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Theorems · Theorem · group theory

MulActionWithZero.zero_smul

∀ {M₀ : Type u_2} {A : Type u_7} {inst : MonoidWithZero M₀} {inst_1 : Zero A} [self : MulActionWithZero M₀ A] (m : A),
  0 • m = 0

Scalar multiplication by the scalar 0 is 0.

Defined in
Mathlib.Algebra.GroupWithZero.Action.Defs
Cited by
2 results in Mathlib
Foundations
Depth 6 from the axioms · uses no axioms
Assumes
MulActionWithZero
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Around this declaration

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MulActionWithZero.subsingleton · cited by 3MulActionWithZero.subsing…IsSMulRegular.subsingleton · cited by 1IsSMulRegular.subsingletonMonoidWithZero · cited by 456MonoidWithZeroMulActionWithZero · cited by 79MulActionWithZeroMulActionWithZero.zero_smulCITED BYCITES

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Cited by2

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