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A sort of definitionally proof-irrelevant propositions introduced in "Definitional Proof-Irrelevance without K" and implemented by Agda (as Prop) and Coq (as SProp).

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Coq Induction on Hypothesis destroys the Hypothesis

The induction tactic tends to forget about the values of concrete arguments (e.g., nil on in_order_merge.) One possible fix is to use remember to convert the nil argument to a variable: Lemma iom_l_ni …
Joshua Gancher's user avatar