Theorems · Theorem · group theory
smul_div_assoc
∀ {α : Type u_5} {β : Type u_6} [inst : DivInvMonoid β] [inst_1 : SMul α β] [IsScalarTower α β β] (r : α) (x y : β),
r • x / y = r • (x / y)Note that the IsScalarTower α β β typeclass argument is usually satisfied by Algebra α β.
- Defined in
- Mathlib.Algebra.Group.Action.Defs
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses propext
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.
- IsScalarTowerstatement and proof · cited by 3,896
- div_eq_mul_invproof · cited by 715
- DivInvMonoidstatement and proof · cited by 103
- smul_mul_assocproof · cited by 77
Cited by2
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.haarScalarFactor_smulproof · cited by 1
- MeasureTheory.Measure.addHaarScalarFactor_smulproof · cited by 1