Definition tycontext_eqv (Delta Delta' : tycontext) : Prop :=
(forall id, (temp_types Delta) ! id = (temp_types Delta') ! id)
/\ (forall id, (var_types Delta) ! id = (var_types Delta') ! id)
/\ ret_type Delta = ret_type Delta'
/\ (forall id, (glob_types Delta) ! id = (glob_types Delta') ! id)
/\ (forall id, (glob_specs Delta) ! id = (glob_specs Delta') ! id)
/\ (forall id, (annotations Delta) ! id = (annotations Delta') ! id).

Lemma tycontext_eqv_spec: forall Delta Delta',
tycontext_eqv Delta Delta' <-> tycontext_sub Delta Delta' /\ tycontext_sub Delta' Delta.