Every person, firm or corporation, which shall furnish to any general contractor or to any subcontractor mentioned in sections one and two of this article, any materials, machinery or other equipment or supplies necessary to the completion of any building or other structure mentioned in this article, or improvement appurtenant thereto, for use in the erection, construction, repair or removal thereof, by virtue of a contract between such general contractor or subcontractor and the materialman or furnisher of machinery, or other supplies or equipment necessary to the completion of such general contract, shall have such a lien for his compensation as is mentioned in section one of this article.