src/HOL/Parity.thy
changeset 33318 ddd97d9dfbfb
parent 31718 7715d4d3586f
child 33358 3495dbba0da2
equal deleted inserted replaced
33298:dfda74619509 33318:ddd97d9dfbfb
    26 
    26 
    27 instance ..
    27 instance ..
    28 
    28 
    29 end
    29 end
    30 
    30 
       
    31 lemma transfer_int_nat_relations:
       
    32   "even (int x) \<longleftrightarrow> even x"
       
    33   by (simp add: even_nat_def)
       
    34 
       
    35 declare TransferMorphism_int_nat[transfer add return:
       
    36   transfer_int_nat_relations
       
    37 ]
    31 
    38 
    32 lemma even_zero_int[simp]: "even (0::int)" by presburger
    39 lemma even_zero_int[simp]: "even (0::int)" by presburger
    33 
    40 
    34 lemma odd_one_int[simp]: "odd (1::int)" by presburger
    41 lemma odd_one_int[simp]: "odd (1::int)" by presburger
    35 
    42 
   308   qed
   315   qed
   309 qed
   316 qed
   310 
   317 
   311 subsection {* General Lemmas About Division *}
   318 subsection {* General Lemmas About Division *}
   312 
   319 
       
   320 (*FIXME move to Divides.thy*)
       
   321 
   313 lemma Suc_times_mod_eq: "1<k ==> Suc (k * m) mod k = 1" 
   322 lemma Suc_times_mod_eq: "1<k ==> Suc (k * m) mod k = 1" 
   314 apply (induct "m")
   323 apply (induct "m")
   315 apply (simp_all add: mod_Suc)
   324 apply (simp_all add: mod_Suc)
   316 done
   325 done
   317 
   326