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Polymorphism: add a comment about the infamous quantifier-ordering issue with induction

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Adam Chlipala 2017-02-15 10:01:49 -05:00
parent cf4d06c222
commit 643d44e524
1 changed files with 7 additions and 0 deletions
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7
Polymorphism.v
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@ -189,6 +189,13 @@ Proof.
equality. equality.
Qed. Qed.
(* IMPORTANT NOTE: the proof above would *not* have worked with the orders of
* variables [ls] and [acc] swapped in the lemma statement! Try the proof that
* way to see what goes wrong. The problem is that the induction hypothesis
* would be too weak. A single [acc] value would be fixed for the whole proof,
* while we need [acc] to *vary* throughout the induction, by retaining a
* universal quantifier for it in the IH. *)
(* Concatenating the empty list has no effect. *) (* Concatenating the empty list has no effect. *)
Lemma app_nil : forall A (ls : list A), Lemma app_nil : forall A (ls : list A),
ls ++ [] = ls. ls ++ [] = ls.