Lemma 22.28.4. Let $R$ be a ring. Let $(A, \text{d})$ and $(B, \text{d})$ be differential graded $R$-algebras. Let $M$ be a differential graded $(A, B)$-bimodule. There exists a homomorphism $P \to M$ of differential graded $(A, B)$-bimodules which is a quasi-isomorphism such that $P$ has property (P) as defined above.

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