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Blockchains operating at the global scale demand high-performance byzantine fault-tolerant (BFT) consensus protocols. Most classic PBFT-like protocols suffer from an issue known as the leader bottleneck, which severely limits their throughput and resource utilization. Recently, Directed Acyclic Graph, or DAG-based protocols, have emerged as a promising approach for eliminating the leader bottleneck and achieving better performance. They attain higher throughput by separating data dissemination and block ordering. However, their safety and liveness logic is also significantly more elaborate. So far, most DAG-based protocols have only enjoyed on-paper security proofs, and it is not clear how to construct formal proofs of these protocols efficiently. We introduce LiDO-DAG, a concurrent object model that abstracts the common logic of these protocols. LiDO-DAG is constructed by combining a DAG abstraction and LiDO, a recently proposed abstraction for leader-based consensus. To demonstrate that our framework enables rapid validation of new DAG-based protocol designs, we implemented LiDO-DAG in Coq and applied it to three recent DAG-based protocols, including Narwhal, Bullshark, and Sailfish. Our framework readily yields mechanized safety and liveness proofs for all three protocols, which are also the first mechanized liveness proofs of any DAG-based protocol. Our framework has also revealed an optimization for Sailfish that improves its worst-case latency.