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Gaëtan Gilbert
Iris
Commits
5eb4474a
Commit
5eb4474a
authored
1 year ago
by
Ralf Jung
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make iApply greatest_fixpoint_paco work in more cases
parent
f0e490d1
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iris/bi/lib/fixpoint.v
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-1
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iris/bi/lib/fixpoint.v
tests/fixpoint.ref
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tests/fixpoint.ref
tests/fixpoint.v
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tests/fixpoint.v
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28 additions
and
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iris/bi/lib/fixpoint.v
+
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@@ -312,7 +312,7 @@ Section greatest_coind.
Qed
.
Local
Existing
Instance
paco_mono
.
Lemma
greatest_fixpoint_paco
`{
!
NonExpansive
Φ
}
:
Lemma
greatest_fixpoint_paco
(
Φ
:
A
→
PROP
)
`{
!
NonExpansive
Φ
}
:
□
(
∀
y
,
Φ
y
-∗
F
(
bi_greatest_fixpoint
(
λ
Ψ
a
,
Φ
a
∨
F
Ψ
a
))
y
)
-∗
∀
x
,
Φ
x
-∗
bi_greatest_fixpoint
F
x
.
Proof
using
Type
*.
...
...
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tests/fixpoint.ref
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tests/fixpoint.v
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From
iris
.
bi
Require
Import
lib
.
fixpoint
.
From
iris
.
proofmode
Require
Import
proofmode
.
From
iris
.
prelude
Require
Import
options
.
Section
fixpoint
.
Context
{
PROP
:
bi
}
`{
!
BiInternalEq
PROP
}
{
A
:
ofe
}
(
F
:
(
A
→
PROP
)
→
(
A
→
PROP
))
`{
!
BiMonoPred
F
}
.
Definition
L
:=
bi_least_fixpoint
F
.
Definition
G
:=
bi_greatest_fixpoint
F
.
(* Make sure the lemmas apply without having to repeat the induction predicate [Φ]. *)
Lemma
ind_test
(
a
:
A
)
:
∀
x
,
L
x
-∗
x
≡
a
.
Proof
.
iApply
(
least_fixpoint_ind
F
);
first
by
solve_proper
.
Undo
.
iApply
(
least_fixpoint_ind_wf
F
);
first
by
solve_proper
.
Undo
.
Abort
.
Lemma
coind_test
(
a
:
A
)
:
∀
x
,
x
≡
a
-∗
G
x
.
Proof
.
iApply
(
greatest_fixpoint_coind
F
);
first
by
solve_proper
.
Undo
.
iApply
(
greatest_fixpoint_paco
F
);
first
by
solve_proper
.
Undo
.
Abort
.
End
fixpoint
.
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