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David Swasey
coqstdpp
Commits
5f737816
Commit
5f737816
authored
Jan 30, 2015
by
Robbert Krebbers
Browse files
Type punning for lookup/alter on values.
parent
5644d68f
Changes
1
Hide whitespace changes
Inline
Sidebyside
theories/list.v
View file @
5f737816
...
...
@@ 1972,6 +1972,15 @@ Section Forall_Exists.
Proof
.
intros
H
.
apply
Forall_proper
.
red
;
apply
H
.
done
.
Qed
.
Lemma
Forall_not
l
:
length
l
≠
0
→
Forall
(
not
∘
P
)
l
→
¬
Forall
P
l
.
Proof
.
by
destruct
2
;
inversion
1
.
Qed
.
Lemma
Forall_and
{
Q
}
l
:
Forall
(
λ
x
,
P
x
∧
Q
x
)
l
↔
Forall
P
l
∧
Forall
Q
l
.
Proof
.
split
;
[
induction
1
;
constructor
;
naive_solver
].
intros
[
Hl
Hl'
]
;
revert
Hl'
;
induction
Hl
;
inversion_clear
1
;
auto
.
Qed
.
Lemma
Forall_and_l
{
Q
}
l
:
Forall
(
λ
x
,
P
x
∧
Q
x
)
l
→
Forall
P
l
.
Proof
.
rewrite
Forall_and
;
tauto
.
Qed
.
Lemma
Forall_and_r
{
Q
}
l
:
Forall
(
λ
x
,
P
x
∧
Q
x
)
l
→
Forall
Q
l
.
Proof
.
rewrite
Forall_and
;
tauto
.
Qed
.
Lemma
Forall_delete
l
i
:
Forall
P
l
→
Forall
P
(
delete
i
l
).
Proof
.
intros
H
.
revert
i
.
by
induction
H
;
intros
[
i
]
;
try
constructor
.
Qed
.
Lemma
Forall_lookup
l
:
Forall
P
l
↔
∀
i
x
,
l
!!
i
=
Some
x
→
P
x
.
...
...
@@ 2275,26 +2284,39 @@ Section Forall2.
intros
.
rewrite
!
resize_spec
,
(
Forall2_length
l
k
)
by
done
.
auto
using
Forall2_app
,
Forall2_take
,
Forall2_replicate
.
Qed
.
Lemma
Forall2_resize_
ge_
l
l
k
x
y
n
m
:
P
x
y
→
Forall
(
flip
P
y
)
l
→
n
≤
m
→
Lemma
Forall2_resize_l
l
k
x
y
n
m
:
P
x
y
→
Forall
(
flip
P
y
)
l
→
Forall2
P
(
resize
n
x
l
)
k
→
Forall2
P
(
resize
m
x
l
)
(
resize
m
y
k
).
Proof
.
intros
.
assert
(
n
=
length
k
)
as
>.
intros
.
destruct
(
decide
(
m
≤
n
)).
{
rewrite
<(
resize_resize
l
m
n
)
by
done
.
by
apply
Forall2_resize
.
}
intros
.
assert
(
n
=
length
k
)
;
subst
.
{
by
rewrite
<(
Forall2_length
(
resize
n
x
l
)
k
),
resize_length
.
}
rewrite
(
le_plus_minus
(
length
k
)
m
),
!
resize_plus
,
resize_all
,
drop_all
,
resize_nil
by
done
;
auto
using
Forall2_app
,
Forall2_replicate_r
,
rewrite
(
le_plus_minus
(
length
k
)
m
),
!
resize_plus
,
resize_all
,
drop_all
,
resize_nil
by
lia
.
auto
using
Forall2_app
,
Forall2_replicate_r
,
Forall_resize
,
Forall_drop
,
resize_length
.
Qed
.
Lemma
Forall2_resize_
ge_
r
l
k
x
y
n
m
:
P
x
y
→
Forall
(
P
x
)
k
→
n
≤
m
→
Lemma
Forall2_resize_r
l
k
x
y
n
m
:
P
x
y
→
Forall
(
P
x
)
k
→
Forall2
P
l
(
resize
n
y
k
)
→
Forall2
P
(
resize
m
x
l
)
(
resize
m
y
k
).
Proof
.
intros
.
assert
(
n
=
length
l
)
as
>.
intros
.
destruct
(
decide
(
m
≤
n
)).
{
rewrite
<(
resize_resize
k
m
n
)
by
done
.
by
apply
Forall2_resize
.
}
assert
(
n
=
length
l
)
;
subst
.
{
by
rewrite
(
Forall2_length
l
(
resize
n
y
k
)),
resize_length
.
}
rewrite
(
le_plus_minus
(
length
l
)
m
),
!
resize_plus
,
resize_all
,
drop_all
,
resize_nil
by
done
;
auto
using
Forall2_app
,
Forall2_replicate_l
,
rewrite
(
le_plus_minus
(
length
l
)
m
),
!
resize_plus
,
resize_all
,
drop_all
,
resize_nil
by
lia
.
auto
using
Forall2_app
,
Forall2_replicate_l
,
Forall_resize
,
Forall_drop
,
resize_length
.
Qed
.
Lemma
Forall2_resize_r_flip
l
k
x
y
n
m
:
P
x
y
→
Forall
(
P
x
)
k
→
length
k
=
m
→
Forall2
P
l
(
resize
n
y
k
)
→
Forall2
P
(
resize
m
x
l
)
k
.
Proof
.
intros
??
<
?.
rewrite
<(
resize_all
k
y
)
at
2
.
apply
Forall2_resize_r
with
n
;
auto
using
Forall_true
.
Qed
.
Lemma
Forall2_sublist_lookup_l
l
k
n
i
l'
:
Forall2
P
l
k
→
sublist_lookup
n
i
l
=
Some
l'
→
∃
k'
,
sublist_lookup
n
i
k
=
Some
k'
∧
Forall2
P
l'
k'
.
...
...
@@ 3243,14 +3265,16 @@ Ltac decompose_Forall_hyps :=
let
E
:
=
fresh
in
assert
(
P
x
)
as
E
by
(
apply
(
Forall_lookup_1
P
_
_
_
H
H1
))
;
lazy
beta
in
E

H
:
Forall2
?P
?l
?k

_
=>
lazy
match
goal
with
match
goal
with

H1
:
l
!!
?i
=
Some
?x
,
H2
:
k
!!
?i
=
Some
?y

_
=>
unless
(
P
x
y
)
by
done
;
let
E
:
=
fresh
in
assert
(
P
x
y
)
as
E
by
(
by
apply
(
Forall2_lookup_lr
P
l
k
i
x
y
))
;
lazy
beta
in
E

H1
:
l
!!
_
=
Some
?x

_
=>

H1
:
l
!!
?i
=
Some
?x

_
=>
try
(
match
goal
with
_
:
k
!!
i
=
Some
_

_
=>
fail
2
end
)
;
destruct
(
Forall2_lookup_l
P
_
_
_
_
H
H1
)
as
(?&?&?)

H2
:
k
!!
_
=
Some
?y

_
=>

H2
:
k
!!
?i
=
Some
?y

_
=>
try
(
match
goal
with
_
:
l
!!
i
=
Some
_

_
=>
fail
2
end
)
;
destruct
(
Forall2_lookup_r
P
_
_
_
_
H
H2
)
as
(?&?&?)
end

H
:
Forall3
?P
?l
?l'
?k

_
=>
...
...
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