src/HOL/Nat.thy
changeset 24075 366d4d234814
parent 23852 3736cdf9398b
child 24091 109f19a13872
equal deleted inserted replaced
24074:40f414b87655 24075:366d4d234814
  1090   assumes 1: "t = s" and 2: "u = t"
  1090   assumes 1: "t = s" and 2: "u = t"
  1091   shows "u = s"
  1091   shows "u = s"
  1092   using 2 1 by (rule trans)
  1092   using 2 1 by (rule trans)
  1093 
  1093 
  1094 use "arith_data.ML"
  1094 use "arith_data.ML"
  1095 setup arith_setup
  1095 declaration {* K arith_setup *}
  1096 
  1096 
  1097 text{*The following proofs may rely on the arithmetic proof procedures.*}
  1097 text{*The following proofs may rely on the arithmetic proof procedures.*}
  1098 
  1098 
  1099 lemma le_iff_add: "(m::nat) \<le> n = (\<exists>k. n = m + k)"
  1099 lemma le_iff_add: "(m::nat) \<le> n = (\<exists>k. n = m + k)"
  1100   by (auto simp: le_eq_less_or_eq dest: less_imp_Suc_add)
  1100   by (auto simp: le_eq_less_or_eq dest: less_imp_Suc_add)