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George Pirlea
Iris
Commits
2f0164f4
Commit
2f0164f4
authored
Nov 14, 2017
by
Jacques-Henri Jourdan
Browse files
Expand the explanation of uPred as a subset of sProp monotonous predicates
parent
bf73b3b9
Changes
1
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Inline
Side-by-side
theories/base_logic/upred.v
View file @
2f0164f4
...
@@ -28,7 +28,20 @@ Record uPred (M : ucmraT) : Type := IProp {
...
@@ -28,7 +28,20 @@ Record uPred (M : ucmraT) : Type := IProp {
are monotonous both with respect to the step index and with
are monotonous both with respect to the step index and with
respect to x. However, that would essentially require changing
respect to x. However, that would essentially require changing
(by making it more complicated) the model of many connectives of
(by making it more complicated) the model of many connectives of
the logic, which we don't want. *)
the logic, which we don't want.
This sub-COFE is the sub-COFE of monotonous sProp predicates P
such that the following sProp assertion is valid:
∀ x, (V(x) → P(x)) → P(x)
Where V is the validity predicate.
Another way of saying that this is equivalent to this definition of
uPred is to notice that our definition of uPred is equivalent to
quotienting the COFE of monotonous sProp predicates with the
following (sProp) equivalence relation:
P1 ≡ P2 := ∀ x, V(x) → (P1(x) ↔ P2(x))
whose equivalence classes appear to all have one only canonical
representative such that ∀ x, (V(x) → P(x)) → P(x).
*)
uPred_closed
n1
n2
x
:
uPred_holds
n1
x
→
n2
≤
n1
→
✓
{
n2
}
x
→
uPred_holds
n2
x
uPred_closed
n1
n2
x
:
uPred_holds
n1
x
→
n2
≤
n1
→
✓
{
n2
}
x
→
uPred_holds
n2
x
}.
}.
Arguments
uPred_holds
{
_
}
_
_
_
:
simpl
never
.
Arguments
uPred_holds
{
_
}
_
_
_
:
simpl
never
.
...
...
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