Documentation

Mathlib.Algebra.Star.Prod

Star on product types #

We put a Star structure on product types that operates elementwise.

instance Prod.instStarProd {R : Type u} {S : Type v} [Star R] [Star S] :
Star (R × S)
@[simp]
theorem Prod.fst_star {R : Type u} {S : Type v} [Star R] [Star S] (x : R × S) :
(star x).fst = star x.fst
@[simp]
theorem Prod.snd_star {R : Type u} {S : Type v} [Star R] [Star S] (x : R × S) :
(star x).snd = star x.snd
theorem Prod.star_def {R : Type u} {S : Type v} [Star R] [Star S] (x : R × S) :
star x = (star x.fst, star x.snd)
instance Prod.instStarMulProdInstMul {R : Type u} {S : Type v} [Mul R] [Mul S] [StarMul R] [StarMul S] :
StarMul (R × S)
instance Prod.instStarModuleProdInstStarProdSmul {R : Type u} {S : Type v} {α : Type w} [SMul α R] [SMul α S] [Star α] [Star R] [Star S] [StarModule α R] [StarModule α S] :
StarModule α (R × S)
theorem Units.embed_product_star {R : Type u} [Monoid R] [StarMul R] (u : Rˣ) :