Theorems · Definition · combinatorics
Infinite.natEmbedding
(α : Type u_4) → [Infinite α] → ℕ ↪ α
Embedding of ℕ into an infinite type.
- Defined in
- Mathlib.Data.Fintype.EquivFin
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Infinite
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.
- Function.Embeddingstatement · cited by 988
- Infinitestatement and proof · cited by 352
Cited by14
Results whose statement or proof uses this declaration.
- Cardinal.lt_aleph0proof · cited by 19
- Set.Infinite.natEmbeddingproof · cited by 10
- Infinite.exists_subset_card_eqproof · cited by 5
- ClassGroup.distinctElemsproof · cited by 4
- Fin.Embedding.exists_embedding_disjoint_range_of_add_le_ENat_cardproof · cited by 2
- Module.finite_dual_iffproof · cited by 2
- SimpleGraph.completeMultipartiteGraph.not_cliqueFree_of_infiniteproof · cited by 2
- WellFoundedLT.finite_of_sSupIndepproof · cited by 2
- exists_seq_infinite_isOpen_pairwise_disjointproof · cited by 1
- Infinite.exists_strictMono_or_strictAntiproof · cited by 1
- ringKrullDim_add_enatCard_le_ringKrullDim_mvPolynomialproof · cited by 0
- NormedSpace.noncompactSpaceproof · cited by 0