Theorems · Theorem · combinatorics
Finset.mem_preimage
∀ {α : Type u} {β : Type v} {f : α → β} {s : Finset β} {hf : Set.InjOn f (f ⁻¹' ↑s)} {x : α},
x ∈ s.preimage f hf ↔ f x ∈ s- Defined in
- Mathlib.Data.Finset.Preimage
- Cited by
- 12 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.
Cites6
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
- Finset.preimagestatement · cited by 108
- Set.Finite.mem_toFinsetproof · cited by 74
Cited by12
Results whose statement or proof uses this declaration.
- YoungDiagram.exists_notMem_rowproof · cited by 5
- HasSum.nat_add_neg_add_oneproof · cited by 5
- Filter.tendsto_finset_preimage_atTop_atTopproof · cited by 4
- linearIndependent_sumproof · cited by 3
- MeasureTheory.piContent_tendsto_zeroproof · cited by 1
- Finset.monotone_preimageproof · cited by 1
- Function.Injective.map_atTop_finsetProd_eqproof · cited by 1
- Function.Injective.map_atTop_finsetSum_eqproof · cited by 1
- Finset.preimage_subsetproof · cited by 0
- UniqueAdd.addHom_preimageproof · cited by 0
- UniqueMul.mulHom_preimageproof · cited by 0
- convexIndependent_iff_finsetproof · cited by 0