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Theorems · Theorem · group theory

DistribSMul.smul_add

∀ {M : Type u_12} {A : Type u_13} {inst : AddZeroClass A} [self : DistribSMul M A] (a : M) (x y : A),
  a • (x + y) = a • x + a • y

Scalar multiplication distributes across addition

Defined in
Mathlib.Algebra.GroupWithZero.Action.Defs
Cited by
1 results in Mathlib
Foundations
Depth 4 from the axioms · uses no axioms
Assumes
DistribSMul
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Around this declaration

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smul_add · cited by 263smul_addDistribSMul.toAddMonoidHom · cited by 20DistribSMul.toAddMonoidHomAddZeroClass · cited by 1237AddZeroClassDistribSMul · cited by 117DistribSMulDistribSMul.smul_addCITED BYCITES

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