Multi-level type formers
Definition.
A cwf with a universe
U
is said to have
U
-small dependent functions if we have
fun
(
lam
,
app
)
:
(
A
:
Tm
Γ
U
)
→
(
B
:
Ty
(
Γ
▹
El
A
))
→
Ty
Γ
:
Tm
(
Γ
▹
El
A
)
B
≅
Tm
Γ
(
fun
A
B
)