Impredicative encodings of W-types and M-types are proven to satisfy the eta rules and induction and coinduction, extending AFS18.
Inductive Definitions in the system Coq - Rules and Properties
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Master Thesis Impredicative Encodings of Inductive and Coinductive Types
Impredicative encodings of W-types and M-types are proven to satisfy the eta rules and induction and coinduction, extending AFS18.