Theorems · Theorem · group theory
nsmulAddMonoidHom_apply
∀ {α : Type u_1} [inst : AddCommMonoid α] (n : ℕ) (x : α), (nsmulAddMonoidHom n) x = n • x- Defined in
- Mathlib.Algebra.Group.Hom.Basic
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext
- Assumes
- AddCommMonoid
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.
- DFunLike.coestatement and proof · cited by 62,936
- AddCommMonoidstatement and proof · cited by 12,281
- AddMonoidHomstatement · cited by 3,230
- nsmulAddMonoidHomstatement and proof · cited by 24
Cited by9
Results whose statement or proof uses this declaration.
- AddCommGroup.isAddTorsion_quotient_range_nsmulAddMonoidHomproof · cited by 2
- AddCircle.isAddQuotientCoveringMap_nsmulproof · cited by 1
- AddEquiv.map_range_nsmulAddMonoidHomproof · cited by 1
- Int.range_nsmulAddMonoidHomproof · cited by 1
- AddSubgroup.isFiniteRelIndex_map_nsmulAddMonoidHom_of_fgproof · cited by 1
- AddSubgroup.addSubgroupOf_map_nsmulAddMonoidHom_eq_rangeproof · cited by 1
- IsAddCyclic.card_nsmulAddMonoidHom_rangeproof · cited by 1
- AddSubgroup.nsmulAddMonoidHom_injective_of_isTorsionFreeproof · cited by 0
- Submodule.isFiniteRelIndex_of_map_linearMapMulLeft_leproof · cited by 0