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Rodolphe Lepigre
Iris
Commits
786857a6
Commit
786857a6
authored
Sep 01, 2016
by
Robbert Krebbers
Browse files
Relate ≼ and ⊆ on coPset and gset.
parent
36159b49
Changes
2
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Inline
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algebra/coPset.v
View file @
786857a6
...
...
@@ -27,6 +27,13 @@ Section coPset.
repeat
(
simpl
||
case_decide
)
;
first
[
apply
(
f_equal
CoPset
)|
done
|
exfalso
]
;
set_solver
by
eauto
.
Lemma
coPset_included
X
Y
:
CoPset
X
≼
CoPset
Y
↔
X
⊆
Y
.
Proof
.
split
.
-
move
=>
[[
Z
|]]
;
simpl
;
try
case_decide
;
set_solver
.
-
intros
(
Z
&->&?)%
subseteq_disjoint_union_L
.
exists
(
CoPset
Z
).
coPset_disj_solve
.
Qed
.
Lemma
coPset_disj_valid_inv_l
X
Y
:
✓
(
CoPset
X
⋅
Y
)
→
∃
Y'
,
Y
=
CoPset
Y'
∧
X
⊥
Y'
.
Proof
.
destruct
Y
;
repeat
(
simpl
||
case_decide
)
;
by
eauto
.
Qed
.
...
...
algebra/gset.v
View file @
786857a6
...
...
@@ -28,6 +28,13 @@ Section gset.
repeat
(
simpl
||
case_decide
)
;
first
[
apply
(
f_equal
GSet
)|
done
|
exfalso
]
;
set_solver
by
eauto
.
Lemma
coPset_included
X
Y
:
GSet
X
≼
GSet
Y
↔
X
⊆
Y
.
Proof
.
split
.
-
move
=>
[[
Z
|]]
;
simpl
;
try
case_decide
;
set_solver
.
-
intros
(
Z
&->&?)%
subseteq_disjoint_union_L
.
exists
(
GSet
Z
).
gset_disj_solve
.
Qed
.
Lemma
gset_disj_valid_inv_l
X
Y
:
✓
(
GSet
X
⋅
Y
)
→
∃
Y'
,
Y
=
GSet
Y'
∧
X
⊥
Y'
.
Proof
.
destruct
Y
;
repeat
(
simpl
||
case_decide
)
;
by
eauto
.
Qed
.
Lemma
gset_disj_union
X
Y
:
X
⊥
Y
→
GSet
X
⋅
GSet
Y
=
GSet
(
X
∪
Y
).
...
...
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