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Iris
stdpp
Commits
4933fa76
Commit
4933fa76
authored
Jun 06, 2018
by
Ralf Jung
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also provide a composition for the function space
parent
cee2597b
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theories/telescopes.v
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theories/telescopes.v
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4933fa76
...
...
@@ -104,13 +104,22 @@ Proof.
rewrite
IH
.
done
.
Qed
.
(** We can define the identity function of the [-t>] function space. *)
(** We can define the identity function and composition of the [-t>] function
space. *)
Definition
tele_id
{
TT
:
tele
}
:
TT
-
t
>
TT
:
=
tele_bind
id
.
Lemma
tele_id_eq
{
TT
:
tele
}
(
x
:
TT
)
:
tele_id
x
=
x
.
Proof
.
unfold
tele_id
.
rewrite
tele_app_bind
.
done
.
Qed
.
Definition
tele_compose
{
TT1
TT2
TT3
:
tele
}
:
(
TT2
-
t
>
TT3
)
→
(
TT1
-
t
>
TT2
)
→
(
TT1
-
t
>
TT3
)
:
=
λ
t1
t2
,
tele_bind
(
compose
(
tele_app
t1
)
(
tele_app
t2
)).
Lemma
tele_compose_eq
{
TT1
TT2
TT3
:
tele
}
(
f
:
TT2
-
t
>
TT3
)
(
g
:
TT1
-
t
>
TT2
)
x
:
tele_compose
f
g
$
x
=
(
f
∘
g
)
x
.
Proof
.
unfold
tele_compose
.
rewrite
tele_app_bind
.
done
.
Qed
.
(** Notation *)
Notation
"'[tele' x .. z ]"
:
=
(
TeleS
(
fun
x
=>
..
(
TeleS
(
fun
z
=>
TeleO
))
..))
...
...
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