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Simon Spies
Iris
Commits
e2efc09c
Commit
e2efc09c
authored
Feb 11, 2016
by
Ralf Jung
Browse files
Merge branch 'master' of gitlab.mpi-sws.org:FP/iris-coq
parents
6ca92264
eb563833
Changes
2
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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
.
...
...
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