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Adam
stdpp
Commits
613153f3
Commit
613153f3
authored
4 years ago
by
Robbert Krebbers
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Intuition for decidability of `red` in `wn_sn`.
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613153f3
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@@ -280,6 +280,10 @@ Section properties.
Lemma
wn_step_rtc
x
y
:
wn
R
y
→
rtc
R
x
y
→
wn
R
x
.
Proof
.
induction
2
;
eauto
using
wn_step
.
Qed
.
(** The following theorem requires that [red R] is decidable. The intuition
for this requirement is that [wn R] is a very "positive" statement as it
points out a particular trace. In contrast, [sn R] just says "this also holds
for all successors", there is no "data"/"trace" there. *)
Lemma
sn_wn
`{
!∀
y
,
Decision
(
red
R
y
)}
x
:
sn
R
x
→
wn
R
x
.
Proof
.
induction
1
as
[
x
_
IH
]
.
destruct
(
decide
(
red
R
x
))
as
[[
x'
?]|?]
.
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