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Rice Wine
Iris
Commits
bcc8b376
Commit
bcc8b376
authored
Feb 08, 2018
by
Robbert Krebbers
Browse files
Document BI axioms in terms of the axioms in the ordered RA model.
parent
33620b9d
Changes
1
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Inline
Side-by-side
theories/bi/interface.v
View file @
bcc8b376
...
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@@ -112,20 +112,27 @@ Section bi_mixin.
bi_mixin_plainly_absorbing
P
Q
:
bi_plainly
P
∗
Q
⊢
bi_plainly
P
;
(* Persistently *)
(* In the ordered RA model: `core` is monotone *)
bi_mixin_persistently_mono
P
Q
:
(
P
⊢
Q
)
→
bi_persistently
P
⊢
bi_persistently
Q
;
(* In the ordered RA model: `core` is idempotent *)
bi_mixin_persistently_idemp_2
P
:
bi_persistently
P
⊢
bi_persistently
(
bi_persistently
P
)
;
bi_mixin_plainly_persistently_1
P
:
bi_plainly
(
bi_persistently
P
)
⊢
bi_plainly
P
;
(* In the ordered RA model [P ⊢ □ emp] (which can currently still be derived
from the plainly axioms, which will be removed): `ε ≼ core x` *)
bi_mixin_persistently_forall_2
{
A
}
(
Ψ
:
A
→
PROP
)
:
(
∀
a
,
bi_persistently
(
Ψ
a
))
⊢
bi_persistently
(
∀
a
,
Ψ
a
)
;
bi_mixin_persistently_exist_1
{
A
}
(
Ψ
:
A
→
PROP
)
:
bi_persistently
(
∃
a
,
Ψ
a
)
⊢
∃
a
,
bi_persistently
(
Ψ
a
)
;
(* In the ordered RA model: [x ≼ₑₓₜ y → core x ≼ core y] *)
bi_mixin_persistently_absorbing
P
Q
:
bi_persistently
P
∗
Q
⊢
bi_persistently
P
;
(* In the ordered RA model: [ε ≼ core x] *)
bi_mixin_persistently_and_sep_elim
P
Q
:
bi_persistently
P
∧
Q
⊢
(
emp
∧
P
)
∗
Q
;
}.
...
...
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