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Tej Chajed
iris
Commits
1a2cd3fd
Commit
1a2cd3fd
authored
Feb 13, 2015
by
Ralf Jung
Browse files
make the discrete metric more general: for any setoid
parent
c5fc5262
Changes
2
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Inline
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lib/ModuRes/CSetoid.v
View file @
1a2cd3fd
...
...
@@ 402,3 +402,10 @@ Section OptDefs.
Qed
.
End
OptDefs
.
Section
DiscreteType
.
Context
{
T
:
Type
}.
Program
Instance
discreteType
:
Setoid
T
:
=
mkType
(@
eq
T
).
End
DiscreteType
.
lib/ModuRes/MetricCore.v
View file @
1a2cd3fd
...
...
@@ 870,22 +870,26 @@ Qed.
(** Discrete spaces are proper metric spaces (discrete meaning that the distance
is 1 if elements are diffent and 0 for equal elements. Equality here is
propositional Coq equality. *)
Section
Discrete
.
Context
{
T
:
Type
}.
Program
Instance
discreteType
:
Setoid
T
:
=
mkType
(@
eq
T
).
Section
DiscreteMetric
.
Context
{
T
:
Type
}
{
T_type
:
Setoid
T
}.
Definition
discreteDist
n
(
x
y
:
T
)
:
=
match
n
with
O
=>
True

_
=>
x
=
y

_
=>
x
=
=
y
end
.
Global
Arguments
discreteDist
n
x
y
/
.
Program
Instance
discreteMetric
:
metric
T
:
=
mkMetr
discreteDist
.
Next
Obligation
.
split
;
intros
HEq
;
[
specialize
(
HEq
1
)

intros
[

n
]
]
;
inversion
HEq
;
subst
;
simpl
;
reflexivity
.
intros
x
y
Heq
x'
y'
Heq'
.
split
;
(
destruct
n
as
[
n
]
;
[
reflexivity

simpl
]).

intros
Heqx
.
rewrite
<
Heq
,
<
Heq'
.
assumption
.

intros
Heqy
.
rewrite
Heq
,
Heq'
.
assumption
.
Qed
.
Next
Obligation
.
split
;
intros
Heq
.

now
apply
(
Heq
1
).

intros
[
n
]
;
tauto
.
Qed
.
Next
Obligation
.
destruct
n
as
[
n
]
;
intros
x
y
HS
;
simpl
in
*
;
[
symmetry
]
;
tauto
.
...
...
@@ 903,11 +907,11 @@ Section Discrete.
Next
Obligation
.
intros
n
;
exists
1
;
simpl
;
intros
[
i
]
HLe
;
[
inversion
HLe
].
destruct
n
as
[
n
]
;
[
exact
I
].
assert
(
HT
:
=
chain_cauchy
σ
_
1
(
S
i
)
1
)
;
inversion
HT
.
rewrite
H0
;
reflexivity
.
assert
(
HT
:
=
chain_cauchy
σ
_
1
(
S
i
)
1
)
.
rewrite
HT
.
reflexivity
.
Qed
.
End
Discrete
.
End
Discrete
Metric
.
Section
Option
.
Context
`
{
cT
:
cmetric
T
}.
...
...
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