`BookProof.ChapterA3.bilC_ext` {A B : Matrix (Fin 4) (Fin 4) ℂ} (hA : Aᵀ = A) (hB : Bᵀ = B) (h : ∀ x : Fin 4 → ℂ, bilC A x = bilC B x) : A = B

Proved

BookProof.ChapterA3.bilC_ext

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterA3h.

BookProof.ChapterA3.bilC_ext {A B : Matrix (Fin 4) (Fin 4) ℂ} (hA : Aᵀ = A) (hB : Bᵀ = B) (h : ∀ x : Fin 4 → ℂ, bilC A x = bilC B x) : A = B

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

Preamble

-- Generated from ChapterA3h.lean — theorem BookProof.ChapterA3.bilC_ext
import Mathlib
import Definitions.Def_ChapterA3h
import Definitions.Def_ChapterA3
open BookProof.ChapterA3


open Matrix
open scoped ComplexConjugate

Formal statement

theorem BookProof.ChapterA3.bilC_ext {A B : Matrix (Fin 4) (Fin 4) ℂ} (hA : Aᵀ = A) (hB : Bᵀ = B)
    (h : ∀ x : Fin 4 → ℂ, bilC A x = bilC B x) : A = B := by sorry

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