diff options
Diffstat (limited to 'theories/Lists')
| -rw-r--r-- | theories/Lists/List.v | 19 |
1 files changed, 11 insertions, 8 deletions
diff --git a/theories/Lists/List.v b/theories/Lists/List.v index 6a1554d102..f050f11170 100644 --- a/theories/Lists/List.v +++ b/theories/Lists/List.v @@ -1413,13 +1413,16 @@ End Fold_Right_Recursor. Lemma existsb_exists : forall l, existsb l = true <-> exists x, In x l /\ f x = true. Proof. - induction l; simpl; intuition. - inversion H. - firstorder. - destruct (orb_prop _ _ H1); firstorder. - firstorder. - subst. - rewrite H2; auto. + induction l as [ | a m IH ]; split; simpl. + - easy. + - intros [x [[]]]. + - rewrite orb_true_iff; intros [ H | H ]. + + exists a; auto. + + rewrite IH in H; destruct H as [ x [ Hxm Hfx ] ]. + exists x; auto. + - intros [ x [ [ Hax | Hxm ] Hfx ] ]. + + now rewrite Hax, Hfx. + + destruct IH as [ _ -> ]; eauto with bool. Qed. Lemma existsb_nth : forall l n d, n < length l -> @@ -2747,7 +2750,7 @@ Section Exists_Forall. Proof. split. - induction 1; firstorder; subst; auto. - - induction l; firstorder. + - induction l; firstorder auto with datatypes. Qed. Lemma Forall_nth l : |