Theorems · Definition · combinatorics
Finset.preimage
{α : Type u} → {β : Type v} → (s : Finset β) → (f : α → β) → Set.InjOn f (f ⁻¹' ↑s) → Finset αPreimage of s : Finset β under a map f injective on f ⁻¹' s as a Finset.
- Defined in
- Mathlib.Data.Finset.Preimage
- Cited by
- 108 results in Mathlib
- Foundations
- Depth 67 from the axioms, rests on 1,080 definitions · 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.
- 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.toFinsetproof · cited by 351
Cited by113
Results whose statement or proof uses this declaration.
- Finsupp.comapDomainproof · cited by 40
- Finset.coe_preimagestatement · cited by 28
- Finset.mem_preimagestatement · cited by 12
- SummationFilter.comapproof · cited by 9
- Finset.image_preimagestatement · cited by 8
- HasSum.sigmaproof · cited by 8
- Finset.sum_preimagestatement · cited by 6
- Finsupp.comapDomain_single_of_not_mem_rangeproof · cited by 6
- HasProd.sigmaproof · cited by 5
- Submodule.fg_of_fg_map_injectiveproof · cited by 5
- HasSum.nat_add_neg_add_oneproof · cited by 5
- SummationFilter.comap_filterstatement · cited by 5