Theorems · Theorem · group theory
Set.mem_inv_smul_set_iff
∀ {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⁻¹ • A ↔ a • x ∈ A- Cited by
- 12 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses propext, Quot.sound
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
- Groupstatement and proof · cited by 6,238
- MulActionstatement and proof · cited by 1,294
- Set.smulSetstatement · cited by 608
Cited by12
Results whose statement or proof uses this declaration.
- Set.mem_inv_smul_set_iff₀proof · cited by 13
- MulAction.set_mem_fixedBy_of_movedBy_subsetproof · cited by 1
- smul_singleton_mem_nhds_of_sigmaCompactproof · cited by 1
- Subgroup.mem_inv_pointwise_smul_iffproof · cited by 1
- AddSubmonoid.mem_inv_pointwise_smul_iffproof · cited by 0
- ValuationSubring.mem_inv_pointwise_smul_iffproof · cited by 0
- Subring.mem_inv_pointwise_smul_iffproof · cited by 0
- Set.mem_invOf_smul_setproof · cited by 0
- MulAction.set_mem_fixedBy_of_subset_fixedByproof · cited by 0
- Subsemiring.mem_inv_pointwise_smul_iffproof · cited by 0
- AddSubgroup.mem_inv_pointwise_smul_iffproof · cited by 0
- Submonoid.mem_inv_pointwise_smul_iffproof · cited by 0