Theorems · Theorem · group theory
Set.smul_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 ⊆ a • B ↔ A ⊆ B- Cited by
- 10 results in Mathlib
- Foundations
- Depth 17 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
- MulAction.injectiveproof · cited by 24
- Set.image_subset_image_iffproof · cited by 13
Cited by10
Results whose statement or proof uses this declaration.
- Set.smul_set_subset_smul_set_iff₀proof · cited by 7
- Subgroup.pointwise_smul_le_pointwise_smul_iffproof · cited by 1
- Monoid.CoprodI.lift_word_ping_pongproof · cited by 1
- Subsemiring.pointwise_smul_le_pointwise_smul_iffproof · cited by 0
- ValuationSubring.pointwise_smul_le_pointwise_smul_iffproof · cited by 0
- Subring.pointwise_smul_le_pointwise_smul_iffproof · cited by 0
- AddSubgroup.pointwise_smul_le_pointwise_smul_iffproof · cited by 0
- AddSubmonoid.pointwise_smul_le_pointwise_smul_iffproof · cited by 0
- Submonoid.pointwise_smul_le_pointwise_smul_iffproof · cited by 0
- MulAction.smul_subset_of_set_mem_fixedByproof · cited by 0