Theorems · Theorem · group theory
AddSubmonoidClass.mk_nsmul
∀ {M : Type u_5} [inst : AddMonoid M] {A : Type u_4} [inst_1 : SetLike A M] [inst_2 : AddSubmonoidClass A M] {S : A}
(x : M) (hx : x ∈ S) (n : ℕ), n • ⟨x, hx⟩ = ⟨n • x, ⋯⟩- Defined in
- Mathlib.Algebra.Group.Submonoid.Defs
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses no axioms
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.
- AddMonoidstatement and proof · cited by 2,864
- SetLikestatement and proof · cited by 1,084
- AddSubmonoidClassstatement and proof · cited by 346
- nsmul_memstatement · cited by 26
Cited by1
Results whose statement or proof uses this declaration.
- AddSubmonoid.nsmul_exponent_eq_zeroproof · cited by 1