Theorems · Theorem · group theory
Set.smul_mem_smul_set_iff
∀ {α : Type u_2} {β : Type u_3} [inst : Group α] [inst_1 : MulAction α β] {s : Set β} {a : α} {x : β},
a • x ∈ a • s ↔ x ∈ s- Cited by
- 14 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
- Function.Injective.mem_set_imageproof · cited by 53
- MulAction.injectiveproof · cited by 24
Cited by14
Results whose statement or proof uses this declaration.
- Set.smul_mem_smul_set_iff₀proof · cited by 9
- MulAction.mem_stabilizer_setproof · cited by 1
- AffineSubspace.smul_mem_smul_iffproof · cited by 1
- MulAction.IsBlock.orbit_stabilizer_eqproof · cited by 1
- exists_smul_notMem_of_subset_orbit_closureproof · cited by 1
- MulAction.IsBlock.stabilizer_leproof · cited by 1
- ValuationSubring.smul_mem_pointwise_smul_iffproof · cited by 0
- Submonoid.smul_mem_pointwise_smul_iffproof · cited by 0
- Subring.smul_mem_pointwise_smul_iffproof · cited by 0
- Subgroup.smul_mem_pointwise_smul_iffproof · cited by 0
- DiscreteTiling.PlacedTile.smul_mem_smul_iffproof · cited by 0
- Subsemiring.smul_mem_pointwise_smul_iffproof · cited by 0