diff --git a/4a1s/MFES/PL - Aula 5.md b/4a1s/MFES/PL - Aula 5.md
index 7e8d280..9565f97 100644
--- a/4a1s/MFES/PL - Aula 5.md	
+++ b/4a1s/MFES/PL - Aula 5.md	
@@ -44,7 +44,14 @@ pred Invs {
   	//ALTERNATIVELY
   	//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)
-  	
+
+  	//a node with the same hash as two others in the same hash cannot be prox of them two
+  	all x, y, z:Node, w : Key | (x.key = w and y.key = w and z.key = w and x.prox = z) implies y.prox!=z
+
+
+
+
+
 
 
   	//MAY BE WORNG STUFF
@@ -54,7 +61,9 @@ pred Invs {
   	//the prox node of another node may be empty
   	all x: Node, y : Node | x.prox = y or not x.prox = y
 
-//all x : Node | x.prox.key != x.key
+  	//the sequence of nodes associated with the same hash should not loop
+  	//all x : Node | x.prox.key != x.key
+
 
 
   	//WORNG STUFF