Theorems · Theorem · group theory
AddCommute.add_left
∀ {S : Type u_3} [inst : AddSemigroup S] {a b c : S}, AddCommute a c → AddCommute b c → AddCommute (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
- 1 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
- Assumes
- AddSemigroup
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.
- AddCommutestatement and proof · cited by 185
- AddSemigroupstatement and proof · cited by 136
- AddSemiconjBy.add_leftproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Finset.noncommSum_add_distrib_auxproof · cited by 1