Theorems · Theorem · group theory
Set.mem_smul_set_iff_inv_smul_mem
∀ {α : Type u_2} {β : Type u_3} [inst : Group α] [inst_1 : MulAction α β] {A : Set β} {a : α} {x : β},
x ∈ a • A ↔ a⁻¹ • x ∈ A- Cited by
- 18 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Groupstatement and proof · cited by 6,238
- Set.imageproof · cited by 5,609
- MulActionstatement and proof · cited by 1,294
- Set.smulSetstatement · cited by 608
- MulAction.toPermproof · cited by 30
- Set.mem_image_equivproof · cited by 22
Cited by18
Results whose statement or proof uses this declaration.
- Set.mem_smul_set_iff_inv_smul_mem₀proof · cited by 28
- Subgroup.mem_pointwise_smul_iff_inv_smul_memproof · cited by 3
- SubMulAction.IsPretransitive.isPretransitive_ofFixingSubgroup_interproof · cited by 2
- MulAction.fixedBy_mem_fixedBy_of_commuteproof · cited by 2
- MulAction.IsBlock.of_subsetproof · cited by 1
- cauchy_davenport_minOrder_mulproof · cited by 1
- SpectrumRestricts.smul_of_nonnegproof · cited by 1
- MeasureTheory.IsFundamentalDomain.absolutelyContinuous_mapproof · cited by 1
- Set.conj_mem_fixingSubgroupproof · cited by 1
- MeasureTheory.IsFundamentalDomain.essSup_measure_restrictproof · cited by 1
- ProfiniteGrp.toLimitFun_continuousproof · cited by 0
- Submonoid.mem_pointwise_smul_iff_inv_smul_memproof · cited by 0