diff options
Diffstat (limited to 'theories/MSets/MSetList.v')
| -rw-r--r-- | theories/MSets/MSetList.v | 21 |
1 files changed, 8 insertions, 13 deletions
diff --git a/theories/MSets/MSetList.v b/theories/MSets/MSetList.v index d9b1fd9b..fb0d1ad9 100644 --- a/theories/MSets/MSetList.v +++ b/theories/MSets/MSetList.v @@ -56,7 +56,7 @@ Module Ops (X:OrderedType) <: WOps X. Definition singleton (x : elt) := x :: nil. - Fixpoint remove x s := + Fixpoint remove x s : t := match s with | nil => nil | y :: l => @@ -228,16 +228,14 @@ Module MakeRaw (X: OrderedType) <: RawSets X. Notation Inf := (lelistA X.lt). Notation In := (InA X.eq). - (* TODO: modify proofs in order to avoid these hints *) - Hint Resolve (@Equivalence_Reflexive _ _ X.eq_equiv). - Hint Immediate (@Equivalence_Symmetric _ _ X.eq_equiv). - Hint Resolve (@Equivalence_Transitive _ _ X.eq_equiv). + Existing Instance X.eq_equiv. + Hint Extern 20 => solve [order]. Definition IsOk s := Sort s. Class Ok (s:t) : Prop := ok : Sort s. - Hint Resolve @ok. + Hint Resolve ok. Hint Unfold Ok. Instance Sort_Ok s `(Hs : Sort s) : Ok s := { ok := Hs }. @@ -343,7 +341,6 @@ Module MakeRaw (X: OrderedType) <: RawSets X. induction s; simpl; intros. intuition. inv; auto. elim_compare x a; inv; rewrite !InA_cons, ?IHs; intuition. - left; order. Qed. Lemma remove_inf : @@ -402,8 +399,8 @@ Module MakeRaw (X: OrderedType) <: RawSets X. Global Instance union_ok s s' : forall `(Ok s, Ok s'), Ok (union s s'). Proof. repeat rewrite <- isok_iff; revert s s'. - induction2; constructors; try apply @ok; auto. - apply Inf_eq with x'; auto; apply union_inf; auto; apply Inf_eq with x; auto. + induction2; constructors; try apply @ok; auto. + apply Inf_eq with x'; auto; apply union_inf; auto; apply Inf_eq with x; auto; order. change (Inf x' (union (x :: l) l')); auto. Qed. @@ -412,7 +409,6 @@ Module MakeRaw (X: OrderedType) <: RawSets X. In x (union s s') <-> In x s \/ In x s'. Proof. induction2; try rewrite ?InA_cons, ?Hrec, ?Hrec'; intuition; inv; auto. - left; order. Qed. Lemma inter_inf : @@ -440,7 +436,6 @@ Module MakeRaw (X: OrderedType) <: RawSets X. Proof. induction2; try rewrite ?InA_cons, ?Hrec, ?Hrec'; intuition; inv; auto; try sort_inf_in; try order. - left; order. Qed. Lemma diff_inf : @@ -477,7 +472,7 @@ Module MakeRaw (X: OrderedType) <: RawSets X. equal s s' = true <-> Equal s s'. Proof. induction s as [ | x s IH]; intros [ | x' s'] Hs Hs'; simpl. - intuition. + intuition reflexivity. split; intros H. discriminate. assert (In x' nil) by (rewrite H; auto). inv. split; intros H. discriminate. assert (In x nil) by (rewrite <-H; auto). inv. inv. @@ -825,7 +820,7 @@ Module MakeRaw (X: OrderedType) <: RawSets X. Lemma compare_spec_aux : forall s s', CompSpec eq L.lt s s' (compare s s'). Proof. - induction s as [|x s IH]; intros [|x' s']; simpl; intuition. + induction s as [|x s IH]; intros [|x' s']; simpl; intuition. elim_compare x x'; auto. Qed. |