vault backup: 2023-11-13 12:51:23

4a1s/MFES/PL - Aula 8.md

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+
+```c
+module Offices
+
+  type office = One | Two | Three
+  type person = Ana | Nuno | Pedro | Maria
+
+  predicate hasOffice (person) (office)
+
+  axiom A1 : forall p:person. exists o:office. hasOffice p o
+  axiom A2 : forall p:person, o1 o2 : office.
+    hasOffice p o1 /\ hasOffice p o2 -> o1 = o2
+  
+  axiom B : forall o1 o2 : office. hasOffice Pedro o1 /\ hasOffice Nuno o2 ->
+      o1 <> o2
+  
+  predicate alone (p:person) = forall o:office. forall p1:person.
+    (hasOffice p o) /\ hasOffice p1 o -> p = p1
+
+  axiom C : alone Ana -> alone Pedro
+  axiom D : forall p1 p2 p3: person, o:office.
+    hasOffice p1 o /\ hasOffice p2 o /\ hasOffice p3 o ->
+        p1 = p2 \/ p1 = p3 \/ p3 = p2
+
+  goal sanity_test : false (*check if the model makes sense*)
+  
+  goal g1 : hasOffice Maria One -> alone Maria
+  goal g2 : forall o1:office. (hasOffice Ana o1 /\ hasOffice Nuno o1) -> 
+      exists o2:office. hasOffice Pedro o2 /\ hasOffice Maria o2 
+
+  predicate empty (o:office) = forall p:person. not (hasOffice p o)
+  
+  lemma atMostOneEmpty : forall o1 o2: office. empty o1 /\ empty o2 ->
+      o1 = o2
+
+end 
+```
+
+