--- /dev/null
+let divides_b =
+(function n -> (function m -> (Matita_nat_compare.eqb (Matita_nat_div_and_mod.mod_ m n) Matita_nat_nat.O)))
+;;
+
+let smallest_factor =
+(function n ->
+(match n with
+ Matita_nat_nat.O -> Matita_nat_nat.O
+ | Matita_nat_nat.S(p) ->
+(match p with
+ Matita_nat_nat.O -> (Matita_nat_nat.S(Matita_nat_nat.O))
+ | Matita_nat_nat.S(q) -> (Matita_nat_minimization.min_aux q (Matita_nat_nat.S((Matita_nat_nat.S(Matita_nat_nat.O)))) (function m -> (Matita_nat_compare.eqb (Matita_nat_div_and_mod.mod_ (Matita_nat_nat.S((Matita_nat_nat.S(q)))) m) Matita_nat_nat.O))))
+)
+)
+;;
+
+let primeb =
+(function n ->
+(match n with
+ Matita_nat_nat.O -> Matita_datatypes_bool.False
+ | Matita_nat_nat.S(p) ->
+(match p with
+ Matita_nat_nat.O -> Matita_datatypes_bool.False
+ | Matita_nat_nat.S(q) -> (Matita_nat_compare.eqb (smallest_factor (Matita_nat_nat.S((Matita_nat_nat.S(q))))) (Matita_nat_nat.S((Matita_nat_nat.S(q))))))
+)
+)
+;;
+