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0d471f47
Commit
0d471f47
authored
Dec 20, 2016
by
Ralf Jung
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show lemma about big_sepL and zip_with
parent
1c9e8581
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#3447
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in 10 minutes and 55 seconds
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2 changed files
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29 additions
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1 deletion
+29
-1
theories/base_logic/big_op.v
theories/base_logic/big_op.v
+28
-0
theories/heap_lang/lifting.v
theories/heap_lang/lifting.v
+1
-1
No files found.
theories/base_logic/big_op.v
View file @
0d471f47
...
...
@@ -312,6 +312,34 @@ Section list.
Proof
.
rewrite
/
big_opL
.
apply
_
.
Qed
.
End
list
.
Section
list2
.
Context
{
A
:
Type
}.
Implicit
Types
l
:
list
A
.
Implicit
Types
Φ
Ψ
:
nat
→
A
→
uPred
M
.
(* Some lemmas depend on the generalized versions of the above ones. *)
Lemma
big_sepL_zip_with
{
B
C
}
Φ
f
(
l1
:
list
B
)
(
l2
:
list
C
)
:
([
∗
list
]
k
↦
x
∈
zip_with
f
l1
l2
,
Φ
k
x
)
⊣
⊢
([
∗
list
]
k
↦
x
∈
l1
,
∀
y
,
⌜
l2
!!
k
=
Some
y
⌝
→
Φ
k
(
f
x
y
)).
Proof
.
revert
Φ
l2
;
induction
l1
;
intros
Φ
l2
;
first
by
rewrite
/=
big_sepL_nil
.
destruct
l2
;
simpl
.
{
rewrite
big_sepL_nil
.
apply
(
anti_symm
_
)
;
last
exact
:
True_intro
.
(* TODO: Can this be done simpler? *)
rewrite
-(
big_sepL_mono
(
λ
_
_
,
True
%
I
)).
-
rewrite
big_sepL_forall
.
apply
forall_intro
=>
k
.
apply
forall_intro
=>
b
.
apply
impl_intro_r
.
apply
True_intro
.
-
intros
k
b
_
.
apply
forall_intro
=>
c
.
apply
impl_intro_l
.
rewrite
right_id
.
apply
pure_elim'
.
done
.
}
rewrite
!
big_sepL_cons
.
apply
sep_proper
;
last
exact
:
IHl1
.
apply
(
anti_symm
_
).
-
apply
forall_intro
=>
c'
.
simpl
.
apply
impl_intro_r
.
eapply
pure_elim
;
first
exact
:
and_elim_r
.
intros
[=->].
apply
and_elim_l
.
-
rewrite
(
forall_elim
c
).
simpl
.
eapply
impl_elim
;
first
done
.
apply
pure_intro
.
done
.
Qed
.
End
list2
.
(** ** Big ops over finite maps *)
Section
gmap
.
...
...
theories/heap_lang/lifting.v
View file @
0d471f47
...
...
@@ -64,7 +64,7 @@ Lemma wp_bind {E e} K Φ :
WP
e
@
E
{{
v
,
WP
fill
K
(
of_val
v
)
@
E
{{
Φ
}}
}}
⊢
WP
fill
K
e
@
E
{{
Φ
}}.
Proof
.
exact
:
wp_ectx_bind
.
Qed
.
Lemma
wp_bind
_ctx
i
{
E
e
}
Ki
Φ
:
Lemma
wp_bindi
{
E
e
}
Ki
Φ
:
WP
e
@
E
{{
v
,
WP
fill_item
Ki
(
of_val
v
)
@
E
{{
Φ
}}
}}
⊢
WP
fill_item
Ki
e
@
E
{{
Φ
}}.
Proof
.
exact
:
weakestpre
.
wp_bind
.
Qed
.
...
...
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