Theorems · Theorem · ring theory

Unitary.smul_mem_of_mem

∀ {R : Type u_1} {A : Type u_2} [inst : Monoid R] [inst_1 : Monoid A] [inst_2 : MulAction R A] [SMulCommClass R A A]
  [IsScalarTower R A A] [inst_5 : StarMul R] [inst_6 : StarMul A] [StarModule R A] {r : R} {a : A},
  r ∈ unitary R → a ∈ unitary A → r • a ∈ unitary A

Defined in

Mathlib.Algebra.Star.Unitary

Cited by

1 results in Mathlib

Foundations

Depth 24 from the axioms · uses propext, Quot.sound

Assumes

MonoidMonoidMulActionSMulCommClassIsScalarTowerStarMulStarMulStarModule