Theorems · Theorem · group theory
AddCommute.function_commute_add_left
∀ {G : Type u_1} [inst : AddSemigroup G] {a b : G}, AddCommute a b → Function.Commute (fun x => a + x) fun x => b + x- Defined in
- Mathlib.Algebra.Group.Commute.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses propext
- Assumes
- AddSemigroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- Function.Commutestatement · cited by 54
- AddSemiconjBy.function_semiconj_add_leftproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- AddCommute.addOrderOf_add_dvd_lcmproof · cited by 3
- AddCommute.addOrderOf_add_eq_mul_addOrderOf_of_coprimeproof · cited by 3