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`BookProof.ChapterF6.mgSum_mapRange_pred` (T : α →₀ ℕ) : mgSum (T.mapRange (fun n => n - 1) (by norm_num)) = mgSum T - T.support.card

Proved
BookProof.ChapterF6.mgSum_mapRange_pred

by leonardopedro · Oct 8, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterF6.

BookProof.ChapterF6.mgSum_mapRange_pred (T : α →₀ ℕ) : mgSum (T.mapRange (fun n => n - 1) (by norm_num)) = mgSum T - T.support.card

Formalization note: Lean 4 identifier BookProof.ChapterF6.mgSum_mapRange_pred.

Preamble
-- Generated from ChapterF6.lean — theorem BookProof.ChapterF6.mgSum_mapRange_pred
import Mathlib
import Definitions.Def_ChapterF6
open BookProof.ChapterF6


open scoped BigOperators


variable {α : Type*} [DecidableEq α]
Formal statement
theorem BookProof.ChapterF6.mgSum_mapRange_pred (T : α →₀ ℕ) :
    mgSum (T.mapRange (fun n => n - 1) (by norm_num)) = mgSum T - T.support.card := by sorry

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