Theorems · Theorem · group theory
Set.mul_mem_mul
∀ {α : Type u_2} [inst : Mul α] {s t : Set α} {a b : α}, a ∈ s → b ∈ t → a * b ∈ s * t- Cited by
- 22 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
- Assumes
- Mul
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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
- Set.mulstatement · cited by 297
- Set.mem_image2_of_memproof · cited by 40
Cited by22
Results whose statement or proof uses this declaration.
- Subgroup.coe_mul_of_left_le_normalizer_rightproof · cited by 2
- SemigroupIdeal.coe_closureproof · cited by 2
- Set.list_prod_mem_list_prodproof · cited by 1
- GroupWithZero.isOpen_singleton_zeroproof · cited by 1
- JoinedIn.mulproof · cited by 1
- Set.Nontrivial.mul_leftproof · cited by 1
- Set.MapsTo.mulproof · cited by 1
- Subgroup.closure_mul_image_mul_eq_topproof · cited by 1
- closure_subset_mul_left_of_mem_nhds_one_of_invproof · cited by 1
- AddSubmonoid.closure_mul_closureproof · cited by 1
- closure_subset_mul_right_of_mem_nhds_one_of_invproof · cited by 1
- MeasureTheory.Measure.measure_isHaarMeasure_eq_smul_of_isEverywherePosproof · cited by 1