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Jonas Kastberg
iris
Commits
94861f1d
Commit
94861f1d
authored
Feb 21, 2017
by
Ralf Jung
Browse files
fixpointK_ind
parent
b582ab47
Changes
1
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Inline
Side-by-side
theories/algebra/ofe.v
View file @
94861f1d
...
...
@@ -330,6 +330,16 @@ Section fixpointK.
Lemma
fixpointK_proper
:
(
∀
z
,
f
z
≡
g
z
)
→
fixpointK
k
f
≡
fixpointK
k
g
.
Proof
.
setoid_rewrite
equiv_dist
;
naive_solver
eauto
using
fixpointK_ne
.
Qed
.
End
fixpointK_ne
.
Lemma
fixpointK_ind
(
P
:
A
→
Prop
)
:
Proper
((
≡
)
==>
impl
)
P
→
(
∃
x
,
P
x
)
→
(
∀
x
,
P
x
→
P
(
f
x
))
→
(
∀
(
c
:
chain
A
),
(
∀
n
,
P
(
c
n
))
→
P
(
compl
c
))
→
P
(
fixpointK
k
f
).
Proof
.
intros
?
Hst
Hincr
Hlim
.
rewrite
/
fixpointK
.
eapply
fixpoint_ind
;
[
done
..|
|
done
].
clear
-
Hincr
.
intros
.
induction
k
;
first
done
.
simpl
.
auto
.
Qed
.
End
fixpointK
.
(** Mutual fixpoints *)
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