Theorems · Theorem · combinatorics
Finset.mem_image
∀ {α : Type u_1} {β : Type u_2} [inst : DecidableEq β] {f : α → β} {s : Finset α} {b : β},
b ∈ Finset.image f s ↔ ∃ a ∈ s, f a = b- Defined in
- Mathlib.Data.Finset.Image
- Cited by
- 105 results in Mathlib
- Foundations
- Depth 74 from the axioms, rests on 1,371 definitions · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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
- Finset.imagestatement · cited by 910
- Finset.valproof · cited by 438
Cited by105
Results whose statement or proof uses this declaration.
- Finset.mem_image_of_memproof · cited by 81
- HasSum.nat_add_negproof · cited by 10
- Finset.card_bijproof · cited by 10
- Finset.mem_sym_iffproof · cited by 9
- Finset.exists_max_imageproof · cited by 8
- Finset.sum_of_injOnproof · cited by 8
- HasSum.nat_add_neg_add_oneproof · cited by 5
- Finset.sum_image'proof · cited by 5
- alternatingGroup.isMultiplyPretransitiveproof · cited by 4
- Polynomial.mem_coeffs_iffproof · cited by 4
- BoxIntegral.unitPartition.mem_prepartition_iffproof · cited by 4
- CompleteLattice.isCompactElement_finsetSupproof · cited by 3