`BookProof.ChapterF8.online_cost_independent_of_M` (M M' d m K₂ k : ℕ) : totalCost M d m K₂ k + offlineCost M' d k = totalCost M' d m K₂ k + offlineCost M d k

Proved

BookProof.ChapterF8.online_cost_independent_of_M

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterF8.

BookProof.ChapterF8.online_cost_independent_of_M (M M' d m K₂ k : ℕ) : totalCost M d m K₂ k + offlineCost M' d k = totalCost M' d m K₂ k + offlineCost M d k

Formalization note: Lean 4 identifier BookProof.ChapterF8.online_cost_independent_of_M.

Preamble

-- Generated from ChapterF8.lean — theorem BookProof.ChapterF8.online_cost_independent_of_M
import Mathlib
import Definitions.Def_ChapterF8
open BookProof.ChapterF8


noncomputable section

open scoped BigOperators

Formal statement

theorem BookProof.ChapterF8.online_cost_independent_of_M (M M' d m K₂ k : ℕ) :
    totalCost M d m K₂ k + offlineCost M' d k
      = totalCost M' d m K₂ k + offlineCost M d k := by sorry

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