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Theorems · Theorem · group theory

List.smul_sum

∀ {M : Type u_1} {N : Type u_2} [inst : AddMonoid N] [inst_1 : DistribSMul M N] {r : M} {l : List N},
  r • l.sum = (List.map (fun x => r • x) l).sum
Defined in
Mathlib.Algebra.BigOperators.GroupWithZero.Action
Cited by
3 results in Mathlib
Foundations
Depth 12 from the axioms · uses propext
Assumes
AddMonoidDistribSMul
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

PiTensorProduct.norm_eval_le_projectiveSeminorm · cited by 2PiTensorProduct.norm_eval…PiTensorProduct.lifts_smul · cited by 1PiTensorProduct.lifts_smulTrivSqZeroExt.snd_list_prod · cited by 0TrivSqZeroExt.snd_list_pr…AddMonoid · cited by 2864AddMonoidDistribSMul · cited by 117DistribSMulmap_list_sum · cited by 31map_list_sumDistribSMul.toAddMonoidHom · cited by 20DistribSMul.toAddMonoidHomList.smul_sumCITED BYCITES

Cites4

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Cited by3

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