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Theorems · Theorem · group theory

mul_zsmul

∀ {α : Type u_1} [inst : SubtractionMonoid α] (a : α) (m n : ℤ), (m * n) • a = m • n • a
Defined in
Mathlib.Algebra.Group.Basic
Cited by
5 results in Mathlib
Foundations
Depth 17 from the axioms · uses propext
Assumes
SubtractionMonoid
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Around this declaration

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

Function.Antiperiodic.even_zsmul_periodic · cited by 2Antiperiodic.even_zsmul_p…zsmul_comm · cited by 1zsmul_commAddSubgroup.isLeast_of_closure_iff_eq_abs · cited by 0AddSubgroup.isLeast_of_cl…AddCommGroup.ModEq.zsmul · cited by 0ModEq.zsmulAddMonoidHom.map_addCyclic · cited by 0AddMonoidHom.map_addCyclicSubtractionMonoid · cited by 208SubtractionMonoidmul_zsmul' · cited by 16mul_zsmul'mul_zsmulCITED BYCITES

Cites2

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Cited by5

Results whose statement or proof uses this declaration.