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Theorems · Theorem · group theory

AddMonoidHom.map_nsmul

∀ {M : Type u_4} {N : Type u_5} [inst : AddMonoid M] [inst_1 : AddMonoid N] (f : M →+ N) (n : ℕ) (a : M),
  f (n • a) = n • f a
Defined in
Mathlib.Algebra.Group.Hom.Defs
Cited by
18 results in Mathlib
Foundations
Depth 12 from the axioms · uses no axioms
Assumes
AddMonoidAddMonoid
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

AddMonoid.ext · cited by 7AddMonoid.extaddOrderOf_injective · cited by 5addOrderOf_injectiveMultiset.map_nsmul · cited by 4Multiset.map_nsmulMultiset.card_nsmul · cited by 3Multiset.card_nsmulIsAddTorsion.extension_closed · cited by 2IsAddTorsion.extension_cl…AddMonoidHom.isOfFinAddOrder · cited by 2AddMonoidHom.isOfFinAddOr…Circle.exp_nsmul · cited by 1Circle.exp_nsmulPi.single_nsmul · cited by 1Pi.single_nsmulnsmul_lie · cited by 1nsmul_lieFinsupp.toMultiset_map · cited by 1Finsupp.toMultiset_mapMultiset.nsmul_replicate · cited by 1Multiset.nsmul_replicateWithBot.coe_nsmul · cited by 1WithBot.coe_nsmulReal.Angle.natCast_mul_eq_nsmul · cited by 0Angle.natCast_mul_eq_nsmulCategoryTheory.Functor.map_nsmul · cited by 0Functor.map_nsmulNonneg.nsmul_coe · cited by 0Nonneg.nsmul_coeDFunLike.coe · cited by 62936DFunLike.coeAddMonoidHom · cited by 3230AddMonoidHomAddMonoid · cited by 2864AddMonoidmap_nsmul · cited by 41map_nsmulAddMonoidHom.map_nsmulCITED BYCITES

Cites4

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by18

Results whose statement or proof uses this declaration.