`BookProof.ChapterF6.mgStep_apply_le` (k : ℕ) (T : α →₀ ℕ) (x y : α) : (mgStep k T x) y ≤ T y + (if y = x then 1 else 0)

Proved

BookProof.ChapterF6.mgStep_apply_le

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterF6.

BookProof.ChapterF6.mgStep_apply_le (k : ℕ) (T : α →₀ ℕ) (x y : α) : (mgStep k T x) y ≤ T y + (if y = x then 1 else 0)

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

Preamble

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


open scoped BigOperators


variable {α : Type*} [DecidableEq α]

Formal statement

theorem BookProof.ChapterF6.mgStep_apply_le (k : ℕ) (T : α →₀ ℕ) (x y : α) :
    (mgStep k T x) y ≤ T y + (if y = x then 1 else 0) := by sorry

View graph