Theorems · Theorem · order theory
Set.Infinite.image
∀ {α : Type u} {β : Type v} {s : Set α} {f : α → β}, Set.InjOn f s → s.Infinite → (f '' s).InfiniteAlias of the reverse direction of Set.infinite_image_iff.
- Defined in
- Mathlib.Data.Set.Finite.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- Set.imagestatement · cited by 5,609
- Set.InjOnstatement and proof · cited by 543
- Set.Infinitestatement · cited by 263
- Set.infinite_image_iffproof · cited by 7
Cited by6
Results whose statement or proof uses this declaration.
- Nat.card_image_of_injOnproof · cited by 3
- Set.Infinite.image2_leftproof · cited by 1
- Set.Infinite.image2_rightproof · cited by 1
- Polynomial.existsUnique_hilbertPolyproof · cited by 1
- Set.ncard_sumEquiv_symm_applyproof · cited by 1
- bergelsonproof · cited by 0