diff options
Diffstat (limited to 'theories/Lists/SetoidList.v')
| -rw-r--r-- | theories/Lists/SetoidList.v | 22 |
1 files changed, 11 insertions, 11 deletions
diff --git a/theories/Lists/SetoidList.v b/theories/Lists/SetoidList.v index 0c5fe55b27..cab4c23df1 100644 --- a/theories/Lists/SetoidList.v +++ b/theories/Lists/SetoidList.v @@ -30,7 +30,7 @@ Inductive InA (x : A) : list A -> Prop := | InA_cons_hd : forall y l, eqA x y -> InA x (y :: l) | InA_cons_tl : forall y l, InA x l -> InA x (y :: l). -Hint Constructors InA. +Hint Constructors InA : core. (** TODO: it would be nice to have a generic definition instead of the previous one. Having [InA = Exists eqA] raises too @@ -62,7 +62,7 @@ Inductive NoDupA : list A -> Prop := | NoDupA_nil : NoDupA nil | NoDupA_cons : forall x l, ~ InA x l -> NoDupA l -> NoDupA (x::l). -Hint Constructors NoDupA. +Hint Constructors NoDupA : core. (** An alternative definition of [NoDupA] based on [ForallOrdPairs] *) @@ -93,7 +93,7 @@ Inductive eqlistA : list A -> list A -> Prop := | eqlistA_cons : forall x x' l l', eqA x x' -> eqlistA l l' -> eqlistA (x::l) (x'::l'). -Hint Constructors eqlistA. +Hint Constructors eqlistA : core. (** We could also have written [eqlistA = Forall2 eqA]. *) @@ -107,8 +107,8 @@ Definition eqarefl := (@Equivalence_Reflexive _ _ eqA_equiv). Definition eqatrans := (@Equivalence_Transitive _ _ eqA_equiv). Definition eqasym := (@Equivalence_Symmetric _ _ eqA_equiv). -Hint Resolve eqarefl eqatrans. -Hint Immediate eqasym. +Hint Resolve eqarefl eqatrans : core. +Hint Immediate eqasym : core. Ltac inv := invlist InA; invlist sort; invlist lelistA; invlist NoDupA. @@ -154,14 +154,14 @@ Lemma InA_eqA : forall l x y, eqA x y -> InA x l -> InA y l. Proof. intros l x y H H'. rewrite <- H. auto. Qed. -Hint Immediate InA_eqA. +Hint Immediate InA_eqA : core. Lemma In_InA : forall l x, In x l -> InA x l. Proof. simple induction l; simpl; intuition. subst; auto. Qed. -Hint Resolve In_InA. +Hint Resolve In_InA : core. Lemma InA_split : forall l x, InA x l -> exists l1 y l2, eqA x y /\ l = l1++y::l2. @@ -786,12 +786,12 @@ Hypothesis ltA_compat : Proper (eqA==>eqA==>iff) ltA. Let sotrans := (@StrictOrder_Transitive _ _ ltA_strorder). -Hint Resolve sotrans. +Hint Resolve sotrans : core. Notation InfA:=(lelistA ltA). Notation SortA:=(sort ltA). -Hint Constructors lelistA sort. +Hint Constructors lelistA sort : core. Lemma InfA_ltA : forall l x y, ltA x y -> InfA y l -> InfA x l. @@ -814,7 +814,7 @@ Lemma InfA_eqA l x y : eqA x y -> InfA y l -> InfA x l. Proof using eqA_equiv ltA_compat. intros H; now rewrite H. Qed. -Hint Immediate InfA_ltA InfA_eqA. +Hint Immediate InfA_ltA InfA_eqA : core. Lemma SortA_InfA_InA : forall l x a, SortA l -> InfA a l -> InA x l -> ltA a x. @@ -1005,7 +1005,7 @@ Qed. End Filter. End Type_with_equality. -Hint Constructors InA eqlistA NoDupA sort lelistA. +Hint Constructors InA eqlistA NoDupA sort lelistA : core. Arguments equivlistA_cons_nil {A} eqA {eqA_equiv} x l _. Arguments equivlistA_nil_eq {A} eqA {eqA_equiv} l _. |