Difference between two residue-class sums

Proved

WorkbookSyntax.plus_44891

by wamlart · Sep 12, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbookrepaired-notationsource-checked

Among positive integers at most2011, let $A$ be the sum of those congruent to1 modulo3 and $B$ the sum of those congruent to2 modulo3. Then $A-B=1341$ .

Notation repair: Replaced the obsolete finite-sum binder “in” with the current “∈” notation. The ranges, summands, hypotheses and conclusion are unchanged.

Source: Lean-Workbook record lean_workbook_plus_44891 (Apache-2.0). Original declaration.

Preamble

import Mathlib
open Nat

Formal statement

theorem WorkbookSyntax.plus_44891 (A B : ℕ) (hA : A = ∑ i ∈ Finset.filter (λ x => x % 3 = 1) (Finset.Icc 1 2011), i) (hB : B = ∑ i ∈ Finset.filter (λ x => x % 3 = 2) (Finset.Icc 1 2011), i) : A - B = 1341   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_44891; finite-sum notation repair; Apache-2.0

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