`BookProof.ChapterA3.hasDerivAt_det_line` (A : Matrix (Fin n) (Fin n) ℝ) : HasDerivAt (fun t : ℝ => (1 + t • A).det) A.trace 0

Proved

BookProof.ChapterA3.hasDerivAt_det_line

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterA3f.

BookProof.ChapterA3.hasDerivAt_det_line (A : Matrix (Fin n) (Fin n) ℝ) : HasDerivAt (fun t : ℝ => (1 + t • A).det) A.trace 0

Formalization note: Lean 4 identifier BookProof.ChapterA3.hasDerivAt_det_line.

Preamble

-- Generated from ChapterA3f.lean — theorem BookProof.ChapterA3.hasDerivAt_det_line
import Mathlib
import Definitions.Def_ChapterA3f
import Definitions.Def_ChapterA3
open BookProof.ChapterA3


open Matrix NormedSpace
open scoped Norms.Operator


variable {n : ℕ}

Formal statement

theorem BookProof.ChapterA3.hasDerivAt_det_line (A : Matrix (Fin n) (Fin n) ℝ) :
    HasDerivAt (fun t : ℝ => (1 + t • A).det) A.trace 0 := by sorry

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