solve_ndisj: solve more goals involving chains of differences

tests/solve_ndisj.v

@@ -35,3 +35,11 @@ Proof. solve_ndisj. Qed.
 Lemma test7 N :
   ↑N ⊆@{coPset} ⊤ ∖ ∅.
 Proof. solve_ndisj. Qed.
+
+Lemma test8 N1 N2 :
+  ⊤ ∖ (↑N1 ∪ ↑N2) ⊆@{coPset} ⊤ ∖ ↑N1.@"counter".
+Proof. solve_ndisj. Qed.
+
+Lemma test9 N1 N2 :
+  ⊤ ∖ (↑N1 ∪ ↑N2) ⊆@{coPset} ⊤ ∖ ↑N1.@"counter" ∖ ↑N1.@"state" ∖ ↑N2.
+Proof. solve_ndisj. Qed.

theories/namespaces.v

@@ -84,6 +84,11 @@ Local Definition coPset_empty_subseteq := empty_subseteq (C:=coPset).
 Global Hint Resolve coPset_empty_subseteq : ndisj.
 Local Definition coPset_union_least := union_least (C:=coPset).
 Global Hint Resolve coPset_union_least : ndisj.
+(** For goals like [X ⊆ L ∪ R], backtrack for the two sides. *)
+Local Definition coPset_union_subseteq_l' := union_subseteq_l' (C:=coPset).
+Global Hint Resolve coPset_union_subseteq_l' | 50 : ndisj.
+Local Definition coPset_union_subseteq_r' := union_subseteq_r' (C:=coPset).
+Global Hint Resolve coPset_union_subseteq_r' | 50 : ndisj.
 (** Fallback, loses lots of information but lets other rules make progress. *)
 Local Definition coPset_subseteq_difference_l := subseteq_difference_l (C:=coPset).
 Global Hint Resolve coPset_subseteq_difference_l | 100 : ndisj.

theories/sets.v

@@ -385,8 +385,12 @@ Section semi_set.
 
   Lemma union_subseteq_l X Y : X ⊆ X ∪ Y.
   Proof. set_solver. Qed.
+  Lemma union_subseteq_l' X X' Y : X ⊆ X' → X ⊆ X' ∪ Y.
+  Proof. set_solver. Qed.
   Lemma union_subseteq_r X Y : Y ⊆ X ∪ Y.
   Proof. set_solver. Qed.
+  Lemma union_subseteq_r' X Y Y' : Y ⊆ Y' → Y ⊆ X ∪ Y'.
+  Proof. set_solver. Qed.
   Lemma union_least X Y Z : X ⊆ Z → Y ⊆ Z → X ∪ Y ⊆ Z.
   Proof. set_solver. Qed.