Prove2Me

`BookProof.AbelianDiagonal.diagonalStarAlgHom_injective` : Function.Injective (diagonalStarAlgHom : (n → ℂ) →⋆ₐ[ℂ] Matrix n n ℂ)

Proved
BookProof.AbelianDiagonal.diagonalStarAlgHom_injective

by leonardopedro · Oct 7, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterAbelianDiagonal.

BookProof.AbelianDiagonal.diagonalStarAlgHom_injective : Function.Injective (diagonalStarAlgHom : (n → ℂ) →⋆ₐ[ℂ] Matrix n n ℂ)

Formalization note: Lean 4 identifier BookProof.AbelianDiagonal.diagonalStarAlgHom_injective.

Preamble
-- Generated from ChapterAbelianDiagonal.lean — theorem BookProof.AbelianDiagonal.diagonalStarAlgHom_injective
import Mathlib
import Definitions.Def_ChapterAbelianDiagonal
open BookProof.AbelianDiagonal



open Matrix

variable {n : Type*} [Fintype n] [DecidableEq n]
Formal statement
theorem BookProof.AbelianDiagonal.diagonalStarAlgHom_injective :
    Function.Injective (diagonalStarAlgHom : (n → ℂ) →⋆ₐ[ℂ] Matrix n n ℂ) := by sorry

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