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Simon Spies
stdpp
Commits
89217996
Commit
89217996
authored
Jun 27, 2019
by
Simon Spies
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simplify proof of seqZ_cons
parent
7393911a
Pipeline
#18024
canceled with stage
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theories/list.v
theories/list.v
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theories/list.v
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89217996
...
@@ 3351,12 +3351,10 @@ Section seqZ.
...
@@ 3351,12 +3351,10 @@ Section seqZ.
Proof
.
by
destruct
n
.
Qed
.
Proof
.
by
destruct
n
.
Qed
.
Lemma
seqZ_cons
m
n
:
n
>
0
→
seqZ
m
n
=
m
::
seqZ
(
Z
.
succ
m
)
(
Z
.
pred
n
).
Lemma
seqZ_cons
m
n
:
n
>
0
→
seqZ
m
n
=
m
::
seqZ
(
Z
.
succ
m
)
(
Z
.
pred
n
).
Proof
.
Proof
.
intros
H
.
unfold
seqZ
.
intros
H
.
unfold
seqZ
.
replace
n
with
(
Z
.
succ
(
Z
.
pred
n
))
at
1
by
lia
.
replace
(
Z
.
to_nat
n
)
with
(
S
(
Z
.
to_nat
(
n

1
)))
by
rewrite
Z2Nat
.
inj_succ
by
lia
.
f_equal
/=.
(
rewrite
<
Z2Nat
.
inj_succ
;
[
f_equal
]
;
lia
).
rewrite
<
fmap_seq
,
<
list_fmap_compose
.
simpl
;
f_equal
.
apply
map_ext
;
naive_solver
lia
.
erewrite
<
fmap_seq
,
map_map
,
map_ext
;
eauto
.
intros
;
lia
.
Qed
.
Qed
.
Lemma
seqZ_length
m
n
:
length
(
seqZ
m
n
)
=
Z
.
to_nat
n
.
Lemma
seqZ_length
m
n
:
length
(
seqZ
m
n
)
=
Z
.
to_nat
n
.
Proof
.
unfold
seqZ
;
by
rewrite
fmap_length
,
seq_length
.
Qed
.
Proof
.
unfold
seqZ
;
by
rewrite
fmap_length
,
seq_length
.
Qed
.
...
...
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