Theorems · Theorem · order theory
Set.Nonempty.image
∀ {α : Type u_1} {β : Type u_2} (f : α → β) {s : Set α}, s.Nonempty → (f '' s).Nonempty- Defined in
- Mathlib.Data.Set.Image
- Cited by
- 87 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
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.
- Setstatement and proof · cited by 53,352
- Set.imagestatement and proof · cited by 5,609
- Set.Nonemptystatement and proof · cited by 2,627
- Set.mem_image_of_memproof · cited by 371
Cited by87
Results whose statement or proof uses this declaration.
- Set.image_nonemptyproof · cited by 29
- IsCompact.exists_isMinOnproof · cited by 15
- IsIrreducible.imageproof · cited by 7
- IsGreatest.norm_cfcproof · cited by 6
- IsGreatest.norm_cfcₙproof · cited by 5
- Order.IsNormal.map_sSupproof · cited by 5
- MonotoneOn.map_csSup_of_continuousWithinAtproof · cited by 4
- Finset.sup'_eq_csSup_imageproof · cited by 4
- geometric_hahn_banach_openproof · cited by 4
- JacobsonSpace.of_isOpenEmbeddingproof · cited by 3
- IsCompact.sSup_lt_iff_of_continuousproof · cited by 3
- MonotoneOn.tendsto_nhdsLTproof · cited by 3