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+chapter \<open>Generated by Lem from bool.lem.\<close>
+
+theory "Lem_bool"
+
+imports
+ Main
+
+begin
+
+
+
+(* The type bool is hard-coded, so are true and false *)
+
+(* ----------------------- *)
+(* not *)
+(* ----------------------- *)
+
+(*val not : bool -> bool*)
+(*let not b= match b with
+ | true -> false
+ | false -> true
+end*)
+
+(* ----------------------- *)
+(* and *)
+(* ----------------------- *)
+
+(*val && [and] : bool -> bool -> bool*)
+(*let && b1 b2= match (b1, b2) with
+ | (true, true) -> true
+ | _ -> false
+end*)
+
+
+(* ----------------------- *)
+(* or *)
+(* ----------------------- *)
+
+(*val || [or] : bool -> bool -> bool*)
+(*let || b1 b2= match (b1, b2) with
+ | (false, false) -> false
+ | _ -> true
+end*)
+
+
+(* ----------------------- *)
+(* implication *)
+(* ----------------------- *)
+
+(*val --> [imp] : bool -> bool -> bool*)
+(*let --> b1 b2= match (b1, b2) with
+ | (true, false) -> false
+ | _ -> true
+end*)
+
+
+(* ----------------------- *)
+(* equivalence *)
+(* ----------------------- *)
+
+(*val <-> [equiv] : bool -> bool -> bool*)
+(*let <-> b1 b2= match (b1, b2) with
+ | (true, true) -> true
+ | (false, false) -> true
+ | _ -> false
+end*)
+
+
+(* ----------------------- *)
+(* xor *)
+(* ----------------------- *)
+
+(*val xor : bool -> bool -> bool*)
+
+end