equal
deleted
inserted
replaced
195 |
195 |
196 lemma FACT[import_const "FACT" : fact]: |
196 lemma FACT[import_const "FACT" : fact]: |
197 "fact (id 0) = id (bit1 0) \<and> (\<forall>n. fact (Suc n) = Suc n * fact n)" |
197 "fact (id 0) = id (bit1 0) \<and> (\<forall>n. fact (Suc n) = Suc n * fact n)" |
198 by simp |
198 by simp |
199 |
199 |
200 import_const_map MOD : mod |
200 import_const_map MOD : modulo |
201 import_const_map DIV : divide |
201 import_const_map DIV : divide |
202 |
202 |
203 lemma DIVISION_0: |
203 lemma DIVISION_0: |
204 "\<forall>m n::nat. if n = id 0 then m div n = id 0 \<and> m mod n = m else m = m div n * n + m mod n \<and> m mod n < n" |
204 "\<forall>m n::nat. if n = id 0 then m div n = id 0 \<and> m mod n = m else m = m div n * n + m mod n \<and> m mod n < n" |
205 by simp |
205 by simp |