`BookProof.ChapterF6.mgD_cons` (k : ℕ) (T : α →₀ ℕ) (x : α) (xs : List α) : mgD k T (x :: xs) = (if 0 < T x ∨ T.support.card < k then 0 else 1) + mgD k (mgStep k T x) xs

Proved

BookProof.ChapterF6.mgD_cons

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterF6.

BookProof.ChapterF6.mgD_cons (k : ℕ) (T : α →₀ ℕ) (x : α) (xs : List α) : mgD k T (x :: xs) = (if 0 < T x ∨ T.support.card < k then 0 else 1) + mgD k (mgStep k T x) xs

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

Preamble

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


open scoped BigOperators


variable {α : Type*} [DecidableEq α]

Formal statement

theorem BookProof.ChapterF6.mgD_cons (k : ℕ) (T : α →₀ ℕ) (x : α) (xs : List α) :
    mgD k T (x :: xs) =
      (if 0 < T x ∨ T.support.card < k then 0 else 1) + mgD k (mgStep k T x) xs := by sorry

View graph