Two incompatible congruences

Proved

WorkbookSource.plus_7450

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

lean-workbooksource-checked

Prove that there are no solutions for x satisfying $x \equiv 4 \pmod{9}$ and $x \equiv 5 \pmod{12}$ .

Source: InternLM Lean-Workbook, record lean_workbook_plus_7450 (Apache-2.0). The complete source proposition and its explicit variable declarations are preserved.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_7450 : ¬ (∃ x : ℕ, x ≡ 4 [ZMOD 9] ∧ x ≡ 5 [ZMOD 12])   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_7450; Apache-2.0

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