Theorems · Theorem · combinatorics
Finset.image_subset_iff
∀ {α : Type u_1} {β : Type u_2} [inst : DecidableEq β] {f : α → β} {s : Finset α} {t : Finset β},
Finset.image f s ⊆ t ↔ ∀ x ∈ s, f x ∈ t- Defined in
- Mathlib.Data.Finset.Image
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 78 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.
Cites4
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.coeproof · cited by 8,199
- Finset.imagestatement and proof · cited by 910
- Set.image_subset_iffproof · cited by 203
Cited by12
Results whose statement or proof uses this declaration.
- Finset.card_le_card_of_injOnproof · cited by 16
- Finset.sum_of_injOnproof · cited by 8
- Finset.image_subset_image₂_rightproof · cited by 8
- Finset.image_subset_image₂_leftproof · cited by 5
- Finset.image_subset_iff_subset_preimageproof · cited by 3
- image_subtype_ne_univ_eq_image_eraseproof · cited by 1
- Finset.sigma_preimage_mk_of_subsetproof · cited by 1
- Finset.prod_of_injOnproof · cited by 1
- Fintype.eval_image_piFinset_subsetproof · cited by 1
- Finset.card_le_of_interleavedproof · cited by 1
- MvPolynomial.coeffs_oneproof · cited by 1
- Finset.zero_smul_finset_subsetproof · cited by 0