[isabelle] apply (cases a b c)

Is there a built-in way to generate subgoals for all cases of a set of

For instance, suppose I have the definitions:

  datatype dt = Num int | Infinity
  fun plus :: "dt ⇒ dt ⇒ dt"
    "plus Infinity _ = Infinity"
  | "plus _ Infinity = Infinity"
  | "plus (Num a) (Num b) = Num (a + b)"

And now that I want to show:

  lemma "plus a b = plus b a"

I would like to be able to type:
    by (cases a b) simp_all

But this is not supported.

I know that I can type:
  by (tactic "(List.foldl (op THEN_ALL_NEW) (fn i => all_tac)
                (List.map (Induct_Tacs.case_tac @{context}) ["a", "b"]) 1)")

But somehow this is not very pleasing!

So, is there a good way to do this?

Would it be worth extending the cases method?


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