Theorems · Theorem · combinatorics
Finset.image_nonempty
∀ {α : Type u_1} {β : Type u_2} [inst : DecidableEq β] {f : α → β} {s : Finset α},
(Finset.image f s).Nonempty ↔ s.Nonempty- 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.
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
- Set.Nonemptyproof · cited by 2,627
- Finset.Nonemptystatement · cited by 1,001
- Finset.imagestatement · cited by 910
- Set.image_nonemptyproof · cited by 29
Cited by12
Results whose statement or proof uses this declaration.
- Finset.Nonempty.imageproof · cited by 25
- Finset.Nonempty.of_imageproof · cited by 12
- Finset.neg_nonempty_iffproof · cited by 4
- Finset.ciSup_mem_imageproof · cited by 4
- Finset.ciInf_mem_imageproof · cited by 3
- Finset.inv_nonempty_iffproof · cited by 2
- Finset.ciInf_eq_min'_imageproof · cited by 1
- finrank_vectorSpan_image_finset_leproof · cited by 1
- HallMarriageTheorem.hall_cond_of_eraseproof · cited by 1
- Finset.smul_finset_nonemptyproof · cited by 0
- Finset.vadd_finset_nonemptyproof · cited by 0
- IsAlgClosed.of_denseRangeproof · cited by 0