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Jonas Kastberg
iris
Commits
10d11277
Commit
10d11277
authored
Mar 31, 2020
by
Robbert Krebbers
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Prove that `≡` is limit preserving.
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b42d1571
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theories/algebra/ofe.v
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10d11277
...
@@ -289,6 +289,13 @@ Section limit_preserving.
...
@@ -289,6 +289,13 @@ Section limit_preserving.
(
∀
y
,
LimitPreserving
(
P
y
))
→
(
∀
y
,
LimitPreserving
(
P
y
))
→
LimitPreserving
(
λ
x
,
∀
y
,
P
y
x
).
LimitPreserving
(
λ
x
,
∀
y
,
P
y
x
).
Proof
.
intros
Hlim
c
Hc
y
.
by
apply
Hlim
.
Qed
.
Proof
.
intros
Hlim
c
Hc
y
.
by
apply
Hlim
.
Qed
.
Lemma
limit_preserving_equiv
`
{!
Cofe
B
}
(
f
g
:
A
→
B
)
:
NonExpansive
f
→
NonExpansive
g
→
LimitPreserving
(
λ
x
,
f
x
≡
g
x
).
Proof
.
intros
Hf
Hg
c
Hc
.
apply
equiv_dist
=>
n
.
by
rewrite
-!
compl_chain_map
!
conv_compl
/=
Hc
.
Qed
.
End
limit_preserving
.
End
limit_preserving
.
(** Fixpoint *)
(** Fixpoint *)
...
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