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5c639877
Commit
5c639877
authored
Mar 12, 2018
by
Ralf Jung
Browse files
note that forall_2 would be derivable in a classical meta-logic
parent
8389920e
Pipeline
#7399
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theories/bi/interface.v
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5c639877
...
...
@@ -58,7 +58,7 @@ Section bi_mixin.
bi_mixin_entails_po
:
PreOrder
bi_entails
;
bi_mixin_equiv_spec
P
Q
:
equiv
P
Q
↔
(
P
⊢
Q
)
∧
(
Q
⊢
P
)
;
(* Non-expansiveness *)
(*
*
Non-expansiveness *)
bi_mixin_pure_ne
n
:
Proper
(
iff
==>
dist
n
)
bi_pure
;
bi_mixin_and_ne
:
NonExpansive2
bi_and
;
bi_mixin_or_ne
:
NonExpansive2
bi_or
;
...
...
@@ -71,9 +71,11 @@ Section bi_mixin.
bi_mixin_wand_ne
:
NonExpansive2
bi_wand
;
bi_mixin_persistently_ne
:
NonExpansive
bi_persistently
;
(* Higher-order logic *)
(*
*
Higher-order logic *)
bi_mixin_pure_intro
P
(
φ
:
Prop
)
:
φ
→
P
⊢
⌜
φ
⌝
;
bi_mixin_pure_elim'
(
φ
:
Prop
)
P
:
(
φ
→
True
⊢
P
)
→
⌜
φ
⌝
⊢
P
;
(* This is actually derivable if we assume excluded middle in Coq,
via [(∀ a, φ a) ∨ (∃ a, ¬φ a)]. *)
bi_mixin_pure_forall_2
{
A
}
(
φ
:
A
→
Prop
)
:
(
∀
a
,
⌜
φ
a
⌝
)
⊢
⌜
∀
a
,
φ
a
⌝
;
bi_mixin_and_elim_l
P
Q
:
P
∧
Q
⊢
P
;
...
...
@@ -93,7 +95,7 @@ Section bi_mixin.
bi_mixin_exist_intro
{
A
}
{
Ψ
:
A
→
PROP
}
a
:
Ψ
a
⊢
∃
a
,
Ψ
a
;
bi_mixin_exist_elim
{
A
}
(
Φ
:
A
→
PROP
)
Q
:
(
∀
a
,
Φ
a
⊢
Q
)
→
(
∃
a
,
Φ
a
)
⊢
Q
;
(* BI connectives *)
(*
*
BI connectives *)
bi_mixin_sep_mono
P
P'
Q
Q'
:
(
P
⊢
Q
)
→
(
P'
⊢
Q'
)
→
P
∗
P'
⊢
Q
∗
Q'
;
bi_mixin_emp_sep_1
P
:
P
⊢
emp
∗
P
;
bi_mixin_emp_sep_2
P
:
emp
∗
P
⊢
P
;
...
...
@@ -102,7 +104,7 @@ Section bi_mixin.
bi_mixin_wand_intro_r
P
Q
R
:
(
P
∗
Q
⊢
R
)
→
P
⊢
Q
-
∗
R
;
bi_mixin_wand_elim_l'
P
Q
R
:
(
P
⊢
Q
-
∗
R
)
→
P
∗
Q
⊢
R
;
(* Persistently *)
(*
*
Persistently *)
(* In the ordered RA model: Holds without further assumptions. *)
bi_mixin_persistently_mono
P
Q
:
(
P
⊢
Q
)
→
<
pers
>
P
⊢
<
pers
>
Q
;
(* In the ordered RA model: `core` is idempotent *)
...
...
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