Theorems · Theorem · group theory
AddMemClass.mk_add_mk
∀ {M : Type u_1} {A : Type u_3} [inst : Add M] [inst_1 : SetLike A M] [hA : AddMemClass A M] (S' : A) (x y : M)
(hx : x ∈ S') (hy : y ∈ S'), ⟨x, hx⟩ + ⟨y, hy⟩ = ⟨x + y, ⋯⟩- Defined in
- Mathlib.Algebra.Group.Subsemigroup.Defs
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
- Assumes
- AddSetLikeAddMemClass
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.
- SetLikestatement and proof · cited by 1,084
- AddMemClass.add_memstatement · cited by 229
- AddMemClassstatement and proof · cited by 17
Cited by2
Results whose statement or proof uses this declaration.
- LieAlgebra.Basis.baseSupp_apply_smul_eproof · cited by 3
- Module.Baer.ExtensionOfMaxAdjoin.extensionToFun_wdproof · cited by 1