Theorems · Theorem · group theory
mem_leftAddCoset
∀ {α : Type u_1} [inst : Add α] {s : Set α} {x : α} (a : α), x ∈ s → a + x ∈ a +ᵥ s- Defined in
- Mathlib.GroupTheory.Coset.Basic
- Cited by
- 4 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.
Cites4
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
- HVAdd.hVAddstatement · cited by 1,820
- Set.vaddSetstatement · cited by 403
- Set.mem_image_of_memproof · cited by 371
Cited by4
Results whose statement or proof uses this declaration.
- normal_of_eq_addCosetsproof · cited by 1
- mem_own_leftAddCosetproof · cited by 1
- ProfiniteGrp.closedAddSubgroup_eq_sInf_openproof · cited by 0