src/HOL/MiniML/Maybe.ML

 qed "option_bind_None";
 
 Addsimps [option_bind_Some,option_bind_None];
 
 (* expansion of option_bind *)
-goal thy
-  "P(option_bind res f) = ((res = None --> P None) & (!s. res = Some s --> P(f s)))";
-by (option.induct_tac "res" 1);
-by (fast_tac (HOL_cs addss !simpset) 1);
-by (Asm_simp_tac 1);
-qed "expand_option_bind";
+goalw thy [option_bind_def] "P(option_bind res f) = \
+\         ((res = None --> P None) & (!s. res = Some s --> P(f s)))";
+br split_option_case 1;
+qed "split_option_bind";
 
 goal thy
   "((option_bind m f) = None) = ((m=None) | (? p. m = Some p & f p = None))";
-by(simp_tac (!simpset addsplits [expand_option_bind]) 1);
+by(simp_tac (!simpset addsplits [split_option_bind]) 1);
 qed "option_bind_eq_None";
 
 Addsimps [option_bind_eq_None];
 
 (* auxiliary lemma *)