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Rodolphe Lepigre
Iris
Commits
0495154c
Commit
0495154c
authored
Apr 04, 2017
by
Jacques-Henri Jourdan
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Upred : explain why things are how they are.
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8f3ebec4
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theories/base_logic/upred.v
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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
.
...
...
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