Theorems · Theorem · group theory
Set.smul_set_inter
∀ {α : Type u_2} {β : Type u_3} [inst : Group α] [inst_1 : MulAction α β] {s t : Set β} {a : α},
a • (s ∩ t) = a • s ∩ a • t- Cited by
- 11 results in Mathlib
- Foundations
- Depth 59 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Groupstatement and proof · cited by 6,238
- MulActionstatement and proof · cited by 1,294
- Set.smulSetstatement · cited by 608
- Set.image_interproof · cited by 34
- MulAction.injectiveproof · cited by 24
Cited by11
Results whose statement or proof uses this declaration.
- MeasureTheory.IsFundamentalDomain.setLIntegral_eq_tsum'proof · cited by 2
- MeasureTheory.Measure.pairwise_aedisjoint_of_aedisjoint_forall_ne_oneproof · cited by 2
- MeasureTheory.IsFundamentalDomain.setIntegral_eq_tsum'proof · cited by 1
- MeasureTheory.measure_inter_inv_smulproof · cited by 1
- MeasureTheory.IsFundamentalDomain.aestronglyMeasurable_on_iffproof · cited by 1
- Set.exists_smul_inter_smul_subset_smul_inv_mul_inter_inv_mulproof · cited by 1
- Set.smul_set_inter₀proof · cited by 0
- MulAction.IsBlock.interproof · cited by 0
- MulAction.stabilizer_inf_stabilizer_le_stabilizer_interproof · cited by 0
- MeasureTheory.fundamentalFrontier_smulproof · cited by 0
- Set.OrdConnected.smulproof · cited by 0