Theorems · Theorem · order theory
Set.image_nonempty
∀ {α : Type u_1} {β : Type u_2} {f : α → β} {s : Set α}, (f '' s).Nonempty ↔ s.Nonempty- Defined in
- Mathlib.Data.Set.Image
- Cited by
- 29 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
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.
- Setstatement and proof · cited by 53,352
- Set.imagestatement · cited by 5,609
- Set.Nonemptystatement and proof · cited by 2,627
- Set.Nonempty.imageproof · cited by 87
- Set.Nonempty.of_imageproof · cited by 4
Cited by29
Results whose statement or proof uses this declaration.
- IsConnected.imageproof · cited by 15
- Finset.image_nonemptyproof · cited by 12
- Finset.map_nonemptyproof · cited by 8
- Function.Surjective.nonempty_preimageproof · cited by 4
- rieszContentAux_image_nonemptyproof · cited by 3
- Archimedean.ratLt'_nonemptyproof · cited by 3
- Set.image_inter_nonempty_iffproof · cited by 3
- ConvexOn.leftDeriv_le_rightDeriv_of_mem_interiorproof · cited by 2
- MeasureTheory.Measure.inf_applyproof · cited by 2
- Set.smul_set_nonemptyproof · cited by 1
- Besicovitch.TauPackage.mem_iUnionUpTo_lastStepproof · cited by 1
- NumberField.mixedEmbedding.fundamentalCone.zero_mem_compactSetproof · cited by 1