`BookProof.TempleSeparationNecessary.witness_apply` (M : ℝ) (x y : E2) : witness M x y = ((-M : ℝ) : ℂ) • (y - (inner ℂ x y : ℂ) • x)

Proved

BookProof.TempleSeparationNecessary.witness_apply

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterTempleSeparationNecessary.

BookProof.TempleSeparationNecessary.witness_apply (M : ℝ) (x y : E2) : witness M x y = ((-M : ℝ) : ℂ) • (y - (inner ℂ x y : ℂ) • x)

Formalization note: Lean 4 identifier BookProof.TempleSeparationNecessary.witness_apply.

Preamble

-- Generated from ChapterTempleSeparationNecessary.lean — theorem BookProof.TempleSeparationNecessary.witness_apply
import Definitions.Def_ChapterRitzCertificate
import Mathlib
import Definitions.Def_ChapterTempleSeparationNecessary
import Definitions.Def_ChapterNavierStokesFarisLavineLift
open BookProof.NavierStokesFlow.FarisLavineLift
open BookProof.NavierStokesFlow.FarisLavineLift.ComparisonData
open BookProof.TempleSeparationNecessary


noncomputable section


open BookProof.RitzCertificate

Formal statement

theorem BookProof.TempleSeparationNecessary.witness_apply (M : ℝ) (x y : E2) :
    witness M x y = ((-M : ℝ) : ℂ) • (y - (inner ℂ x y : ℂ) • x) := by sorry

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