Mathlib Map

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
Assumes
DivInvMonoidSMulIsScalarTower

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.

Cited by2

Results whose statement or proof uses this declaration.