Checklist

Do the main claims made in the abstract and introduction accurately reflect the paper's Did you describe the limitations of your work? Did you discuss any potential negative societal impacts of your work? Did you include the code, data, and instructions needed to reproduce the main experimental results (either in the supplemental material or as a URL)? [No] (b) Did you specify all the training details (e.g., data splits, hyperparameters, how they Did you report error bars (e.g., with respect to the random seed after running experiments multiple times)? Did you include the total amount of compute and the type of resources used (e.g., type Did you include any new assets either in the supplemental material or as a URL? [N/A] Did you discuss whether and how consent was obtained from people whose data you're We start with a lemma that we will repeatedly use in the proofs. If has only one infoset, then Lemma 11 applies.