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Rodolphe Lepigre
Iris
Commits
bcc8b376
Commit
bcc8b376
authored
Feb 08, 2018
by
Robbert Krebbers
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Document BI axioms in terms of the axioms in the ordered RA model.
parent
33620b9d
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theories/bi/interface.v
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theories/bi/interface.v
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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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