Theorems · Theorem · group theory
Set.mem_add
∀ {α : Type u_2} [inst : Add α] {s t : Set α} {a : α}, a ∈ s + t ↔ ∃ x ∈ s, ∃ y ∈ t, x + y = a- Cited by
- 25 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.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Cited by25
Results whose statement or proof uses this declaration.
- IsCompact.add_closedBall_zeroproof · cited by 5
- AddSubgroup.IsComplement.add_eqproof · cited by 5
- MeasureTheory.addHaar_image_le_mul_of_det_ltproof · cited by 4
- Set.mem_finsetSumproof · cited by 4
- Submodule.coe_supproof · cited by 3
- coe_add_coeproof · cited by 3
- Set.IsWF.min_addproof · cited by 3
- Set.mem_sum_list_ofFnproof · cited by 3
- AddSubmonoid.coe_supproof · cited by 2
- closure_subset_add_self_of_mem_nhds_zeroproof · cited by 2
- Set.add_univ_of_zero_memproof · cited by 2
- AddCommGroup.fg_of_descentproof · cited by 1