src/HOL/Import/HOL_Light_Maps.thy
changeset 63950 cdc1e59aa513
parent 63167 0909deb8059b
child 67399 eab6ce8368fa
equal deleted inserted replaced
63949:e7e41db7221b 63950:cdc1e59aa513
   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