Use new set notation for multisets in tests.

tests/multiset_solver.v

@@ -27,48 +27,45 @@ Section test.
     2 < multiplicity x X → X ⊆ Y → 1 < multiplicity x Y.
   Proof. multiset_solver. Qed.
   Lemma test_multiplicity_2 x X :
-    2 < multiplicity x X → {[ x ]} ⊎ {[ x ]} ⊎ {[ x ]} ⊆ X.
+    2 < multiplicity x X → {[ x ;+ x ;+ x ]} ⊆ X.
   Proof. multiset_solver. Qed.
   Lemma test_multiplicity_3 x X :
-    multiplicity x X < 3 → {[ x ]} ⊎ {[ x ]} ⊎ {[ x ]} ⊈ X.
+    multiplicity x X < 3 → {[ x ;+ x ;+ x ]} ⊈ X.
   Proof. multiset_solver. Qed.
 
   Lemma test_elem_of_1 x X : x ∈ X ↔ {[x]} ⊎ ∅ ⊆ X.
   Proof. multiset_solver. Qed.
   Lemma test_elem_of_2 x X : x ∈ X ↔ {[x]} ∪ ∅ ⊆ X.
   Proof. multiset_solver. Qed.
-  Lemma test_elem_of_3 x y X : x ≠ y → x ∈ X → y ∈ X → {[x]} ⊎ {[y]} ⊆ X.
+  Lemma test_elem_of_3 x y X : x ≠ y → x ∈ X → y ∈ X → {[x ;+ y]} ⊆ X.
   Proof. multiset_solver. Qed.
-  Lemma test_elem_of_4 x y X Y : x ≠ y → x ∈ X → y ∈ Y → {[x]} ⊎ {[y]} ⊆ X ∪ Y.
+  Lemma test_elem_of_4 x y X Y : x ≠ y → x ∈ X → y ∈ Y → {[x ;+ y]} ⊆ X ∪ Y.
   Proof. multiset_solver. Qed.
   Lemma test_elem_of_5 x y X Y : x ≠ y → x ∈ X → y ∈ Y → {[x]} ⊆ (X ∪ Y) ∖ {[ y ]}.
   Proof. multiset_solver. Qed.
-  Lemma test_elem_of_6 x y X : {[x]} ⊎ {[y]} ⊆ X → x ∈ X ∧ y ∈ X.
+  Lemma test_elem_of_6 x y X : {[x ;+ y]} ⊆ X → x ∈ X ∧ y ∈ X.
   Proof. multiset_solver. Qed.
 
   Lemma test_big_1 x1 x2 x3 x4 :
-    {[ x1 ]} ⊎ {[ x2 ]} ⊎ {[ x3 ]} ⊎ {[ x4 ]} ⊎ {[ x4 ]} ⊆@{gmultiset A}
-      {[ x1 ]} ⊎ {[ x1 ]} ⊎ {[ x2 ]} ⊎ {[ x3 ]} ⊎ {[ x4 ]} ⊎ {[ x4 ]}.
+    {[ x1 ;+ x2 ;+ x3 ;+ x4 ;+ x4 ]} ⊆@{gmultiset A}
+      {[ x1 ;+ x1 ;+ x2 ;+ x3 ;+ x4 ;+ x4 ]}.
   Proof. multiset_solver. Qed.
   Lemma test_big_2 x1 x2 x3 x4 X :
     2 ≤ multiplicity x4 X →
-    {[ x1 ]} ⊎ {[ x2 ]} ⊎ {[ x3 ]} ⊎ {[ x4 ]} ⊎ {[ x4 ]} ⊆@{gmultiset A}
-      {[ x1 ]} ⊎ {[ x1 ]} ⊎ {[ x2 ]} ⊎ {[ x3 ]} ⊎ X.
+    {[ x1 ;+ x2 ;+ x3 ;+ x4 ;+ x4 ]} ⊆@{gmultiset A}
+      {[ x1 ;+ x1 ;+ x2 ;+ x3 ]} ⊎ X.
   Proof. multiset_solver. Qed.
   Lemma test_big_3 x1 x2 x3 x4 X :
     4 ≤ multiplicity x4 X →
-    {[ x1 ]} ⊎ {[ x2 ]} ⊎ {[ x3 ]} ⊎ {[ x4 ]} ⊎ {[ x4 ]} ⊎
-      {[ x1 ]} ⊎ {[ x2 ]} ⊎ {[ x3 ]} ⊎ {[ x4 ]} ⊎ {[ x4 ]}
+    {[ x1 ;+ x2 ;+ x3 ;+ x4 ;+ x4 ;+ x1 ;+ x2 ;+ x3 ;+ x4 ;+ x4 ]}
     ⊆@{gmultiset A}
-      {[ x1 ]} ⊎ {[ x1 ]} ⊎ {[ x2 ]} ⊎ {[ x3 ]} ⊎
-      {[ x1 ]} ⊎ {[ x1 ]} ⊎ {[ x2 ]} ⊎ {[ x3 ]} ⊎ X.
+      {[ x1 ;+ x1 ;+ x2 ;+ x3 ;+ x1 ;+ x1 ;+ x2 ;+ x3 ]} ⊎ X.
   Proof. multiset_solver. Qed.
   Lemma test_big_4 x1 x2 x3 x4 x5 x6 x7 x8 x9 :
-    {[ x1 ]} ⊎ {[ x2 ]} ⊎ {[ x3 ]} ⊎ {[ x4 ]} ⊎ {[ x4 ]} ⊎
-      {[ x5 ]} ⊎ {[ x6 ]} ⊎ {[ x7 ]} ⊎ {[ x8 ]} ⊎ {[ x8 ]} ⊎ {[ x9 ]}
+    {[ x1 ;+ x2 ;+ x3 ;+ x4 ;+ x4 ;+ x5 ;+ x6 ;+ x7 ;+ x8 ;+ x8 ;+ x9 ]}
     ⊆@{gmultiset A}
-      {[ x1 ]} ⊎ {[ x1 ]} ⊎ {[ x2 ]} ⊎ {[ x3 ]} ⊎ {[ x4 ]} ⊎ {[ x4 ]} ⊎
-      {[ x5 ]} ⊎ {[ x5 ]} ⊎ {[ x6 ]} ⊎ {[ x7 ]} ⊎ {[ x9 ]} ⊎ {[ x8 ]} ⊎ {[ x8 ]}.
+      {[ x1 ;+ x1 ;+ x2 ;+ x3 ;+ x4 ;+ x4 ;+
+         x5 ;+ x5 ;+ x6 ;+ x7 ;+ x9 ;+ x8 ;+ x8 ]}.
   Proof. multiset_solver. Qed.
 
   Lemma test_firstorder_1 (P : A → Prop) x X :