`BookProof.ChapterPvmMeasure.Pvm.norm_sq_nonneg` (E : Set X) (u : H) : 0 ≤ ‖P.p E u‖ ^ 2

Proved

BookProof.ChapterPvmMeasure.Pvm.norm_sq_nonneg

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterPvmMeasure.

BookProof.ChapterPvmMeasure.Pvm.norm_sq_nonneg (E : Set X) (u : H) : 0 ≤ ‖P.p E u‖ ^ 2

Formalization note: Lean 4 identifier BookProof.ChapterPvmMeasure.Pvm.norm_sq_nonneg.

Preamble

-- Generated from ChapterPvmMeasure.lean — theorem BookProof.ChapterPvmMeasure.Pvm.norm_sq_nonneg
import Mathlib
import Definitions.Def_ChapterPvmMeasure
open BookProof.ChapterPvmMeasure
open BookProof.ChapterPvmMeasure


open MeasureTheory
open scoped InnerProductSpace


variable {X : Type*} [MeasurableSpace X]
variable {H : Type*} [NormedAddCommGroup H] [InnerProductSpace ℂ H]

variable (P : Pvm X H)

Formal statement

theorem BookProof.ChapterPvmMeasure.Pvm.norm_sq_nonneg (E : Set X) (u : H) : 0 ≤ ‖P.p E u‖ ^ 2 := by sorry

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