diff --git a/.obsidian/workspace.json b/.obsidian/workspace.json
index 3389e81..d379108 100644
--- a/.obsidian/workspace.json
+++ b/.obsidian/workspace.json
@@ -13,31 +13,7 @@
             "state": {
               "type": "markdown",
               "state": {
-                "file": "4a1s/CP/PL - Aula 4.md",
-                "mode": "source",
-                "source": false
-              }
-            }
-          },
-          {
-            "id": "ecf80ed41f9d298e",
-            "type": "leaf",
-            "state": {
-              "type": "markdown",
-              "state": {
-                "file": "4a1s/RAS/Notas Projeto RAS.md",
-                "mode": "source",
-                "source": false
-              }
-            }
-          },
-          {
-            "id": "cca189cd61cd7fe5",
-            "type": "leaf",
-            "state": {
-              "type": "markdown",
-              "state": {
-                "file": "4a1s/MFES/PL - Aula 5.md",
+                "file": "4a1s/MFES/PL - Aula 4.md",
                 "mode": "source",
                 "source": false
               }
@@ -109,7 +85,7 @@
             "state": {
               "type": "backlink",
               "state": {
-                "file": "4a1s/CP/PL - Aula 4.md",
+                "file": "4a1s/MFES/PL - Aula 4.md",
                 "collapseAll": false,
                 "extraContext": false,
                 "sortOrder": "alphabetical",
@@ -126,7 +102,7 @@
             "state": {
               "type": "outgoing-link",
               "state": {
-                "file": "4a1s/CP/PL - Aula 4.md",
+                "file": "4a1s/MFES/PL - Aula 4.md",
                 "linksCollapsed": false,
                 "unlinkedCollapsed": true
               }
@@ -149,7 +125,7 @@
             "state": {
               "type": "outline",
               "state": {
-                "file": "4a1s/CP/PL - Aula 4.md"
+                "file": "4a1s/MFES/PL - Aula 4.md"
               }
             }
           },
@@ -182,7 +158,7 @@
       "digitalgarden:Digital Garden Publication Center": false
     }
   },
-  "active": "0d5f0081d4a8007c",
+  "active": "3ca14d4a6c304083",
   "lastOpenFiles": [
     "4a1s/MFES/PL - Aula 5.md",
     "4a1s/RAS/Notas Projeto RAS.md",
diff --git a/4a1s/MFES/PL - Aula 5.md b/4a1s/MFES/PL - Aula 5.md
index 5b8fae5..bb46439 100644
--- a/4a1s/MFES/PL - Aula 5.md	
+++ b/4a1s/MFES/PL - Aula 5.md	
@@ -42,7 +42,8 @@ pred Invs {
   	//for all nodes sequentially linked, they must have the same hash
   	all x, y: Node | (x.prox = y) implies x.key.hash = y.key.hash
   	
-  	// for all buckets 
+  	//no node links to nodes associated with a different hash
+  	all x, y: Node | x.key.hash != y.key.hash implies (x.prox != y and y.prox != x)
   
 }