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Dan Frumin
iris-coq
Commits
0ed0d7f9
Commit
0ed0d7f9
authored
Jun 30, 2016
by
Jacques-Henri Jourdan
Browse files
Some properties of imap
parent
cdb38447
Changes
1
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Side-by-side
prelude/list.v
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0ed0d7f9
...
...
@@ -1265,6 +1265,21 @@ Proof.
take_app_alt
by
(
rewrite
?
app_length
,
?
take_length
,
?
Hk
;
lia
).
Qed
.
(
**
**
Properties
of
the
[
imap
]
function
*
)
Lemma
imap_cons
{
B
}
(
f
:
nat
→
A
→
B
)
x
l
:
imap
f
(
x
::
l
)
=
f
0
x
::
imap
(
f
∘
S
)
l
.
Proof
.
unfold
imap
.
simpl
.
f_equal
.
generalize
0.
induction
l
;
intros
n
;
simpl
;
repeat
(
auto
||
f_equal
).
Qed
.
Lemma
imap_ext
{
B
}
(
f
g
:
nat
→
A
→
B
)
l
:
(
∀
i
x
,
f
i
x
=
g
i
x
)
→
imap
f
l
=
imap
g
l
.
Proof
.
unfold
imap
.
intro
EQ
.
generalize
0.
induction
l
;
simpl
;
intros
n
;
f_equal
;
auto
.
Qed
.
(
**
**
Properties
of
the
[
mask
]
function
*
)
Lemma
mask_nil
f
β
s
:
mask
f
β
s
(
@
nil
A
)
=
[].
Proof
.
by
destruct
β
s
.
Qed
.
...
...
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