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+Semantics of FOL
+-- graph theory 
+-- \Sigma \entails \alpha
+-- Lemma : two assignments agree on FV(\alpha) in a structure L, 
+           then  M \entails \alpha under s_1 
+ 			iff 
+                  M \entails \alpha under s_1    
+-- Proof of lemma : terms, atomic formuals. 
+-- Examples : 
+-- L =(R(,))
+   M1=(\nat, <)
+   M2=(\nat, divides)
+   M3=(pow(nat), \subset)
+   formulas : R(x,y) 
+            : \exists x \forall y (R(x,y)). 
+
+   
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+Semantics of FOL
+-- graph theory 
+-- \Sigma \entails \alpha
+-- Lemma : two assignments agree on FV(\alpha) in a structure L, 
+           then  M \entails \alpha under s_1 
+ 			iff 
+                  M \entails \alpha under s_1    
+-- Proof of lemma : terms, atomic formuals. 
+-- Examples : 
+-- L =(R(,))
+   M1=(\nat, <)
+   M2=(\nat, divides)
+   M3=(pow(nat), \subset)
+   formulas : R(x,y) 
+            : \exists x \forall y (R(x,y)). 
+
+