Theorems · Theorem · group theory
Set.smul_set_subset_iff_subset_inv_smul_set
∀ {α : Type u_2} {β : Type u_3} [inst : Group α] [inst_1 : MulAction α β] {A B : Set β} {a : α}, a • A ⊆ B ↔ A ⊆ a⁻¹ • B- Cited by
- 9 results in Mathlib
- Foundations
- Depth 15 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.
- Setstatement and proof · cited by 53,352
- Groupstatement and proof · cited by 6,238
- Set.preimageproof · cited by 4,946
- MulActionstatement and proof · cited by 1,294
- Set.smulSetstatement · cited by 608
- Set.image_subset_iffproof · cited by 203
- MulAction.toPermproof · cited by 30
- Equiv.image_symm_eq_preimageproof · cited by 17
Cited by9
Results whose statement or proof uses this declaration.
- Set.smul_set_subset_iff₀proof · cited by 6
- Subgroup.pointwise_smul_subset_iffproof · cited by 1
- Finset.smul_finset_subset_iffproof · cited by 1
- ValuationSubring.pointwise_smul_subset_iffproof · cited by 0
- Subring.pointwise_smul_subset_iffproof · cited by 0
- AddSubgroup.pointwise_smul_le_iffproof · cited by 0
- AddSubmonoid.pointwise_smul_le_iffproof · cited by 0
- Submonoid.pointwise_smul_subset_iffproof · cited by 0
- Subsemiring.pointwise_smul_subset_iffproof · cited by 0