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Theorems · Theorem · group theory

AddCommute.nsmul_left

∀ {M : Type u_2} [inst : AddMonoid M] {a b : M}, AddCommute a b → ∀ (n : ℕ), AddCommute (n • a) b
Defined in
Mathlib.Algebra.Group.Commute.Defs
Cited by
3 results in Mathlib
Foundations
Depth 12 from the axioms · uses no axioms
Assumes
AddMonoid
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Around this declaration

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

AddCommute.nsmul_nsmul · cited by 4AddCommute.nsmul_nsmulAddCommute.addOrderOf_dvd_lcm_add · cited by 1AddCommute.addOrderOf_dvd…AddCommute.nsmul_self · cited by 0AddCommute.nsmul_selfAddMonoid · cited by 2864AddMonoidAddCommute · cited by 185AddCommuteAddCommute.symm · cited by 18AddCommute.symmAddCommute.nsmul_right · cited by 4AddCommute.nsmul_rightAddCommute.nsmul_leftCITED BYCITES

Cites4

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

Cited by3

Results whose statement or proof uses this declaration.