Theorems · Theorem · combinatorics
Finset.coe_preimage
∀ {α : Type u} {β : Type v} {f : α → β} (s : Finset β) (hf : Set.InjOn f (f ⁻¹' ↑s)), ↑(s.preimage f hf) = f ⁻¹' ↑s- Defined in
- Mathlib.Data.Finset.Preimage
- Cited by
- 28 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Finsetstatement and proof · cited by 13,712
- SetLike.coestatement and proof · cited by 8,199
- Set.preimagestatement and proof · cited by 4,946
- Set.InjOnstatement and proof · cited by 543
- Set.Finite.coe_toFinsetproof · cited by 124
- Finset.preimagestatement · cited by 108
Cited by28
Results whose statement or proof uses this declaration.
- Finsupp.comapDomain_singleproof · cited by 9
- Finset.image_preimageproof · cited by 8
- Submodule.fg_of_fg_map_injectiveproof · cited by 5
- Finset.sum_preimage'proof · cited by 3
- SimpleGraph.cliqueSet_mapproof · cited by 3
- Finset.preimage_mapproof · cited by 1
- Subgroup.rank_closure_finset_le_cardproof · cited by 1
- AddSubgroup.rank_closure_finset_le_cardproof · cited by 1
- Finset.image_add_leftproof · cited by 1
- Finset.image_mul_leftproof · cited by 1
- Finset.preimage_unionproof · cited by 1
- Finset.image_add_rightproof · cited by 1