Theorems · Theorem · group theory
Set.smul_set_empty
∀ {α : Type u_2} {β : Type u_3} [inst : SMul α β] {a : α}, a • ∅ = ∅- Cited by
- 19 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SMul
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Set.smulSetstatement · cited by 608
- Set.image_emptyproof · cited by 73
Cited by19
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.addHaar_smulproof · cited by 13
- Real.sInf_smul_of_nonnegproof · cited by 3
- MulAction.IsBlock.emptyproof · cited by 1
- MulAction.IsBlock.of_subsetproof · cited by 1
- ediam_smul₀proof · cited by 1
- MulAction.IsBlock.smul_eq_smul_of_subsetproof · cited by 1
- MulAction.aestabilizer_emptyproof · cited by 1
- MulAction.stabilizer_emptyproof · cited by 1
- Real.sInf_smul_of_nonposproof · cited by 1
- closure_smul₀proof · cited by 1
- balanced_emptyproof · cited by 1
- Real.sSup_smul_of_nonnegproof · cited by 1