improve f_equiv and solve_proper; use them in a few more places

prelude/tactics.v

@@ -257,22 +257,28 @@ Ltac f_equiv :=
             let H := fresh "Proper" in
             assert (Proper (R ==> R ==> R) f) as H by (eapply _);
             apply H; clear H; f_equiv
-          (* Next, try to infer the relation *)
+          (* Next, try to infer the relation. Unfortunately, there is an instance
+             of Proper for (eq ==> _), which will always be matched. *)
+          (* TODO: Can we exclude that instance? *)
           (* TODO: If some of the arguments are the same, we could also
              query for "pointwise_relation"'s. But that leads to a combinatorial
              explosion about which arguments are and which are not the same. *)
           | |- ?R (?f ?x) (?f _) =>
-            let R1 := fresh "R" in let H := fresh "Proper" in
+            let R1 := fresh "R" in let H := fresh "HProp" in
             let T := type of x in evar (R1: relation T);
             assert (Proper (R1 ==> R) f) as H by (subst R1; eapply _);
             subst R1; apply H; clear H; f_equiv
           | |- ?R (?f ?x ?y) (?f _ _) =>
             let R1 := fresh "R" in let R2 := fresh "R" in
-            let H := fresh "Proper" in
+            let H := fresh "HProp" in
             let T1 := type of x in evar (R1: relation T1);
             let T2 := type of y in evar (R2: relation T2);
             assert (Proper (R1 ==> R2 ==> R) f) as H by (subst R1 R2; eapply _);
             subst R1 R2; apply H; clear H; f_equiv
+           (* In case the function symbol differs, but the arguments are the same,
+              maybe we have a pointwise_relation in our context. *)
+           | H : pointwise_relation _ ?R ?f ?g |- ?R (?f ?x) (?g ?x) =>
+             apply H; f_equiv
          end | idtac (* Let the user solve this goal *)
         ].
 
@@ -289,6 +295,10 @@ Ltac solve_proper :=
          end;
   (* Unfold the head symbol, which is the one we are proving a new property about *)
   lazymatch goal with
+  | |- ?R (?f _ _ _ _ _ _ _ _) (?f _ _ _ _ _ _ _ _) => unfold f
+  | |- ?R (?f _ _ _ _ _ _ _) (?f _ _ _ _ _ _ _) => unfold f
+  | |- ?R (?f _ _ _ _ _ _) (?f _ _ _ _ _ _) => unfold f
+  | |- ?R (?f _ _ _ _ _) (?f _ _ _ _ _) => unfold f
   | |- ?R (?f _ _ _ _) (?f _ _ _ _) => unfold f
   | |- ?R (?f _ _ _) (?f _ _ _) => unfold f
   | |- ?R (?f _ _) (?f _ _) => unfold f
@@ -296,6 +306,7 @@ Ltac solve_proper :=
   end;
   solve [ f_equiv ].
 
+
 (** Given a tactic [tac2] generating a list of terms, [iter tac1 tac2]
 runs [tac x] for each element [x] until [tac x] succeeds. If it does not
 suceed for any element of the generated list, the whole tactic wil fail. *)

program_logic/auth.v

@@ -40,7 +40,7 @@ Section auth.
   Implicit Types γ : gname.
 
   Global Instance auth_own_ne n γ : Proper (dist n ==> dist n) (auth_own γ).
-  Proof. by rewrite auth_own_eq /auth_own_def=> a b ->. Qed.
+  Proof. rewrite auth_own_eq; solve_proper. Qed.
   Global Instance auth_own_proper γ : Proper ((≡) ==> (≡)) (auth_own γ).
   Proof. by rewrite auth_own_eq /auth_own_def=> a b ->. Qed.
   Global Instance auth_own_timeless γ a : TimelessP (auth_own γ a).

program_logic/sts.v

@@ -52,22 +52,20 @@ Section sts.
   (** Setoids *)
   Global Instance sts_inv_ne n γ :
     Proper (pointwise_relation _ (dist n) ==> dist n) (sts_inv γ).
-  Proof. by intros φ1 φ2 Hφ; rewrite /sts_inv; setoid_rewrite Hφ. Qed.
+  Proof. solve_proper. Qed.
   Global Instance sts_inv_proper γ :
     Proper (pointwise_relation _ (≡) ==> (≡)) (sts_inv γ).
-  Proof. by intros φ1 φ2 Hφ; rewrite /sts_inv; setoid_rewrite Hφ. Qed.
+  Proof. solve_proper. Qed.
   Global Instance sts_ownS_proper γ : Proper ((≡) ==> (≡) ==> (≡)) (sts_ownS γ).
-  Proof.
-    intros S1 S2 HS T1 T2 HT. by rewrite !sts_ownS_eq /sts_ownS_def HS HT.
-  Qed.
+  Proof. rewrite sts_ownS_eq. solve_proper. Qed.
   Global Instance sts_own_proper γ s : Proper ((≡) ==> (≡)) (sts_own γ s).
-  Proof. intros T1 T2 HT. by rewrite !sts_own_eq /sts_own_def HT. Qed.
+  Proof. rewrite sts_own_eq. solve_proper. Qed.
   Global Instance sts_ctx_ne n γ N :
     Proper (pointwise_relation _ (dist n) ==> dist n) (sts_ctx γ N).
-  Proof. by intros φ1 φ2 Hφ; rewrite /sts_ctx Hφ. Qed.
+  Proof. solve_proper. Qed.
   Global Instance sts_ctx_proper γ N :
     Proper (pointwise_relation _ (≡) ==> (≡)) (sts_ctx γ N).
-  Proof. by intros φ1 φ2 Hφ; rewrite /sts_ctx Hφ. Qed.
+  Proof. solve_proper. Qed.
 
   (* The same rule as implication does *not* hold, as could be shown using
      sts_frag_included. *)