Dependent product types in a universe
Definition.
A universe
(
U
,
El
)
is said to
have dependent product types
if we have the following
dprod
(
dpair
,
dproj
)
:
(
A
:
U
)
→
(
B
:
El
A
→
U
)
→
U
:
(
a
:
El
A
)
×
El
(
B
a
)
≅
El
(
dprod
A
B
)
Contrast the more traditional type-theoretic formulation.
