`BookProof.ChapterCPTHamiltonian.kinSum_sq` (k : Fin 3 → ℝ) : (∑ j : Fin 3, (k j : ℂ) • Kin j) * (∑ j : Fin 3, (k j : ℂ) • Kin j) = (∑ j : Fin 3, (k j : ℂ) ^ 2) • (1 :...

Proved

BookProof.ChapterCPTHamiltonian.kinSum_sq

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterCPTHamiltonian.

BookProof.ChapterCPTHamiltonian.kinSum_sq (k : Fin 3 → ℝ) : (∑ j : Fin 3, (k j : ℂ) • Kin j) * (∑ j : Fin 3, (k j : ℂ) • Kin j) = (∑ j : Fin 3, (k j : ℂ) ^ 2) • (1 : Matrix (Fin 4) (Fin 4) ℂ)

Formalization note: Lean 4 identifier BookProof.ChapterCPTHamiltonian.kinSum_sq.

Preamble

-- Generated from ChapterCPTHamiltonian.lean — theorem BookProof.ChapterCPTHamiltonian.kinSum_sq
import Definitions.Def_ChapterA3
import Mathlib
import Definitions.Def_ChapterCPTHamiltonian
open BookProof.ChapterCPTHamiltonian


open Matrix


open BookProof.ChapterA3

Formal statement

theorem BookProof.ChapterCPTHamiltonian.kinSum_sq (k : Fin 3 → ℝ) :
    (∑ j : Fin 3, (k j : ℂ) • Kin j) * (∑ j : Fin 3, (k j : ℂ) • Kin j)
      = (∑ j : Fin 3, (k j : ℂ) ^ 2) • (1 : Matrix (Fin 4) (Fin 4) ℂ) := by sorry

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