Theorems · Theorem · group theory
Set.add_mem_add
∀ {α : Type u_2} [inst : Add α] {s t : Set α} {a b : α}, a ∈ s → b ∈ t → a + b ∈ s + t- Cited by
- 30 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
- Assumes
- Add
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.addstatement · cited by 338
- Set.mem_image2_of_memproof · cited by 40
Cited by30
Results whose statement or proof uses this declaration.
- gauge_add_leproof · cited by 4
- Convex.combo_interior_closure_mem_interiorproof · cited by 3
- AddSubgroup.coe_add_of_left_le_normalizer_rightproof · cited by 2
- Convex.combo_closure_interior_mem_interiorproof · cited by 2
- StrictConvex.addproof · cited by 2
- AddSemigroupIdeal.coe_closureproof · cited by 2
- Set.MapsTo.addproof · cited by 1
- IsPathConnected.addproof · cited by 1
- Set.Nontrivial.add_leftproof · cited by 1
- IsTopologicalAddGroup.exist_openAddSubgroup_sub_clopen_nhds_of_zeroproof · cited by 1
- Set.list_sum_mem_list_sumproof · cited by 1
- JoinedIn.addproof · cited by 1