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stdpp
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e37edc7e
Commit
e37edc7e
authored
Jan 17, 2018
by
Robbert Krebbers
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Relate `forallb`/`existsb` to `Forall`/`Exists`.
parent
b6d58ca6
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theories/list.v
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e37edc7e
...
@@ -2331,6 +2331,11 @@ Section Forall_Exists.
...
@@ -2331,6 +2331,11 @@ Section Forall_Exists.
end
.
end
.
End
Forall_Exists
.
End
Forall_Exists
.
Lemma
forallb_True
(
f
:
A
→
bool
)
xs
:
forallb
f
xs
↔
Forall
f
xs
.
Proof
.
split
.
induction
xs
;
naive_solver
.
induction
1
;
naive_solver
.
Qed
.
Lemma
existb_True
(
f
:
A
→
bool
)
xs
:
existsb
f
xs
↔
Exists
f
xs
.
Proof
.
split
.
induction
xs
;
naive_solver
.
induction
1
;
naive_solver
.
Qed
.
Lemma
replicate_as_Forall
(
x
:
A
)
n
l
:
Lemma
replicate_as_Forall
(
x
:
A
)
n
l
:
replicate
n
x
=
l
↔
length
l
=
n
∧
Forall
(
x
=)
l
.
replicate
n
x
=
l
↔
length
l
=
n
∧
Forall
(
x
=)
l
.
Proof
.
rewrite
replicate_as_elem_of
,
Forall_forall
.
naive_solver
.
Qed
.
Proof
.
rewrite
replicate_as_elem_of
,
Forall_forall
.
naive_solver
.
Qed
.
...
...
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