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Iris
stdpp
Commits
dbbda8cb
Commit
dbbda8cb
authored
Aug 26, 2014
by
Robbert Krebbers
Browse files
Prove that lockset ⊆ dom memory.
parent
7f9c5994
Changes
3
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Inline
Side-by-side
theories/base.v
View file @
dbbda8cb
...
...
@@ -815,6 +815,10 @@ Section prod_relation.
End
prod_relation
.
(** ** Other *)
Lemma
and_wlog_l
(
P
Q
:
Prop
)
:
(
Q
→
P
)
→
Q
→
(
P
∧
Q
).
Proof
.
tauto
.
Qed
.
Lemma
and_wlog_r
(
P
Q
:
Prop
)
:
P
→
(
P
→
Q
)
→
(
P
∧
Q
).
Proof
.
tauto
.
Qed
.
Instance
:
∀
A
B
(
x
:
B
),
Commutative
(=)
(
λ
_
_
:
A
,
x
).
Proof
.
red
.
trivial
.
Qed
.
Instance
:
∀
A
(
x
:
A
),
Associative
(=)
(
λ
_
_
:
A
,
x
).
...
...
theories/collections.v
View file @
dbbda8cb
...
...
@@ -35,6 +35,10 @@ Section simple_collection.
Qed
.
Lemma
collection_positive_l_alt
X
Y
:
X
≢
∅
→
X
∪
Y
≢
∅
.
Proof
.
eauto
using
collection_positive_l
.
Qed
.
Lemma
elem_of_singleton_1
x
y
:
x
∈
{[
y
]}
→
x
=
y
.
Proof
.
by
rewrite
elem_of_singleton
.
Qed
.
Lemma
elem_of_singleton_2
x
y
:
x
=
y
→
x
∈
{[
y
]}.
Proof
.
by
rewrite
elem_of_singleton
.
Qed
.
Lemma
elem_of_subseteq_singleton
x
X
:
x
∈
X
↔
{[
x
]}
⊆
X
.
Proof
.
split
.
...
...
theories/numbers.v
View file @
dbbda8cb
...
...
@@ -264,7 +264,11 @@ Arguments Z.modulo _ _ : simpl never.
Arguments
Z
.
quot
_
_
:
simpl
never
.
Arguments
Z
.
rem
_
_
:
simpl
never
.
Lemma
Z_mod_pos
a
b
:
0
<
b
→
0
≤
a
`
mod
`
b
.
Lemma
Z_to_nat_neq_0_pos
x
:
Z
.
to_nat
x
≠
0
%
nat
→
0
<
x
.
Proof
.
by
destruct
x
.
Qed
.
Lemma
Z_to_nat_neq_0_nonneg
x
:
Z
.
to_nat
x
≠
0
%
nat
→
0
≤
x
.
Proof
.
by
destruct
x
.
Qed
.
Lemma
Z_mod_pos
x
y
:
0
<
y
→
0
≤
x
`
mod
`
y
.
Proof
.
apply
Z
.
mod_pos_bound
.
Qed
.
Hint
Resolve
Z
.
lt_le_incl
:
zpos
.
...
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