src/HOL/Wellfounded_Relations.ML
changeset 10996 74e970389def
parent 10653 55f33da63366
child 11142 42181d7cd7b2
equal deleted inserted replaced
10995:ef0b521698b7 10996:74e970389def
   196 qed "wf_weak_decr_stable";
   196 qed "wf_weak_decr_stable";
   197 
   197 
   198 (* special case: <= *)
   198 (* special case: <= *)
   199 
   199 
   200 Goal "(m, n) : pred_nat^* = (m <= n)";
   200 Goal "(m, n) : pred_nat^* = (m <= n)";
   201 by (simp_tac (simpset() addsimps [less_eq, reflcl_trancl RS sym] 
   201 by (simp_tac (simpset() addsimps [less_eq, thm"reflcl_trancl" RS sym] 
   202                         delsimps [reflcl_trancl]) 1);
   202                         delsimps [thm"reflcl_trancl"]) 1);
   203 by (arith_tac 1);
   203 by (arith_tac 1);
   204 qed "le_eq";
   204 qed "le_eq";
   205 
   205 
   206 Goal "ALL i. f (Suc i) <= ((f i)::nat) ==> EX i. ALL k. f (i+k) = f i";
   206 Goal "ALL i. f (Suc i) <= ((f i)::nat) ==> EX i. ALL k. f (i+k) = f i";
   207 by (res_inst_tac [("r","pred_nat")] wf_weak_decr_stable 1);
   207 by (res_inst_tac [("r","pred_nat")] wf_weak_decr_stable 1);