Theorems · Theorem · group theory
SMulCommClass.smul_comm
∀ {M : Type u_9} {N : Type u_10} {α : Type u_11} {inst : SMul M α} {inst_1 : SMul N α} [self : SMulCommClass M N α]
(m : M) (n : N) (a : α), m • n • a = n • m • a• is left commutative
- Defined in
- Mathlib.Algebra.Group.Action.Defs
- Cited by
- 143 results in Mathlib
- Foundations
- Depth 4 from the axioms, rests on 8 definitions · uses no axioms
- Assumes
- SMulCommClass
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SMulCommClassstatement and proof · cited by 1,927
Cited by144
Results whose statement or proof uses this declaration.
- SMulCommClass.symmproof · cited by 67
- mul_smul_commproof · cited by 65
- SMulCommClass.of_commMonoidproof · cited by 42
- Derivation.leibniz_powproof · cited by 10
- meromorphicOrderAt_smulproof · cited by 10
- MeromorphicAt.invproof · cited by 9
- smul_smul_smul_commproof · cited by 8
- Module.End.disjoint_genEigenspaceproof · cited by 7
- smul_algebraMapproof · cited by 7
- isBoundedBilinearMap_smulproof · cited by 5
- ConvexOn.smulproof · cited by 4
- SameRay.transproof · cited by 4