. Proof, We prove by induction on ? that it is ?-well-formed. Hence, by Theorem 4.5.10, it is well-typed

@. Suppose and ?. , We have global_wf ? 0 = true, for all (u ? v) ? ?, rewrite_wf ? 0 (u ? v) and is_confluent ? = ext_true. By induction hypothesis, ? 0 is ?-well-formed. By soundness of rewrite_wf (Lemma 6.5.3), the rewrite rules in ? are weakly well-formed for ? 0 and are of Bibliography, 2014.

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