`BookProof.ChapterPauliGrover.pauliX_parametrizes_delta` (y : Fin 2) : ‖pauliX y 0‖ ^ 2 = (if y = 1 then 1 else 0 : ℝ)

Proved

BookProof.ChapterPauliGrover.pauliX_parametrizes_delta

by leonardopedro · Oct 10, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterPauliGrover.

BookProof.ChapterPauliGrover.pauliX_parametrizes_delta (y : Fin 2) : ‖pauliX y 0‖ ^ 2 = (if y = 1 then 1 else 0 : ℝ)

Formalization note: Lean 4 identifier BookProof.ChapterPauliGrover.pauliX_parametrizes_delta.

Preamble

-- Generated from ChapterPauliGrover.lean — theorem BookProof.ChapterPauliGrover.pauliX_parametrizes_delta
import Definitions.Def_ChapterConditional
import Mathlib
import Definitions.Def_ChapterPauliGrover
open BookProof.ChapterPauliGrover


open scoped BigOperators Matrix ComplexConjugate
open Matrix
open BookProof.ChapterConditional

Formal statement

theorem BookProof.ChapterPauliGrover.pauliX_parametrizes_delta (y : Fin 2) :
    ‖pauliX y 0‖ ^ 2 = (if y = 1 then 1 else 0 : ℝ) := by sorry

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