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Theorems · Definition · logic and foundations

Denumerable.ofEquiv

(α : Type u_3) → {β : Type u_4} → [Denumerable α] → β ≃ α → Denumerable β

Denumerability is conserved by equivalences. This is transitivity of equivalence the denumerable way.

Defined in
Mathlib.Logic.Denumerable
Cited by
1 results in Mathlib
Foundations
Depth 18 from the axioms · uses propext, Quot.sound
Assumes
Denumerable
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Denumerable.ofEquiv_ofNat · cited by 7Denumerable.ofEquiv_ofNatDenumerable.ofEncodableOfInfinite · cited by 3Denumerable.ofEncodableOf…Nat.Subtype.denumerable · cited by 0Subtype.denumerableEquiv · cited by 8337EquivEncodable · cited by 140EncodableDenumerable · cited by 28DenumerableEncodable.ofEquiv · cited by 2Encodable.ofEquivDenumerable.ofEquivCITED BYCITES

Cites4

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.