src/HOL/Codatatype/BNF_Library.thy

 
 lemma obj_sum_step:
   "\<lbrakk>\<forall>x. s = f (Inr (Inl x)) \<longrightarrow> P; \<forall>x. s = f (Inr (Inr x)) \<longrightarrow> P\<rbrakk> \<Longrightarrow> \<forall>x. s = f (Inr x) \<longrightarrow> P"
 by (metis obj_sumE)
 
+lemma sum_map_if:
+"sum_map f g (if p then Inl x else Inr y) = (if p then Inl (f x) else Inr (g y))"
+by simp
+
+lemma sum_case_if:
+"sum_case f g (if p then Inl x else Inr y) = (if p then f x else g y)"
+by simp
+
 lemma not_arg_cong_Inr: "x \<noteq> y \<Longrightarrow> Inr x \<noteq> Inr y"
 by simp
 
 end