theory SingleLet
imports "../NewParser"
begin

atom_decl name

ML {* val _ = cheat_alpha_eqvt := true *}

nominal_datatype trm =
  Var "name"
| App "trm" "trm"
| Lam x::"name" t::"trm"  bind_set x in t
| Let a::"assg" t::"trm"  bind_set "bn a" in t
and assg =
  As "name" "trm"
binder
  bn::"assg \<Rightarrow> atom set"
where
  "bn (As x t) = {atom x}"

thm alpha_trm_raw_alpha_assg_raw_alpha_bn_raw.intros[no_vars]
thm trm_assg.fv
thm trm_assg.supp
thm trm_assg.eq_iff
thm trm_assg.bn
thm trm_assg.perm
thm trm_assg.induct
thm trm_assg.inducts
thm trm_assg.distinct
ML {* Sign.of_sort @{theory} (@{typ trm}, @{sort fs}) *}
thm trm_assg.fv[simplified trm_assg.supp(1-2)]

setup {* Context.theory_map (Nominal_ThmDecls.add_thm @{thm "permute_pure"}) *}
declare permute_trm_raw_permute_assg_raw.simps[eqvt]
declare alpha_gen_eqvt[eqvt]
equivariance alpha_trm_raw


end