End MSUBST_DENOTE_TC_ASSERT.
Definition legal_tc_init (Delta: tycontext): tc_assert -> Prop :=
fix legal_tc_init (tc: tc_assert): Prop :=
match tc with
| tc_andp' tc1 tc2 => legal_tc_init tc1 /\ legal_tc_init tc2
| tc_orp' tc1 tc2 => legal_tc_init tc1 /\ legal_tc_init tc2
| tc_initialized i t => (temp_types Delta) ! i = Some t
| _ => True
end.

Lemma temp_tc_initialized: forall Delta i t v,
(temp_types Delta) ! i = Some t ->
local (tc_environ Delta) && local (locald_denote (temp i v))
|-- denote_tc_initialized i t.