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stdpp
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e1d492b8
Commit
e1d492b8
authored
Mar 15, 2017
by
Robbert Krebbers
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Tweak inhabited proofs for vectors.
parent
cb021200
Pipeline
#4063
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in 2 minutes and 43 seconds
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theories/vector.v
theories/vector.v
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theories/vector.v
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e1d492b8
...
...
@@ 356,12 +356,12 @@ Qed.
Lemma
vlookup_insert_self
{
A
n
}
i
(
v
:
vec
A
n
)
:
vinsert
i
(
v
!!!
i
)
v
=
v
.
Proof
.
by
induction
v
;
inv_fin
i
;
intros
;
f_equal
/=.
Qed
.
(* Vectors can be inhabited. *)
Global
Instance
vec_nil_inh
T
:
Inhabited
(
vec
T
0
)
:
=
populate
[#].
(** The function [vreplicate n x] generates a vector with length [n] of elements
with value [x]. *)
Fixpoint
vreplicate
{
A
}
(
n
:
nat
)
(
x
:
A
)
:
vec
A
n
:
=
match
n
with
0
=>
[#]

S
n
=>
x
:::
vreplicate
n
x
end
.
Global
Instance
vec_inh
T
n
:
Inhabited
T
→
Inhabited
(
vec
T
n
).
Proof
.
intros
HT
.
induction
n
;
[
apply
_
].
destruct
IHn
as
[
v
].
destruct
HT
as
[
x
].
exact
(
populate
(
x
:::
v
)).
Qed
.
(* Vectors can be inhabited. *)
Global
Instance
vec_0_inhabited
T
:
Inhabited
(
vec
T
0
)
:
=
populate
[#].
Global
Instance
vec_inhabited
`
{
Inhabited
T
}
n
:
Inhabited
(
vec
T
n
)
:
=
populate
(
vreplicate
n
inhabitant
).
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