Theorems · Theorem · group theory
Set.subset_smul_set_iff
∀ {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⁻¹ • A ⊆ B- Cited by
- 13 results in Mathlib
- Foundations
- Depth 16 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
- Equiv.image_eq_preimage_symmproof · cited by 64
- MulAction.toPermproof · cited by 30
Cited by13
Results whose statement or proof uses this declaration.
- Set.subset_smul_set_iff₀proof · cited by 8
- Finset.subset_smul_finset_iffproof · cited by 2
- Equiv.Perm.swap_mem_stabilizerproof · cited by 2
- Equiv.Perm.exists_mem_stabilizer_isThreeCycle_of_two_lt_ncardproof · cited by 1
- MulAction.isInvariantBlock_iff_isFixedBlockproof · cited by 1
- Subgroup.subset_pointwise_smul_iffproof · cited by 1
- AddSubgroup.le_pointwise_smul_iffproof · cited by 0
- ValuationSubring.subset_pointwise_smul_iffproof · cited by 0
- Subring.subset_pointwise_smul_iffproof · cited by 0
- isApproximateSubgroup_oneproof · cited by 0
- Submonoid.subset_pointwise_smul_iffproof · cited by 0
- AddSubmonoid.le_pointwise_smul_iffproof · cited by 0