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Iris
Iris
Commits
d6389a35
Commit
d6389a35
authored
Jun 01, 2016
by
Robbert Krebbers
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Not all [Qp]s are [frac]s, so make the notation only parsing.
parent
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algebra/frac.v
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d6389a35
...
...
@@ -2,10 +2,9 @@ From Coq.QArith Require Import Qcanon.
From
iris
.
algebra
Require
Export
cmra
.
From
iris
.
algebra
Require
Import
upred
.
Notation
frac
:
=
Qp
.
Notation
frac
:
=
Qp
(
only
parsing
)
.
Section
frac
.
Canonical
Structure
fracC
:
=
leibnizC
frac
.
Instance
frac_valid
:
Valid
frac
:
=
λ
x
,
(
x
≤
1
)%
Qc
.
...
...
@@ -19,20 +18,16 @@ Proof.
rewrite
-{
1
}(
Qcplus_0_r
x
)
-
Qcplus_le_mono_l
;
auto
using
Qclt_le_weak
.
Qed
.
Canonical
Structure
fracR
:
=
discreteR
frac
frac_ra_mixin
.
End
frac
.
(** Internalized properties *)
Lemma
frac_equivI
{
M
}
(
x
y
:
frac
)
:
x
≡
y
⊣
⊢
(
x
=
y
:
uPred
M
).
Lemma
frac_equivI
{
M
}
(
x
y
:
frac
)
:
x
≡
y
⊣
⊢
(
x
=
y
:
uPred
M
).
Proof
.
by
uPred
.
unseal
.
Qed
.
Lemma
frac_validI
{
M
}
(
x
:
frac
)
:
✓
x
⊣
⊢
(
■
(
x
≤
1
)%
Qc
:
uPred
M
).
Lemma
frac_validI
{
M
}
(
x
:
frac
)
:
✓
x
⊣
⊢
(
■
(
x
≤
1
)%
Qc
:
uPred
M
).
Proof
.
by
uPred
.
unseal
.
Qed
.
(** Exclusive *)
Global
Instance
frac_full_exclusive
:
Exclusive
1
%
Qp
.
Proof
.
move
=>
?
/
Qcle_not_lt
[]
;
simpl
in
*.
by
rewrite
-{
1
}(
Qcplus_0_r
1
)
-
Qcplus_lt_mono_l
.
move
=>
y
/
Qcle_not_lt
[]
/=.
by
rewrite
-{
1
}(
Qcplus_0_r
1
)
-
Qcplus_lt_mono_l
.
Qed
.
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