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Theorems · Theorem · group theory

Commute.mul_right

∀ {S : Type u_3} [inst : Semigroup S] {a b c : S}, Commute a b → Commute a c → Commute a (b * c)

If a commutes with both b and c, then it commutes with their product.

Defined in
Mathlib.Algebra.Group.Commute.Defs
Cited by
5 results in Mathlib
Foundations
Depth 7 from the axioms · uses no axioms
Assumes
Semigroup
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Around this declaration

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

Commute.list_prod_right · cited by 2Commute.list_prod_rightAlgebra.commute_of_mem_adjoin_of_forall_mem_commute · cited by 1Algebra.commute_of_mem_ad…Finset.noncommProd_mul_distrib_aux · cited by 1Finset.noncommProd_mul_di…Commute.orderOf_dvd_lcm_mul · cited by 1Commute.orderOf_dvd_lcm_m…MonoidHom.commute_noncommPiCoprod · cited by 0MonoidHom.commute_noncomm…Commute · cited by 639CommuteSemigroup · cited by 202SemigroupSemiconjBy.mul_right · cited by 5SemiconjBy.mul_rightCommute.mul_rightCITED BYCITES

Cites3

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Cited by5

Results whose statement or proof uses this declaration.