Theorems · Theorem · group theory
Set.smul_set_nonempty
∀ {α : Type u_2} {β : Type u_3} [inst : SMul α β] {s : Set β} {a : α}, (a • s).Nonempty ↔ s.Nonempty- Cited by
- 1 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
- Assumes
- SMul
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.Nonemptystatement · cited by 2,627
- Set.smulSetstatement · cited by 608
- Set.image_nonemptyproof · cited by 29
Cited by1
Results whose statement or proof uses this declaration.
- smul_singleton_mem_nhds_of_sigmaCompactproof · cited by 1