Skip to content
GitLab
Projects
Groups
Snippets
Help
Loading...
Help
What's new
10
Help
Support
Community forum
Keyboard shortcuts
?
Submit feedback
Contribute to GitLab
Sign in / Register
Toggle navigation
Open sidebar
Simon Spies
Iris
Commits
e2efc09c
Commit
e2efc09c
authored
Feb 11, 2016
by
Ralf Jung
Browse files
Options
Browse Files
Download
Plain Diff
Merge branch 'master' of gitlab.mpi-sws.org:FP/iris-coq
parents
6ca92264
eb563833
Changes
2
Hide whitespace changes
Inline
Side-by-side
Showing
2 changed files
with
4 additions
and
21 deletions
+4
-21
algebra/cmra.v
algebra/cmra.v
+4
-0
prelude/numbers.v
prelude/numbers.v
+0
-21
No files found.
algebra/cmra.v
View file @
e2efc09c
...
...
@@ -272,8 +272,12 @@ Lemma cmra_unit_preserving x y : x ≼ y → unit x ≼ unit y.
Proof
.
rewrite
!
cmra_included_includedN
;
eauto
using
cmra_unit_preservingN
.
Qed
.
Lemma
cmra_included_unit
x
:
unit
x
≼
x
.
Proof
.
by
exists
x
;
rewrite
cmra_unit_l
.
Qed
.
Lemma
cmra_preservingN_l
n
x
y
z
:
x
≼
{
n
}
y
→
z
⋅
x
≼
{
n
}
z
⋅
y
.
Proof
.
by
intros
[
z1
Hz1
]
;
exists
z1
;
rewrite
Hz1
(
associative
op
).
Qed
.
Lemma
cmra_preserving_l
x
y
z
:
x
≼
y
→
z
⋅
x
≼
z
⋅
y
.
Proof
.
by
intros
[
z1
Hz1
]
;
exists
z1
;
rewrite
Hz1
(
associative
op
).
Qed
.
Lemma
cmra_preservingN_r
n
x
y
z
:
x
≼
{
n
}
y
→
x
⋅
z
≼
{
n
}
y
⋅
z
.
Proof
.
by
intros
;
rewrite
-!(
commutative
_
z
)
;
apply
cmra_preservingN_l
.
Qed
.
Lemma
cmra_preserving_r
x
y
z
:
x
≼
y
→
x
⋅
z
≼
y
⋅
z
.
Proof
.
by
intros
;
rewrite
-!(
commutative
_
z
)
;
apply
cmra_preserving_l
.
Qed
.
...
...
prelude/numbers.v
View file @
e2efc09c
...
...
@@ -28,10 +28,6 @@ Notation "x ≤ y ≤ z ≤ z'" := (x ≤ y ∧ y ≤ z ∧ z ≤ z')%nat : nat_
Notation
"(≤)"
:
=
le
(
only
parsing
)
:
nat_scope
.
Notation
"(<)"
:
=
lt
(
only
parsing
)
:
nat_scope
.
Infix
"≥"
:
=
ge
:
nat_scope
.
Notation
"(≥)"
:
=
ge
(
only
parsing
)
:
nat_scope
.
Notation
"(>)"
:
=
gt
(
only
parsing
)
:
nat_scope
.
Infix
"`div`"
:
=
Nat
.
div
(
at
level
35
)
:
nat_scope
.
Infix
"`mod`"
:
=
Nat
.
modulo
(
at
level
35
)
:
nat_scope
.
...
...
@@ -108,10 +104,6 @@ Notation "(<)" := Pos.lt (only parsing) : positive_scope.
Notation
"(~0)"
:
=
xO
(
only
parsing
)
:
positive_scope
.
Notation
"(~1)"
:
=
xI
(
only
parsing
)
:
positive_scope
.
Infix
"≥"
:
=
Pos
.
ge
:
positive_scope
.
Notation
"(≥)"
:
=
Pos
.
ge
(
only
parsing
)
:
positive_scope
.
Notation
"(>)"
:
=
Pos
.
gt
(
only
parsing
)
:
positive_scope
.
Arguments
Pos
.
of_nat
_
:
simpl
never
.
Instance
positive_eq_dec
:
∀
x
y
:
positive
,
Decision
(
x
=
y
)
:
=
Pos
.
eq_dec
.
Instance
positive_inhabited
:
Inhabited
positive
:
=
populate
1
.
...
...
@@ -187,11 +179,6 @@ Notation "x < y ≤ z" := (x < y ∧ y ≤ z)%N : N_scope.
Notation
"x ≤ y ≤ z ≤ z'"
:
=
(
x
≤
y
∧
y
≤
z
∧
z
≤
z'
)%
N
:
N_scope
.
Notation
"(≤)"
:
=
N
.
le
(
only
parsing
)
:
N_scope
.
Notation
"(<)"
:
=
N
.
lt
(
only
parsing
)
:
N_scope
.
Infix
"≥"
:
=
N
.
ge
:
N_scope
.
Notation
"(≥)"
:
=
N
.
ge
(
only
parsing
)
:
N_scope
.
Notation
"(>)"
:
=
N
.
gt
(
only
parsing
)
:
N_scope
.
Infix
"`div`"
:
=
N
.
div
(
at
level
35
)
:
N_scope
.
Infix
"`mod`"
:
=
N
.
modulo
(
at
level
35
)
:
N_scope
.
...
...
@@ -226,10 +213,6 @@ Notation "x ≤ y ≤ z ≤ z'" := (x ≤ y ∧ y ≤ z ∧ z ≤ z') : Z_scope.
Notation
"(≤)"
:
=
Z
.
le
(
only
parsing
)
:
Z_scope
.
Notation
"(<)"
:
=
Z
.
lt
(
only
parsing
)
:
Z_scope
.
Infix
"≥"
:
=
Z
.
ge
:
Z_scope
.
Notation
"(≥)"
:
=
Z
.
ge
(
only
parsing
)
:
Z_scope
.
Notation
"(>)"
:
=
Z
.
gt
(
only
parsing
)
:
Z_scope
.
Infix
"`div`"
:
=
Z
.
div
(
at
level
35
)
:
Z_scope
.
Infix
"`mod`"
:
=
Z
.
modulo
(
at
level
35
)
:
Z_scope
.
Infix
"`quot`"
:
=
Z
.
quot
(
at
level
35
)
:
Z_scope
.
...
...
@@ -345,10 +328,6 @@ Notation "x ≤ y ≤ z ≤ z'" := (x ≤ y ∧ y ≤ z ∧ z ≤ z') : Qc_scope
Notation
"(≤)"
:
=
Qcle
(
only
parsing
)
:
Qc_scope
.
Notation
"(<)"
:
=
Qclt
(
only
parsing
)
:
Qc_scope
.
Infix
"≥"
:
=
Qcge
:
Qc_scope
.
Notation
"(≥)"
:
=
Qcge
(
only
parsing
)
:
Qc_scope
.
Notation
"(>)"
:
=
Qcgt
(
only
parsing
)
:
Qc_scope
.
Hint
Extern
1
(
_
≤
_
)
=>
reflexivity
||
discriminate
.
Arguments
Qred
_
:
simpl
never
.
...
...
Write
Preview
Markdown
is supported
0%
Try again
or
attach a new file
.
Attach a file
Cancel
You are about to add
0
people
to the discussion. Proceed with caution.
Finish editing this message first!
Cancel
Please
register
or
sign in
to comment