySmall_of_fully_faithfulproof · cited by 2
- CategoryTheory.wellPowered_of_isDetectingproof · cited by 2
- CategoryTheory.Limits.Types.hasColimit_iff_small_colimitTypeproof · cited by 2
- CategoryTheory.Precoverage.small_subsheafify_of_smallproof · cited by 1
- CategoryTheory.HasExt.hasSmallLocalizedShiftedHom_of_isLE_of_isGEproof · cited by 0
- Manifold.IsSubmersionAtOfComplement.smallproof · cited by 0
- CategoryTheory.ObjectProperty.Small.of_leproof · cited by 0
- Manifold.IsImmersionAtOfComplement.smallproof · cited by 0