`BookProof.ChapterPvmMeasure.Pvm.add_of_disjoint` {E F : Set X} (hE : MeasurableSet E) (hF : MeasurableSet F) (hd : Disjoint E F) (u : H) : P.p (E ∪ F) u = P.p E u + P.p F u

Proved

BookProof.ChapterPvmMeasure.Pvm.add_of_disjoint

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterPvmMeasure.

BookProof.ChapterPvmMeasure.Pvm.add_of_disjoint {E F : Set X} (hE : MeasurableSet E) (hF : MeasurableSet F) (hd : Disjoint E F) (u : H) : P.p (E ∪ F) u = P.p E u + P.p F u

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

Preamble

-- Generated from ChapterPvmMeasure.lean — theorem BookProof.ChapterPvmMeasure.Pvm.add_of_disjoint
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.add_of_disjoint {E F : Set X} (hE : MeasurableSet E) (hF : MeasurableSet F)
    (hd : Disjoint E F) (u : H) : P.p (E ∪ F) u = P.p E u + P.p F u := by sorry

View graph