Failures and slowdowns compared to intuition
While trying to port a bunch of code to use itauto instead of intuition, we found these strange failures and a slowdown. I did some workarounds for now, but would be grateful for an analysis if these are fundamental limitations or could be fixed in the future.
Require Import Cdcl.Itauto. Require Import List. Goal forall A (s1 s2 s : list A), (forall x : A, In x s1 \/ In x s2 -> In x s) <-> (forall x : A, In x s1 -> In x s) /\ (forall x : A, In x s2 -> In x s). Proof. Fail itauto auto. intuition auto. Qed. Goal forall A B (f : A -> option B) (l : list B) v0, f v0 = None \/ (forall m : B, f v0 = Some m -> In m l) -> forall m : B, f v0 = Some m -> In m l. Proof. Fail itauto congruence. intuition congruence. Qed. Goal forall A a a0 (r l l' : list A), (In a l' <-> In a l /\ ~ In a r) -> ~ (~ In a0 r) -> In a l' <-> (a = a0 \/ In a l) /\ ~ In a r. Proof. (* Loops: itauto auto. *) (* Slow: Time itauto congruence. *) Time split; itauto congruence. Qed.