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Simon Spies
stdpp
Commits
fe66a96f
Commit
fe66a96f
authored
May 24, 2014
by
Robbert Krebbers
Browse files
Restore memory.v
parent
bb9d75d9
Changes
1
Hide whitespace changes
Inline
Side-by-side
theories/list.v
View file @
fe66a96f
...
...
@@ -1849,11 +1849,9 @@ Section Forall_Exists.
Definition
Forall_cons_2
:
=
@
Forall_cons
A
.
Lemma
Forall_forall
l
:
Forall
P
l
↔
∀
x
,
x
∈
l
→
P
x
.
Proof
.
split
.
{
induction
1
;
inversion
1
;
subst
;
auto
.
}
intros
Hin
.
induction
l
;
constructor
.
*
apply
Hin
.
constructor
.
*
apply
IHl
.
intros
??.
apply
Hin
.
by
constructor
.
split
;
[
induction
1
;
inversion
1
;
subst
;
auto
|].
intros
Hin
;
induction
l
as
[|
x
l
IH
]
;
constructor
;
[
apply
Hin
;
constructor
|].
apply
IH
.
intros
??.
apply
Hin
.
by
constructor
.
Qed
.
Lemma
Forall_nil
:
Forall
P
[]
↔
True
.
Proof
.
done
.
Qed
.
...
...
@@ -1867,9 +1865,8 @@ Section Forall_Exists.
Proof
.
induction
1
;
simpl
;
auto
.
Qed
.
Lemma
Forall_app
l1
l2
:
Forall
P
(
l1
++
l2
)
↔
Forall
P
l1
∧
Forall
P
l2
.
Proof
.
split
.
*
induction
l1
;
inversion
1
;
intuition
.
*
intros
[??]
;
auto
using
Forall_app_2
.
split
;
[
induction
l1
;
inversion
1
;
intuition
|].
intros
[??]
;
auto
using
Forall_app_2
.
Qed
.
Lemma
Forall_true
l
:
(
∀
x
,
P
x
)
→
Forall
P
l
.
Proof
.
induction
l
;
auto
.
Qed
.
...
...
@@ -1881,7 +1878,9 @@ Section Forall_Exists.
Proof
.
split
;
subst
;
induction
1
;
constructor
(
by
firstorder
auto
).
Qed
.
Lemma
Forall_iff
l
(
Q
:
A
→
Prop
)
:
(
∀
x
,
P
x
↔
Q
x
)
→
Forall
P
l
↔
Forall
Q
l
.
Proof
.
intros
H
.
apply
Forall_proper
.
red
.
apply
H
.
done
.
Qed
.
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_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
.
...
...
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