Adapt w.r.t. coq/coq#12512.

theories/binders.v

@@ -81,7 +81,7 @@ Section binder_delete_insert.
   Proof. destruct b; solve_proper. Qed.
 
   Lemma binder_delete_empty {A} b : binder_delete b ∅ =@{M A} ∅.
-  Proof. destruct b; simpl; auto using delete_empty. Qed.
+  Proof. epose delete_empty; destruct b; simpl; auto. Qed.
 
   Lemma lookup_binder_delete_None {A} (m : M A) b s :
     binder_delete b m !! s = None ↔ b = BNamed s ∨ m !! s = None.

theories/fin_map_dom.v

@@ -125,8 +125,8 @@ Qed.
 Lemma dom_finite {A} (m : M A) : set_finite (dom D m).
 Proof.
   induction m using map_ind; rewrite ?dom_empty, ?dom_insert;
-    eauto using (empty_finite (C:=D)), (union_finite (C:=D)),
-    (singleton_finite (C:=D)).
+    pose (empty_finite (C:=D)); pose (union_finite (C:=D)); pose
+    (singleton_finite (C:=D)); eauto.
 Qed.
 Global Instance dom_proper `{!Equiv A} : Proper ((≡@{M A}) ==> (≡)) (dom D).
 Proof.

theories/fin_maps.v

@@ -795,7 +795,7 @@ Lemma list_to_map_inj {A} (l1 l2 : list (K * A)) :
   NoDup (l1.*1) → NoDup (l2.*1) →
   (list_to_map l1 : M A) = list_to_map l2 → l1 ≡ₚ l2.
 Proof.
-  intros ?? Hl1l2. apply NoDup_Permutation; auto using (NoDup_fmap_1 fst).
+  intros ?? Hl1l2. epose (NoDup_fmap_1 fst); apply NoDup_Permutation; auto.
   intros [i x]. by rewrite !elem_of_list_to_map, Hl1l2.
 Qed.
 Lemma list_to_map_to_list {A} (m : M A) : list_to_map (map_to_list m) = m.
@@ -851,13 +851,13 @@ Lemma map_to_list_singleton {A} i (x : A) :
   map_to_list ({[i:=x]} : M A) = [(i,x)].
 Proof.
   apply Permutation_singleton. unfold singletonM, map_singleton.
-  by rewrite map_to_list_insert, map_to_list_empty by auto using lookup_empty.
+  by rewrite map_to_list_insert, map_to_list_empty by (epose lookup_empty; auto).
 Qed.
 
 Lemma map_to_list_submseteq {A} (m1 m2 : M A) :
   m1 ⊆ m2 → map_to_list m1 ⊆+ map_to_list m2.
 Proof.
-  intros; apply NoDup_submseteq; auto using NoDup_map_to_list.
+  intros; epose NoDup_map_to_list; apply NoDup_submseteq; auto.
   intros [i x]. rewrite !elem_of_map_to_list; eauto using lookup_weaken.
 Qed.
 Lemma map_to_list_fmap {A B} (f : A → B) (m : M A) :
@@ -1755,13 +1755,13 @@ Lemma map_union_cancel_l {A} (m1 m2 m3 : M A) :
   m1 ##ₘ m3 → m2 ##ₘ m3 → m3 ∪ m1 = m3 ∪ m2 → m1 = m2.
 Proof.
   intros. apply (anti_symm (⊆)); apply map_union_reflecting_l with m3;
-    auto using (reflexive_eq (R:=(⊆@{M A}))).
+    pose (reflexive_eq (R:=(⊆@{M A}))); auto.
 Qed.
 Lemma map_union_cancel_r {A} (m1 m2 m3 : M A) :
   m1 ##ₘ m3 → m2 ##ₘ m3 → m1 ∪ m3 = m2 ∪ m3 → m1 = m2.
 Proof.
   intros. apply (anti_symm (⊆)); apply map_union_reflecting_r with m3;
-    auto using (reflexive_eq (R:=(⊆@{M A}))).
+    pose (reflexive_eq (R:=(⊆@{M A}))); auto.
 Qed.
 Lemma map_disjoint_union_l {A} (m1 m2 m3 : M A) :
   m1 ∪ m2 ##ₘ m3 ↔ m1 ##ₘ m3 ∧ m2 ##ₘ m3.

theories/fin_sets.v

@@ -260,9 +260,9 @@ Proof.
   { destruct IH as (x' & Hx' & Hmin); [set_solver|].
     destruct (decide (R x x')).
     - exists x; split; [set_solver|].
-      eauto using (union_minimal (C:=C)), (singleton_minimal (C:=C)), minimal_weaken.
+      epose proof (union_minimal (C:=C)); epose proof (singleton_minimal (C:=C)); eauto using minimal_weaken.
     - exists x'; split; [set_solver|].
-      eauto using (union_minimal (C:=C)), (singleton_minimal_not_above (C:=C)). }
+      epose proof (union_minimal (C:=C)); epose proof (singleton_minimal_not_above (C:=C)); eauto. }
   exists x; split; [set_solver|].
   rewrite HX, (right_id _ (∪)). apply singleton_minimal.
 Qed.

theories/finite.v

@@ -154,10 +154,10 @@ Lemma finite_bijective A `{Finite A} B `{Finite B} :
 Proof.
   split.
   - intros; destruct (proj1 (finite_inj A B)) as [f ?]; auto with lia.
-    exists f; auto using (finite_inj_surj f).
+    exists f; pose proof (finite_inj_surj f); auto.
   - intros (f&?&?). apply (anti_symm (≤)); apply finite_inj.
     + by exists f.
-    + destruct (surj_cancel f) as (g&?); eauto using cancel_inj.
+    + destruct (surj_cancel f) as (g&?); pose proof cancel_inj; eauto.
 Qed.
 Lemma inj_card `{Finite A} `{Finite B} (f : A → B)
   `{!Inj (=) (=) f} : card A ≤ card B.
@@ -274,7 +274,7 @@ Next Obligation.
 Qed.
 Next Obligation.
   intros ?????? [x|y]; rewrite elem_of_app, !elem_of_list_fmap;
-    eauto using @elem_of_enum.
+    pose proof @elem_of_enum; eauto.
 Qed.
 Lemma sum_card `{Finite A, Finite B} : card (A + B) = card A + card B.
 Proof. unfold card. simpl. by rewrite app_length, !fmap_length. Qed.
@@ -297,7 +297,7 @@ Next Obligation.
 Qed.
 Next Obligation.
   intros ?????? [x y]. induction (elem_of_enum x); simpl.
-  - rewrite elem_of_app, !elem_of_list_fmap. eauto using @elem_of_enum.
+  - rewrite elem_of_app, !elem_of_list_fmap. pose proof @elem_of_enum; eauto.
   - rewrite elem_of_app; eauto.
 Qed.
 Lemma prod_card `{Finite A} `{Finite B} : card (A * B) = card A * card B.

theories/numbers.v

@@ -792,10 +792,10 @@ Proof.
     - auto.
     - destruct (help c d a b); [done..|]. naive_solver.
     - apply (inj (Qp_plus a)) in H as ->. destruct (Qp_lower_bound a d) as (q&a'&d'&->&->).
-      eauto 10 using (comm_L Qp_plus). }
+      pose proof comm_L Qp_plus; eauto 10. }
   intros a b c d [e ->]%Qp_lt_sum. rewrite <-(assoc_L _). intros ->%(inj (Qp_plus a)).
   destruct (Qp_lower_bound a d) as (q&a'&d'&->&->).
-  eexists a', q, (q + e)%Qp, d'; split_and?; auto using (comm_L Qp_plus).
+  eexists a', q, (q + e)%Qp, d'; split_and?; pose proof (comm_L Qp_plus); auto.
   - by rewrite (assoc_L _), (comm_L Qp_plus e).
   - by rewrite (assoc_L _), (comm_L Qp_plus a').
 Qed.

theories/sorting.v

@@ -182,7 +182,7 @@ Section merge_sort_correct.
     intros Hl1. revert l2. induction Hl1 as [|x1 l1 IH1];
       induction 1 as [|x2 l2 IH2]; rewrite ?list_merge_cons; simpl;
       repeat case_decide;
-      constructor; eauto using HdRel_list_merge, HdRel_cons, total_not.
+      constructor; epose proof total_not; eauto using HdRel_list_merge, HdRel_cons.
   Qed.
   Lemma merge_Permutation l1 l2 : list_merge R l1 l2 ≡ₚ l1 ++ l2.
   Proof.