Theorems · Theorem · order theory
Finset.exists_subset_injOn_image_eq_of_surjOn
∀ {α : Type u} {β : Type v} [inst : DecidableEq β] {f : α → β} (s : Set α) (t : Finset β),
Set.SurjOn f s ↑t → ∃ u, ↑u ⊆ s ∧ Set.InjOn f ↑u ∧ Finset.image f u = tFinset version of Set.SurjOn.exists_subset_injOn_image_eq.
- Defined in
- Mathlib.Data.Set.Finite.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- Finsetstatement and proof · cited by 13,712
- SetLike.coestatement and proof · cited by 8,199
- Set.imageproof · cited by 5,609
- Set.Finiteproof · cited by 1,814
- Finset.imagestatement · cited by 910
- Set.InjOnstatement and proof · cited by 543
- Set.Finite.toFinsetproof · cited by 351
- Finset.coe_imageproof · cited by 222
- Set.SurjOnstatement and proof · cited by 186
- Set.Finite.coe_toFinsetproof · cited by 124
- Set.Finite.of_finite_imageproof · cited by 20
Cited by3
Results whose statement or proof uses this declaration.
- Ideal.height_le_height_add_spanFinrank_of_leproof · cited by 2
- Ideal.height_le_height_add_of_liesOverproof · cited by 1
- Convexity.IsConvexSet.imageproof · cited by 1