Theorems · Theorem · group theory
Commute.mul_left
∀ {S : Type u_3} [inst : Semigroup S] {a b c : S}, Commute a c → Commute b c → Commute (a * b) cIf both a and b commute with c, then their product commutes with c.
- Defined in
- Mathlib.Algebra.Group.Commute.Defs
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
- Assumes
- Semigroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Commutestatement and proof · cited by 639
- Semigroupstatement and proof · cited by 202
- SemiconjBy.mul_leftproof · cited by 5
Cited by5
Results whose statement or proof uses this declaration.
- Module.End.IsSemisimple.of_mem_adjoin_pairproof · cited by 3
- Commute.cfcHomproof · cited by 2
- Commute.cfcₙHomproof · cited by 2
- Commute.div_leftproof · cited by 2
- Finset.noncommProd_mul_distrib_auxproof · cited by 1