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stdpp
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0e698840
Commit
0e698840
authored
5 years ago
by
Robbert Krebbers
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Merge branch 'set-seq-lemmas' into 'master'
Add lemmas regarding set_seq See merge request
!105
parents
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5998dbf4
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!105
Add lemmas regarding set_seq
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#21134
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5 years ago
Stage: build
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theories/sets.v
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0e698840
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@@ -1082,6 +1082,27 @@ Section set_seq.
SetUnfoldElemOf
x
(
set_seq
(
C
:=
C
)
start
len
)
(
start
≤
x
<
start
+
len
)
.
Proof
.
constructor
;
apply
elem_of_set_seq
.
Qed
.
Lemma
set_seq_len_pos
n
start
len
:
n
∈
set_seq
(
C
:=
C
)
start
len
→
0
<
len
.
Proof
.
rewrite
elem_of_set_seq
.
lia
.
Qed
.
Lemma
set_seq_subseteq
start1
len1
start2
len2
:
0
<
len1
→
set_seq
(
C
:=
C
)
start1
len1
⊆
set_seq
(
C
:=
C
)
start2
len2
↔
start2
≤
start1
∧
start1
+
len1
≤
start2
+
len2
.
Proof
.
intros
Hlen
.
set_unfold
.
split
.
-
intros
Hx
.
pose
proof
(
Hx
start1
)
.
pose
proof
(
Hx
(
start1
+
len1
-
1
))
.
lia
.
-
intros
Heq
x
.
lia
.
Qed
.
Lemma
set_seq_subseteq_len_gt
start1
len1
start2
len2
:
set_seq
(
C
:=
C
)
start1
len1
⊆
set_seq
(
C
:=
C
)
start2
len2
→
len1
≤
len2
.
Proof
.
destruct
len1
as
[|
len1
]
.
-
set_unfold
.
lia
.
-
rewrite
set_seq_subseteq
;
lia
.
Qed
.
Lemma
set_seq_plus_disjoint
start
len1
len2
:
set_seq
(
C
:=
C
)
start
len1
##
set_seq
(
start
+
len1
)
len2
.
Proof
.
set_solver
by
lia
.
Qed
.
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