Some types in the calculus of constructions
We can verify by Check that these types are admissible
and of sort Type.
One can also consider the formal rules of construction od dependant
product, and do the verification manually.
The predicate associated to strictly monotonous functions from
nat to nat has type (nat->nat)->Prop
The pointwise ordering on nat->nat :
fun f g : nat-> nat => forall n:nat, f n <= g n
We can consider for instance a constant
boolean_matrix : nat->nat->Set
such that, if n and p are of type nat,
boolean_matrix n p
is the type of boolean matrices of height n
and width p. This type has sort Set.