src/HOL/ex/BinEx.thy
changeset 12613 279facb4253a
parent 11868 56db9f3a6b3e
child 13187 e5434b822a96
equal deleted inserted replaced
12612:2a64142500f6 12613:279facb4253a
   133 
   133 
   134 lemma "100094 mod 144 = (14::int)"
   134 lemma "100094 mod 144 = (14::int)"
   135   by simp
   135   by simp
   136 
   136 
   137 
   137 
       
   138 text {* \medskip Powers *}
       
   139 
       
   140 lemma "2 ^ 10 = (1024::int)"
       
   141   by simp
       
   142 
       
   143 lemma "-3 ^ 7 = (-2187::int)"
       
   144   by simp
       
   145 
       
   146 lemma "13 ^ 7 = (62748517::int)"
       
   147   by simp
       
   148 
       
   149 lemma "3 ^ 15 = (14348907::int)"
       
   150   by simp
       
   151 
       
   152 lemma "-5 ^ 11 = (-48828125::int)"
       
   153   by simp
       
   154 
       
   155 
   138 subsection {* The Natural Numbers *}
   156 subsection {* The Natural Numbers *}
   139 
   157 
   140 text {* Successor *}
   158 text {* Successor *}
   141 
   159 
   142 lemma "Suc 99999 = 100000"
   160 lemma "Suc 99999 = 100000"
   196 
   214 
   197 lemma "(10000::nat) div 16 = 625"
   215 lemma "(10000::nat) div 16 = 625"
   198   by simp
   216   by simp
   199 
   217 
   200 lemma "(10000::nat) mod 16 = 0"
   218 lemma "(10000::nat) mod 16 = 0"
       
   219   by simp
       
   220 
       
   221 
       
   222 text {* \medskip Powers *}
       
   223 
       
   224 lemma "2 ^ 12 = (4096::nat)"
       
   225   by simp
       
   226 
       
   227 lemma "3 ^ 10 = (59049::nat)"
       
   228   by simp
       
   229 
       
   230 lemma "12 ^ 7 = (35831808::nat)"
       
   231   by simp
       
   232 
       
   233 lemma "3 ^ 14 = (4782969::nat)"
       
   234   by simp
       
   235 
       
   236 lemma "5 ^ 11 = (48828125::nat)"
   201   by simp
   237   by simp
   202 
   238 
   203 
   239 
   204 text {* \medskip Testing the cancellation of complementary terms *}
   240 text {* \medskip Testing the cancellation of complementary terms *}
   205 
   241