`BookProof.ChapterF4.mgStep_support_le` (k : ℕ) (st : (ι → ℕ) × ℕ) (x : ι) (h : mgSupport st.1 ≤ k) : mgSupport (mgStep k st x).1 ≤ k

Proved

BookProof.ChapterF4.mgStep_support_le

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterF4.

BookProof.ChapterF4.mgStep_support_le (k : ℕ) (st : (ι → ℕ) × ℕ) (x : ι) (h : mgSupport st.1 ≤ k) : mgSupport (mgStep k st x).1 ≤ k

Formalization note: Lean 4 identifier BookProof.ChapterF4.mgStep_support_le.

Preamble

-- Generated from ChapterF4.lean — theorem BookProof.ChapterF4.mgStep_support_le
import Mathlib
import Definitions.Def_ChapterF4
import Definitions.Def_ChapterF6
open BookProof.ChapterF6
open BookProof.ChapterF4


open scoped BigOperators Matrix

variable {d k : ℕ}
variable {A : Type*} [NormedRing A] [NormedAlgebra ℂ A] [StarRing A] [ContinuousStar A]
  [CompleteSpace A] [StarModule ℂ A]
variable {α κ Ω : Type*} [Fintype α] [DecidableEq α] [Fintype κ] [DecidableEq κ]
  {mΩ : MeasurableSpace Ω}
variable {ι : Type*} [Fintype ι] [DecidableEq ι]

Formal statement

theorem BookProof.ChapterF4.mgStep_support_le (k : ℕ) (st : (ι → ℕ) × ℕ) (x : ι)
    (h : mgSupport st.1 ≤ k) : mgSupport (mgStep k st x).1 ≤ k := by sorry

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