Skip to content
GitLab
Menu
Projects
Groups
Snippets
Help
Help
Support
Community forum
Keyboard shortcuts
?
Submit feedback
Contribute to GitLab
Sign in / Register
Toggle navigation
Menu
Open sidebar
Tej Chajed
iris
Commits
0495154c
Commit
0495154c
authored
Apr 04, 2017
by
Jacques-Henri Jourdan
Browse files
Upred : explain why things are how they are.
parent
8f3ebec4
Changes
1
Hide whitespace changes
Inline
Side-by-side
theories/base_logic/upred.v
View file @
0495154c
...
...
@@ -8,7 +8,26 @@ Set Default Proof Using "Type".
Record
uPred
(
M
:
ucmraT
)
:
Type
:
=
IProp
{
uPred_holds
:
>
nat
→
M
→
Prop
;
(* [uPred_mono] is used to prove non-expansiveness (guaranteed by
[uPred_ne]). Therefore, it is important that we do not restrict
it to only valid elements. *)
uPred_mono
n
x1
x2
:
uPred_holds
n
x1
→
x1
≼
{
n
}
x2
→
uPred_holds
n
x2
;
(* We have to restrict this to hold only for valid elements,
otherwise this condition is no longer limit preserving, and uPred
does no longer form a COFE (i.e., [uPred_compl] breaks). This is
because the distance and equivalence on this cofe ignores the
truth valid on invalid elements. This, in turns, is required by
the fact that entailment has to ignore invalid elements, which is
itself essential for proving [ownM_valid].
We could, actually, make the following condition true even for
invalid elements: we have proved that uPred is isomorphic to a
sub-COFE of the COFE of predicates that are monotonous both with
respect to the step index and with respect to x. However, that
would essentially require changing (by making more complicated)
the model of many connectives of the logic, which we don't want. *)
uPred_closed
n1
n2
x
:
uPred_holds
n1
x
→
n2
≤
n1
→
✓
{
n2
}
x
→
uPred_holds
n2
x
}.
Arguments
uPred_holds
{
_
}
_
_
_
:
simpl
never
.
...
...
Write
Preview
Markdown
is supported
0%
Try again
or
attach a new file
.
Attach a file
Cancel
You are about to add
0
people
to the discussion. Proceed with caution.
Finish editing this message first!
Cancel
Please
register
or
sign in
to comment