Counting integers avoiding multiples of four and seven

Proved

WorkbookSource.problem_7649

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

lean-workbookrepaired-notationsource-checked

How many positive integers less than $100$ are not divisible by $4$ or $7$ ?

Source: InternLM Lean-Workbook, record lean_workbook_7649 (Apache-2.0). The complete source proposition and its explicit variable declarations are preserved. Notation repair: Update legacy finite-sum notation.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.problem_7649 : ∑ k ∈ Finset.filter (λ x => ¬ (4 ∣ x ∨ 7 ∣ x)) (Finset.range 100), 1 = 64  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_7649; Apache-2.0

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