Prove2Me

`BookProof.ChapterF6.mgT_le_apply_add_mgD` (k : ℕ) (T : α →₀ ℕ) (s : List α) (y : α) : T y + s.count y ≤ (mgT k T s) y + mgD k T s

Proved
BookProof.ChapterF6.mgT_le_apply_add_mgD

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterF6.

BookProof.ChapterF6.mgT_le_apply_add_mgD (k : ℕ) (T : α →₀ ℕ) (s : List α) (y : α) : T y + s.count y ≤ (mgT k T s) y + mgD k T s

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

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


open scoped BigOperators


variable {α : Type*} [DecidableEq α]
Formal statement
theorem BookProof.ChapterF6.mgT_le_apply_add_mgD (k : ℕ) (T : α →₀ ℕ) (s : List α) (y : α) :
    T y + s.count y ≤ (mgT k T s) y + mgD k T s := by sorry

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