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Jonas Kastberg
stdpp
Commits
74d21e01
Commit
74d21e01
authored
Jan 14, 2022
by
Robbert Krebbers
Browse files
Move `elem_of_suffix` to other suffix lemmas.
parent
e58dd720
Changes
1
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Side-by-side
theories/list.v
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74d21e01
...
...
@@ -2078,9 +2078,6 @@ Proof. intros [??]. discriminate_list. Qed.
Lemma
elem_of_prefix
l1
l2
x
:
x
∈
l1
→
l1
`
prefix_of
`
l2
→
x
∈
l2
.
Proof
.
intros
Hin
[
l'
->].
apply
elem_of_app
.
by
left
.
Qed
.
Lemma
elem_of_suffix
l1
l2
x
:
x
∈
l1
→
l1
`
suffix_of
`
l2
→
x
∈
l2
.
Proof
.
intros
Hin
[
l'
->].
apply
elem_of_app
.
by
right
.
Qed
.
(* [prefix] is not a total order, but [l1] and [l2] are always comparable if
they are both prefixes of some [l3]. *)
Lemma
prefix_weak_total
l1
l2
l3
:
...
...
@@ -2230,6 +2227,9 @@ Lemma suffix_length l1 l2 : l1 `suffix_of` l2 → length l1 ≤ length l2.
Proof
.
intros
[?
->].
rewrite
app_length
.
lia
.
Qed
.
Lemma
suffix_cons_not
x
l
:
¬
x
::
l
`
suffix_of
`
l
.
Proof
.
intros
[??].
discriminate_list
.
Qed
.
Lemma
elem_of_suffix
l1
l2
x
:
x
∈
l1
→
l1
`
suffix_of
`
l2
→
x
∈
l2
.
Proof
.
intros
Hin
[
l'
->].
apply
elem_of_app
.
by
right
.
Qed
.
(* [suffix] is not a total order, but [l1] and [l2] are always comparable if
they are both suffixes of some [l3]. *)
Lemma
suffix_weak_total
l1
l2
l3
:
...
...
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