diff options
Diffstat (limited to 'theories/Sorting/Sorted.v')
| -rw-r--r-- | theories/Sorting/Sorted.v | 11 |
1 files changed, 7 insertions, 4 deletions
diff --git a/theories/Sorting/Sorted.v b/theories/Sorting/Sorted.v index 206eb606d2..422316d879 100644 --- a/theories/Sorting/Sorted.v +++ b/theories/Sorting/Sorted.v @@ -71,6 +71,7 @@ Section defs. (forall a l, Sorted l -> P l -> HdRel a l -> P (a :: l)) -> forall l:list A, Sorted l -> P l. Proof. + intros P ? ? l. induction l. firstorder using Sorted_inv. firstorder using Sorted_inv. Qed. @@ -78,7 +79,8 @@ Section defs. Proof. split; [induction 1 as [|a l [|]]| induction 1]; auto using Sorted, LocallySorted, HdRel. - inversion H1; subst; auto using LocallySorted. + match goal with H1 : HdRel a (_ :: _) |- _ => inversion H1 end. + subst; auto using LocallySorted. Qed. (** Strongly sorted: elements of the list are pairwise ordered *) @@ -90,7 +92,7 @@ Section defs. Lemma StronglySorted_inv : forall a l, StronglySorted (a :: l) -> StronglySorted l /\ Forall (R a) l. Proof. - intros; inversion H; auto. + intros a l H; inversion H; auto. Defined. Lemma StronglySorted_rect : @@ -99,7 +101,7 @@ Section defs. (forall a l, StronglySorted l -> P l -> Forall (R a) l -> P (a :: l)) -> forall l, StronglySorted l -> P l. Proof. - induction l; firstorder using StronglySorted_inv. + intros P ? ? l; induction l; firstorder using StronglySorted_inv. Defined. Lemma StronglySorted_rec : @@ -120,7 +122,8 @@ Section defs. Lemma Sorted_extends : Transitive R -> forall a l, Sorted (a::l) -> Forall (R a) l. Proof. - intros. change match a :: l with [] => True | a :: l => Forall (R a) l end. + intros H a l H0. + change match a :: l with [] => True | a :: l => Forall (R a) l end. induction H0 as [|? ? ? ? H1]; [trivial|]. destruct H1; constructor; trivial. eapply Forall_impl; [|eassumption]. |