theory Ex1
imports "../Nominal2"
begin

(* free names in bar are bound in foo *)

atom_decl name

nominal_datatype foo =
  Foo0 "name"
| Foo1 b::"bar" f::"foo" bind (set) "bv b" in f
and bar =
  Bar0 "name"
| Bar1 "name" s::"name" b::"bar" bind (set) s in b
binder
  bv
where
  "bv (Bar0 x) = {}"
| "bv (Bar1 v x b) = {atom v}"


thm foo_bar.fv_defs[no_vars] foo_bar.bn_defs[no_vars]

lemma
  "fv_foo (Foo1 (Bar1 v x (Bar0 x)) (Foo0 v)) = {}"
apply(simp only: foo_bar.fv_defs)
apply(simp only: foo_bar.bn_defs)
apply(simp only: supp_at_base)
apply(simp)
done

end