`BookProof.ChapterCollapseDiagonal.trace_diag_nullDiag_zero` (ρ O : Matrix (Fin n) (Fin n) ℂ) (hρ : IsDiagonal ρ) (hO : ∀ i, O i i = 0) : (ρ * O).trace = 0

Proved

BookProof.ChapterCollapseDiagonal.trace_diag_nullDiag_zero

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterCollapseDiagonal.

BookProof.ChapterCollapseDiagonal.trace_diag_nullDiag_zero (ρ O : Matrix (Fin n) (Fin n) ℂ) (hρ : IsDiagonal ρ) (hO : ∀ i, O i i = 0) : (ρ * O).trace = 0

Formalization note: Lean 4 identifier BookProof.ChapterCollapseDiagonal.trace_diag_nullDiag_zero.

Preamble

-- Generated from ChapterCollapseDiagonal.lean — theorem BookProof.ChapterCollapseDiagonal.trace_diag_nullDiag_zero
import Mathlib
import Definitions.Def_ChapterCollapseDiagonal
open BookProof.ChapterCollapseDiagonal


open scoped BigOperators
open Matrix


variable {n : ℕ}

Formal statement

theorem BookProof.ChapterCollapseDiagonal.trace_diag_nullDiag_zero (ρ O : Matrix (Fin n) (Fin n) ℂ)
    (hρ : IsDiagonal ρ) (hO : ∀ i, O i i = 0) :
    (ρ * O).trace = 0 := by sorry

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