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Why3
why3
Commits
4e44421f
Commit
4e44421f
authored
Feb 15, 2014
by
MARCHE Claude
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updated sessions
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examples/vstte10_inverting/vstte10_inverting_WP_InvertingAnInjection_WP_parameter_inverting2_2.v
...rting_WP_InvertingAnInjection_WP_parameter_inverting2_2.v
+28
-41
examples/vstte10_inverting/why3session.xml
examples/vstte10_inverting/why3session.xml
+3
-3
examples/vstte12_combinators/why3session.xml
examples/vstte12_combinators/why3session.xml
+124
-124
No files found.
examples/vstte10_inverting/vstte10_inverting_WP_InvertingAnInjection_WP_parameter_inverting2_2.v
View file @
4e44421f
(
*
This
file
is
generated
by
Why3
'
s
Coq
driver
*
)
(
*
This
file
is
generated
by
Why3
'
s
Coq
8.4
driver
*
)
(
*
Beware
!
Only
edit
allowed
sections
below
*
)
Require
Import
BuiltIn
.
Require
BuiltIn
.
Require
int
.
Int
.
Require
map
.
Map
.
Require
map
.
MapInjection
.
(
*
Why3
assumption
*
)
Definition
unit
:=
unit
.
...
...
@@ -11,77 +12,64 @@ Definition unit := unit.
(
*
Why3
assumption
*
)
Inductive
array
(
a
:
Type
)
{
a_WT
:
WhyType
a
}
:=
|
mk_array
:
Z
->
(
map
.
Map
.
map
Z
a
)
->
array
a
.
|
mk_array
:
Z
->
(
@
map
.
Map
.
map
Z
_
a
a_WT
)
->
array
a
.
Axiom
array_WhyType
:
forall
(
a
:
Type
)
{
a_WT
:
WhyType
a
}
,
WhyType
(
array
a
).
Existing
Instance
array_WhyType
.
Implicit
Arguments
mk_array
[[
a
]
[
a_WT
]].
(
*
Why3
assumption
*
)
Definition
elts
{
a
:
Type
}
{
a_WT
:
WhyType
a
}
(
v
:
(
array
a
))
:
(
map
.
Map
.
map
Z
a
)
:=
match
v
with
Definition
elts
{
a
:
Type
}
{
a_WT
:
WhyType
a
}
(
v
:
(
@
array
a
a_WT
))
:
(
@
map
.
Map
.
map
Z
_
a
a_WT
)
:=
match
v
with
|
(
mk_array
x
x1
)
=>
x1
end
.
(
*
Why3
assumption
*
)
Definition
length
{
a
:
Type
}
{
a_WT
:
WhyType
a
}
(
v
:
(
array
a
))
:
Z
:=
Definition
length
{
a
:
Type
}
{
a_WT
:
WhyType
a
}
(
v
:
(
@
array
a
a_WT
))
:
Z
:=
match
v
with
|
(
mk_array
x
x1
)
=>
x
end
.
(
*
Why3
assumption
*
)
Definition
get
{
a
:
Type
}
{
a_WT
:
WhyType
a
}
(
a1
:
(
array
a
))
(
i
:
Z
)
:
a
:=
Definition
get
{
a
:
Type
}
{
a_WT
:
WhyType
a
}
(
a1
:
(
@
array
a
a_WT
))
(
i
:
Z
)
:
a
:=
(
map
.
Map
.
get
(
elts
a1
)
i
).
(
*
Why3
assumption
*
)
Definition
set
{
a
:
Type
}
{
a_WT
:
WhyType
a
}
(
a1
:
(
array
a
))
(
i
:
Z
)
(
v
:
a
)
:
(
array
a
)
:=
(
mk_array
(
length
a1
)
(
map
.
Map
.
set
(
elts
a1
)
i
v
)).
Definition
set
{
a
:
Type
}
{
a_WT
:
WhyType
a
}
(
a1
:
(
@
array
a
a_WT
))
(
i
:
Z
)
(
v
:
a
)
:
(
@
array
a
a_WT
)
:=
(
mk_array
(
length
a1
)
(
map
.
Map
.
set
(
elts
a1
)
i
v
)).
(
*
Why3
assumption
*
)
Definition
make
{
a
:
Type
}
{
a_WT
:
WhyType
a
}
(
n
:
Z
)
(
v
:
a
)
:
(
array
a
)
:=
(
mk_array
n
(
map
.
Map
.
const
v
:
(
map
.
Map
.
map
Z
a
))).
Definition
make
{
a
:
Type
}
{
a_WT
:
WhyType
a
}
(
n
:
Z
)
(
v
:
a
)
:
(
@
array
a
a_WT
)
:=
(
mk_array
n
(
map
.
Map
.
const
v
:
(
@
map
.
Map
.
map
Z
_
a
a_WT
))).
(
*
Why3
assumption
*
)
Definition
injective
(
a
:
(
map
.
Map
.
map
Z
Z
))
(
n
:
Z
)
:
Prop
:=
forall
(
i
:
Z
)
(
j
:
Z
),
((
0
%
Z
<=
i
)
%
Z
/
\
(
i
<
n
)
%
Z
)
->
(((
0
%
Z
<=
j
)
%
Z
/
\
(
j
<
n
)
%
Z
)
->
((
~
(
i
=
j
))
->
~
((
map
.
Map
.
get
a
i
)
=
(
map
.
Map
.
get
a
j
)))).
Definition
injective
(
a
:
(
@
array
Z
_
))
(
n
:
Z
)
:
Prop
:=
(
map
.
MapInjection
.
injective
(
elts
a
)
n
).
(
*
Why3
assumption
*
)
Definition
surjective
(
a
:
(
map
.
Map
.
map
Z
Z
))
(
n
:
Z
)
:
Prop
:=
forall
(
i
:
Z
),
((
0
%
Z
<=
i
)
%
Z
/
\
(
i
<
n
)
%
Z
)
->
exists
j
:
Z
,
((
0
%
Z
<=
j
)
%
Z
/
\
(
j
<
n
)
%
Z
)
/
\
((
map
.
Map
.
get
a
j
)
=
i
).
Definition
surjective
(
a
:
(
@
array
Z
_
))
(
n
:
Z
)
:
Prop
:=
(
map
.
MapInjection
.
surjective
(
elts
a
)
n
).
(
*
Why3
assumption
*
)
Definition
range
(
a
:
(
map
.
Map
.
map
Z
Z
))
(
n
:
Z
)
:
Prop
:=
forall
(
i
:
Z
),
((
0
%
Z
<=
i
)
%
Z
/
\
(
i
<
n
)
%
Z
)
->
((
0
%
Z
<=
(
map
.
Map
.
get
a
i
))
%
Z
/
\
((
map
.
Map
.
get
a
i
)
<
n
)
%
Z
).
Axiom
injective_surjective
:
forall
(
a
:
(
map
.
Map
.
map
Z
Z
))
(
n
:
Z
),
(
injective
a
n
)
->
((
range
a
n
)
->
(
surjective
a
n
)).
(
*
Why3
assumption
*
)
Definition
injective1
(
a
:
(
array
Z
))
(
n
:
Z
)
:
Prop
:=
(
injective
(
elts
a
)
n
).
(
*
Why3
assumption
*
)
Definition
surjective1
(
a
:
(
array
Z
))
(
n
:
Z
)
:
Prop
:=
(
surjective
(
elts
a
)
n
).
(
*
Why3
assumption
*
)
Definition
range1
(
a
:
(
array
Z
))
(
n
:
Z
)
:
Prop
:=
(
range
(
elts
a
)
n
).
Definition
range
(
a
:
(
@
array
Z
_
))
(
n
:
Z
)
:
Prop
:=
(
map
.
MapInjection
.
range
(
elts
a
)
n
).
(
*
Why3
goal
*
)
Theorem
WP_parameter_inverting2
:
forall
(
a
:
Z
)
(
n
:
Z
),
forall
(
a1
:
(
map
.
Map
.
map
Z
Z
)),
((
0
%
Z
<=
a
)
%
Z
/
\
((
n
=
a
)
/
\
((
injective
a1
n
)
/
\
(
range
a1
n
))))
->
((
0
%
Z
<=
n
)
%
Z
->
((
0
%
Z
<=
n
)
%
Z
->
let
o
:=
(
n
-
1
%
Z
)
%
Z
in
((
0
%
Z
<=
o
)
%
Z
->
forall
(
b
:
(
map
.
Map
.
map
Z
Z
)),
(
forall
(
j
:
Z
),
((
0
%
Z
<=
j
)
%
Z
/
\
(
j
<
(
o
+
1
%
Z
)
%
Z
)
%
Z
)
->
((
map
.
Map
.
get
b
(
map
.
Map
.
get
a1
j
))
=
j
))
->
((
0
%
Z
<=
n
)
%
Z
->
(
injective
b
n
))))).
(
*
Why3
intros
a
n
a1
(
h1
,(
h2
,(
h3
,
h4
)))
h5
h6
o
h7
b
h8
h9
.
*
)
Theorem
WP_parameter_inverting2
:
forall
(
a
:
Z
)
(
a1
:
(
@
map
.
Map
.
map
Z
_
Z
_
))
(
n
:
Z
),
((
0
%
Z
<=
a
)
%
Z
/
\
((
n
=
a
)
/
\
((
map
.
MapInjection
.
injective
a1
n
)
/
\
(
map
.
MapInjection
.
range
a1
n
))))
->
((
0
%
Z
<=
n
)
%
Z
->
((
0
%
Z
<=
n
)
%
Z
->
let
o
:=
(
n
-
1
%
Z
)
%
Z
in
((
0
%
Z
<=
o
)
%
Z
->
forall
(
b
:
(
@
map
.
Map
.
map
Z
_
Z
_
)),
(
forall
(
j
:
Z
),
((
0
%
Z
<=
j
)
%
Z
/
\
(
j
<
(
o
+
1
%
Z
)
%
Z
)
%
Z
)
->
((
map
.
Map
.
get
b
(
map
.
Map
.
get
a1
j
))
=
j
))
->
((
0
%
Z
<=
n
)
%
Z
->
(
map
.
MapInjection
.
injective
b
n
))))).
(
*
Why3
intros
a
a1
n
(
h1
,(
h2
,(
h3
,
h4
)))
h5
h6
o
h7
b
h8
h9
.
*
)
(
*
YOU
MAY
EDIT
THE
PROOF
BELOW
*
)
intuition
.
intuition
.
red
;
intros
.
unfold
get
;
simpl
.
assert
(
surjective
a1
n
).
apply
injective_surjective
;
assumption
.
assert
(
MapInjection
.
surjective
a1
n
).
apply
MapInjection
.
injective_surjective
;
assumption
.
generalize
(
H11
i
H8
);
unfold
get
;
simpl
;
intros
(
i1
,
(
Hi1
,
Hi2
)).
generalize
(
H11
j
H9
);
unfold
get
;
simpl
;
intros
(
j1
,
(
Hj1
,
Hj2
)).
rewrite
<-
Hi2
.
...
...
@@ -94,4 +82,3 @@ subst.
auto
.
Qed
.
examples/vstte10_inverting/why3session.xml
View file @
4e44421f
...
...
@@ -191,8 +191,8 @@
name=
"expl:VC for inverting"
/>
<proof
prover=
"2"
timelimit=
"
10
"
memlimit=
"0"
timelimit=
"
5
"
memlimit=
"
400
0"
edited=
"vstte10_inverting_WP_InvertingAnInjection_WP_parameter_inverting_1.v"
obsolete=
"false"
archived=
"false"
>
...
...
@@ -409,7 +409,7 @@
edited=
"vstte10_inverting_WP_InvertingAnInjection_WP_parameter_inverting2_2.v"
obsolete=
"false"
archived=
"false"
>
<result
status=
"valid"
time=
"1.0
6
"
/>
<result
status=
"valid"
time=
"1.0
2
"
/>
</proof>
</goal>
<goal
...
...
examples/vstte12_combinators/why3session.xml
View file @
4e44421f
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