Theorems · Theorem · ring theory
Algebra.left_comm
∀ {R : Type u} {A : Type w} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A] (x : A) (r : R)
(y : A), x * ((algebraMap R A) r * y) = (algebraMap R A) r * (x * y)mul_left_comm for Algebras when one element is from the base ring.
- Defined in
- Mathlib.Algebra.Algebra.Defs
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses no axioms
- Assumes
- CommSemiringSemiringAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement · cited by 10,189
- Algebra.algebraMapstatement and proof · cited by 4,706
- mul_assocproof · cited by 1,667
- Algebra.commutesproof · cited by 27
Cited by2
Results whose statement or proof uses this declaration.
- Algebra.mul_smul_commproof · cited by 24
- CliffordAlgebra.mul_ι_mul_ι_mul_commproof · cited by 1