theory Ex2
imports "../NewParser"
begin

text {* example 2 *}
declare [[STEPS = 9]]

atom_decl name

nominal_datatype trm =
  Var "name"
| App "trm" "trm"
| Lam x::"name" t::"trm"          bind_set x in t
| Let p::"pat" "trm" t::"trm"   bind_set "f p" in t
and pat =
  PN
| PS "name"
| PD "name" "name"
binder
  f::"pat \<Rightarrow> atom set"
where
  "f PN = {}"
| "f (PD x y) = {atom x, atom y}"
| "f (PS x) = {atom x}"

thm fv_trm_raw.simps[no_vars] fv_pat_raw.simps[no_vars] fv_f_raw.simps[no_vars] f_raw.simps[no_vars]
thm alpha_trm_raw_alpha_pat_raw_alpha_f_raw.intros[no_vars]




thm trm_pat.bn
thm trm_pat.perm
thm trm_pat.induct
thm trm_pat.distinct
thm trm_pat.fv[simplified trm_pat.supp(1-2)]


end