proposition: Lemma ifb : forall (P: bool -> Prop) (a b c:bool), P(if a then b else c) <-> ((a = true -> P b) /\ (a = false -> P c)).
proof: Proof. intros. destruct a ; intuition try congruence. Qed.
imports: Cdcl.Itauto Uint63 Bool ZArith Lia Coq.Lists.List Coq.ZArith.ZArith Coq.micromega.Lia Bool ZifyClasses Coq.ZArith.ZArith Coq.micromega.Lia Classical