Hint Resolve binds_In AtomSetImpl.singleton_1 in_singleton_subset.
(* *)

Theorem context_fv_mutual :
(forall G (a : tm) A (H: Typing G a A),
fv_tm_tm_tm a [<=] dom G /\ fv_co_co_tm a [<=] dom G /\
fv_tm_tm_tm A [<=] dom G /\ fv_co_co_tm A [<=] dom G)
/\
(forall G phi (H : PropWff G phi),
fv_tm_tm_constraint phi [<=] dom G /\ fv_co_co_constraint phi [<=] dom G)
/\
(forall G D p1 p2 (H : Iso G D p1 p2),
fv_tm_tm_constraint p1 [<=] dom G /\ fv_co_co_constraint p1 [<=] dom G /\
fv_tm_tm_constraint p2 [<=] dom G /\ fv_co_co_constraint p2 [<=] dom G)
/\
(forall G D A B T (H : DefEq G D A B T),
(fv_tm_tm_tm A [<=] dom G /\ fv_co_co_tm A [<=] dom G /\
fv_tm_tm_tm B [<=] dom G /\ fv_co_co_tm B [<=] dom G /\
fv_tm_tm_tm T [<=] dom G /\ fv_co_co_tm T [<=] dom G))
/\
(forall G (H : Ctx G),
(forall x A,
binds x (Tm A)   G ->
fv_tm_tm_tm         A   [<=] dom G /\ fv_co_co_tm         A   [<=] dom G) /\
(forall c phi,
binds c (Co phi) G ->
fv_tm_tm_constraint phi [<=] dom G /\ fv_co_co_constraint phi [<=] dom G)).