Theorems · Theorem · logic and foundations
Function.Injective.countable
∀ {α : Sort u} {β : Sort v} [Countable β] {f : α → β}, Function.Injective f → Countable α- Defined in
- Mathlib.Data.Countable.Defs
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
- Assumes
- Countable
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Countablestatement and proof · cited by 633
- Countable.exists_injective_natproof · cited by 5
Cited by10
Results whose statement or proof uses this declaration.
- Set.Countable.monoproof · cited by 34
- Set.MapsTo.countable_of_injOnproof · cited by 5
- Countable.of_equivproof · cited by 4
- Function.Embedding.countableproof · cited by 4
- Function.Injective.uncountableproof · cited by 4
- Function.Surjective.countableproof · cited by 3
- Set.countable_ofPred_nonempty_of_disjointproof · cited by 2
- Pairwise.countable_of_isOpen_disjointproof · cited by 1
- not_injective_uncountable_countableproof · cited by 0
- TopologicalSpace.Clopens.countable_iff_secondCountableproof · cited by 0