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David Swasey
coq-stdpp
Commits
5061c3cb
Commit
5061c3cb
authored
Mar 09, 2017
by
Robbert Krebbers
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Rename preserving -> mono.
To be consistent with Iris, see Iris commit 9ee62b3a.
parent
81d719c9
Changes
3
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3 changed files
with
19 additions
and
19 deletions
+19
-19
theories/collections.v
theories/collections.v
+11
-11
theories/fin_maps.v
theories/fin_maps.v
+3
-3
theories/gmultiset.v
theories/gmultiset.v
+5
-5
No files found.
theories/collections.v
View file @
5061c3cb
...
...
@@ -346,11 +346,11 @@ Section simple_collection.
Proof
.
set_solver
.
Qed
.
Lemma
elem_of_union_r
x
X
Y
:
x
∈
Y
→
x
∈
X
∪
Y
.
Proof
.
set_solver
.
Qed
.
Lemma
union_
preserving
_l
X
Y1
Y2
:
Y1
⊆
Y2
→
X
∪
Y1
⊆
X
∪
Y2
.
Lemma
union_
mono
_l
X
Y1
Y2
:
Y1
⊆
Y2
→
X
∪
Y1
⊆
X
∪
Y2
.
Proof
.
set_solver
.
Qed
.
Lemma
union_
preserving
_r
X1
X2
Y
:
X1
⊆
X2
→
X1
∪
Y
⊆
X2
∪
Y
.
Lemma
union_
mono
_r
X1
X2
Y
:
X1
⊆
X2
→
X1
∪
Y
⊆
X2
∪
Y
.
Proof
.
set_solver
.
Qed
.
Lemma
union_
preserving
X1
X2
Y1
Y2
:
X1
⊆
X2
→
Y1
⊆
Y2
→
X1
∪
Y1
⊆
X2
∪
Y2
.
Lemma
union_
mono
X1
X2
Y1
Y2
:
X1
⊆
X2
→
Y1
⊆
Y2
→
X1
∪
Y1
⊆
X2
∪
Y2
.
Proof
.
set_solver
.
Qed
.
Global
Instance
union_idemp
:
IdemP
((
≡
)
:
relation
C
)
(
∪
).
...
...
@@ -444,8 +444,8 @@ Section simple_collection.
by
rewrite
reverse_cons
,
union_list_app
,
union_list_singleton
,
(
comm
_
),
IH
.
Qed
.
Lemma
union_list_
preserving
Xs
Ys
:
Xs
⊆
*
Ys
→
⋃
Xs
⊆
⋃
Ys
.
Proof
.
induction
1
;
simpl
;
auto
using
union_
preserving
.
Qed
.
Lemma
union_list_
mono
Xs
Ys
:
Xs
⊆
*
Ys
→
⋃
Xs
⊆
⋃
Ys
.
Proof
.
induction
1
;
simpl
;
auto
using
union_
mono
.
Qed
.
Lemma
empty_union_list
Xs
:
⋃
Xs
≡
∅
↔
Forall
(
≡
∅
)
Xs
.
Proof
.
split
.
...
...
@@ -565,11 +565,11 @@ Section collection.
Lemma
intersection_greatest
X
Y
Z
:
Z
⊆
X
→
Z
⊆
Y
→
Z
⊆
X
∩
Y
.
Proof
.
set_solver
.
Qed
.
Lemma
intersection_
preserving
_l
X
Y1
Y2
:
Y1
⊆
Y2
→
X
∩
Y1
⊆
X
∩
Y2
.
Lemma
intersection_
mono
_l
X
Y1
Y2
:
Y1
⊆
Y2
→
X
∩
Y1
⊆
X
∩
Y2
.
Proof
.
set_solver
.
Qed
.
Lemma
intersection_
preserving
_r
X1
X2
Y
:
X1
⊆
X2
→
X1
∩
Y
⊆
X2
∩
Y
.
Lemma
intersection_
mono
_r
X1
X2
Y
:
X1
⊆
X2
→
X1
∩
Y
⊆
X2
∩
Y
.
Proof
.
set_solver
.
Qed
.
Lemma
intersection_
preserving
X1
X2
Y1
Y2
:
Lemma
intersection_
mono
X1
X2
Y1
Y2
:
X1
⊆
X2
→
Y1
⊆
Y2
→
X1
∩
Y1
⊆
X2
∩
Y2
.
Proof
.
set_solver
.
Qed
.
...
...
@@ -612,12 +612,12 @@ Section collection.
Lemma
difference_disjoint
X
Y
:
X
⊥
Y
→
X
∖
Y
≡
X
.
Proof
.
set_solver
.
Qed
.
Lemma
difference_
preserving
X1
X2
Y1
Y2
:
Lemma
difference_
mono
X1
X2
Y1
Y2
:
X1
⊆
X2
→
Y2
⊆
Y1
→
X1
∖
Y1
⊆
X2
∖
Y2
.
Proof
.
set_solver
.
Qed
.
Lemma
difference_
preserving
_l
X
Y1
Y2
:
Y2
⊆
Y1
→
X
∖
Y1
⊆
X
∖
Y2
.
Lemma
difference_
mono
_l
X
Y1
Y2
:
Y2
⊆
Y1
→
X
∖
Y1
⊆
X
∖
Y2
.
Proof
.
set_solver
.
Qed
.
Lemma
difference_
preserving
_r
X1
X2
Y
:
X1
⊆
X2
→
X1
∖
Y
⊆
X2
∖
Y
.
Lemma
difference_
mono
_r
X1
X2
Y
:
X1
⊆
X2
→
X1
∖
Y
⊆
X2
∖
Y
.
Proof
.
set_solver
.
Qed
.
(** Disjointness *)
...
...
theories/fin_maps.v
View file @
5061c3cb
...
...
@@ -1322,17 +1322,17 @@ Proof. intros. trans m2; auto using map_union_subseteq_l. Qed.
Lemma
map_union_subseteq_r_alt
{
A
}
(
m1
m2
m3
:
M
A
)
:
m2
⊥
ₘ
m3
→
m1
⊆
m3
→
m1
⊆
m2
∪
m3
.
Proof
.
intros
.
trans
m3
;
auto
using
map_union_subseteq_r
.
Qed
.
Lemma
map_union_
preserving
_l
{
A
}
(
m1
m2
m3
:
M
A
)
:
m1
⊆
m2
→
m3
∪
m1
⊆
m3
∪
m2
.
Lemma
map_union_
mono
_l
{
A
}
(
m1
m2
m3
:
M
A
)
:
m1
⊆
m2
→
m3
∪
m1
⊆
m3
∪
m2
.
Proof
.
rewrite
!
map_subseteq_spec
.
intros
???.
rewrite
!
lookup_union_Some_raw
.
naive_solver
.
Qed
.
Lemma
map_union_
preserving
_r
{
A
}
(
m1
m2
m3
:
M
A
)
:
Lemma
map_union_
mono
_r
{
A
}
(
m1
m2
m3
:
M
A
)
:
m2
⊥
ₘ
m3
→
m1
⊆
m2
→
m1
∪
m3
⊆
m2
∪
m3
.
Proof
.
intros
.
rewrite
!(
map_union_comm
_
m3
)
by
eauto
using
map_disjoint_weaken_l
.
by
apply
map_union_
preserving
_l
.
by
apply
map_union_
mono
_l
.
Qed
.
Lemma
map_union_reflecting_l
{
A
}
(
m1
m2
m3
:
M
A
)
:
m3
⊥
ₘ
m1
→
m3
⊥
ₘ
m2
→
m3
∪
m1
⊆
m3
∪
m2
→
m1
⊆
m2
.
...
...
theories/gmultiset.v
View file @
5061c3cb
...
...
@@ -288,12 +288,12 @@ Lemma gmultiset_union_subseteq_l X Y : X ⊆ X ∪ Y.
Proof
.
intros
x
.
rewrite
multiplicity_union
.
omega
.
Qed
.
Lemma
gmultiset_union_subseteq_r
X
Y
:
Y
⊆
X
∪
Y
.
Proof
.
intros
x
.
rewrite
multiplicity_union
.
omega
.
Qed
.
Lemma
gmultiset_union_
preserving
X1
X2
Y1
Y2
:
X1
⊆
X2
→
Y1
⊆
Y2
→
X1
∪
Y1
⊆
X2
∪
Y2
.
Lemma
gmultiset_union_
mono
X1
X2
Y1
Y2
:
X1
⊆
X2
→
Y1
⊆
Y2
→
X1
∪
Y1
⊆
X2
∪
Y2
.
Proof
.
intros
??
x
.
rewrite
!
multiplicity_union
.
by
apply
Nat
.
add_le_mono
.
Qed
.
Lemma
gmultiset_union_
preserving
_l
X
Y1
Y2
:
Y1
⊆
Y2
→
X
∪
Y1
⊆
X
∪
Y2
.
Proof
.
intros
.
by
apply
gmultiset_union_
preserving
.
Qed
.
Lemma
gmultiset_union_
preserving
_r
X1
X2
Y
:
X1
⊆
X2
→
X1
∪
Y
⊆
X2
∪
Y
.
Proof
.
intros
.
by
apply
gmultiset_union_
preserving
.
Qed
.
Lemma
gmultiset_union_
mono
_l
X
Y1
Y2
:
Y1
⊆
Y2
→
X
∪
Y1
⊆
X
∪
Y2
.
Proof
.
intros
.
by
apply
gmultiset_union_
mono
.
Qed
.
Lemma
gmultiset_union_
mono
_r
X1
X2
Y
:
X1
⊆
X2
→
X1
∪
Y
⊆
X2
∪
Y
.
Proof
.
intros
.
by
apply
gmultiset_union_
mono
.
Qed
.
Lemma
gmultiset_subset
X
Y
:
X
⊆
Y
→
size
X
<
size
Y
→
X
⊂
Y
.
Proof
.
intros
.
apply
strict_spec_alt
;
split
;
naive_solver
auto
with
omega
.
Qed
.
...
...
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