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Why3
why3
Commits
4cf56aa6
Commit
4cf56aa6
authored
Feb 13, 2014
by
Jean-Christophe Filliâtre
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update proof sessions
parent
a8c13660
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2
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2 changed files
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414 additions
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396 deletions
+414
-396
examples/verifythis_fm2012_LRS/verifythis_fm2012_lcp_SuffixArray_permut_permutation_1.v
.../verifythis_fm2012_lcp_SuffixArray_permut_permutation_1.v
+35
-17
examples/verifythis_fm2012_LRS/why3session.xml
examples/verifythis_fm2012_LRS/why3session.xml
+379
-379
No files found.
examples/verifythis_fm2012_LRS/verifythis_fm2012_lcp_SuffixArray_permut_permutation_1.v
View file @
4cf56aa6
...
...
@@ -121,10 +121,7 @@ Definition array_eq {a:Type} {a_WT:WhyType a} (a1:(@array a a_WT))
(
*
Why3
assumption
*
)
Definition
exchange
{
a
:
Type
}
{
a_WT
:
WhyType
a
}
(
a1
:
(
@
array
a
a_WT
))
(
a2
:
(
@
array
a
a_WT
))
(
i
:
Z
)
(
j
:
Z
)
:
Prop
:=
((
length
a1
)
=
(
length
a2
))
/
\
(((
0
%
Z
<=
i
)
%
Z
/
\
(
i
<
(
length
a1
))
%
Z
)
/
\
(((
0
%
Z
<=
j
)
%
Z
/
\
(
j
<
(
length
a1
))
%
Z
)
/
\
(((
get
a1
i
)
=
(
get
a2
j
))
/
\
(((
get
a1
j
)
=
(
get
a2
i
))
/
\
forall
(
k
:
Z
),
((
0
%
Z
<=
k
)
%
Z
/
\
(
k
<
(
length
a1
))
%
Z
)
->
((
~
(
k
=
i
))
->
((
~
(
k
=
j
))
->
((
get
a1
k
)
=
(
get
a2
k
)))))))).
(
map
.
MapPermut
.
exchange
(
elts
a1
)
(
elts
a2
)
0
%
Z
(
length
a1
)
i
j
).
(
*
Why3
assumption
*
)
Definition
permut
{
a
:
Type
}
{
a_WT
:
WhyType
a
}
(
a1
:
(
@
array
a
a_WT
))
(
a2
:
(
@
array
...
...
@@ -143,29 +140,50 @@ Definition permut_all {a:Type} {a_WT:WhyType a} (a1:(@array a a_WT))
(
a2
:
(
@
array
a
a_WT
))
:
Prop
:=
((
length
a1
)
=
(
length
a2
))
/
\
(
map
.
MapPermut
.
permut
(
elts
a1
)
(
elts
a2
)
0
%
Z
(
length
a1
)).
Axiom
permut_all_refl
:
forall
{
a
:
Type
}
{
a_WT
:
WhyType
a
}
,
forall
(
a1
:
(
@
array
a
a_WT
)),
(
permut_all
a1
a1
).
Axiom
permut_sub_refl
:
forall
{
a
:
Type
}
{
a_WT
:
WhyType
a
}
,
forall
(
a1
:
(
@
array
a
a_WT
))
(
l
:
Z
)
(
u
:
Z
),
((
0
%
Z
<=
l
)
%
Z
/
\
((
l
<=
u
)
%
Z
/
\
(
u
<=
(
length
a1
))
%
Z
))
->
(
permut_sub
a1
a1
l
u
).
Axiom
exchange_permut_all
:
forall
{
a
:
Type
}
{
a_WT
:
WhyType
a
}
,
forall
(
a1
:
(
@
array
a
a_WT
))
(
a2
:
(
@
array
a
a_WT
))
(
i
:
Z
)
(
j
:
Z
),
(
exchange
a1
a2
i
j
)
->
(
permut_all
a1
a2
).
Axiom
permut_sub_trans
:
forall
{
a
:
Type
}
{
a_WT
:
WhyType
a
}
,
forall
(
a1
:
(
@
array
a
a_WT
))
(
a2
:
(
@
array
a
a_WT
))
(
a3
:
(
@
array
a
a_WT
))
(
l
:
Z
)
(
u
:
Z
),
(
permut_sub
a1
a2
l
u
)
->
((
permut_sub
a2
a3
l
u
)
->
(
permut_sub
a1
a3
l
u
)).
Axiom
exchange_permut_sub
:
forall
{
a
:
Type
}
{
a_WT
:
WhyType
a
}
,
forall
(
a1
:
(
@
array
a
a_WT
))
(
a2
:
(
@
array
a
a_WT
))
(
i
:
Z
)
(
j
:
Z
)
(
l
:
Z
)
(
u
:
Z
),
(
exchange
a1
a2
i
j
)
->
(((
l
<=
i
)
%
Z
/
\
(
i
<
u
)
%
Z
)
->
(((
l
<=
j
)
%
Z
/
\
(
j
<
u
)
%
Z
)
->
((
0
%
Z
<=
l
)
%
Z
->
((
u
<=
(
length
a1
))
%
Z
->
(
permut_sub
a1
a2
l
u
))))).
Axiom
permut_sub_unmodified
:
forall
{
a
:
Type
}
{
a_WT
:
WhyType
a
}
,
forall
(
a1
:
(
@
array
a
a_WT
))
(
a2
:
(
@
array
a
a_WT
))
(
l
:
Z
)
(
u
:
Z
),
(
permut_sub
a1
a2
l
u
)
->
forall
(
i
:
Z
),
(((
0
%
Z
<=
i
)
%
Z
/
\
(
i
<
l
)
%
Z
)
\
/
((
u
<=
i
)
%
Z
/
\
(
i
<
(
length
a1
))
%
Z
))
->
((
get
a2
i
)
=
(
get
a1
i
)).
Axiom
permut_sub_weakening
:
forall
{
a
:
Type
}
{
a_WT
:
WhyType
a
}
,
forall
(
a1
:
(
@
array
a
a_WT
))
(
a2
:
(
@
array
a
a_WT
))
(
l1
:
Z
)
(
u1
:
Z
)
(
l2
:
Z
)
(
u2
:
Z
),
(
permut_sub
a1
a2
l1
u1
)
->
(((
0
%
Z
<=
l2
)
%
Z
/
\
(
l2
<=
l1
)
%
Z
)
->
(((
u1
<=
u2
)
%
Z
/
\
(
u2
<=
(
length
a1
))
%
Z
)
->
(
permut_sub
a1
a2
l2
u2
))).
Axiom
permut_all_sym
:
forall
{
a
:
Type
}
{
a_WT
:
WhyType
a
}
,
forall
(
a1
:
(
@
array
a
a_WT
))
(
a2
:
(
@
array
a
a_WT
)),
(
permut_all
a1
a2
)
->
(
permut_all
a2
a1
).
Axiom
permut_sub_compose
:
forall
{
a
:
Type
}
{
a_WT
:
WhyType
a
}
,
forall
(
a1
:
(
@
array
a
a_WT
))
(
a2
:
(
@
array
a
a_WT
))
(
a3
:
(
@
array
a
a_WT
))
(
l1
:
Z
)
(
u1
:
Z
)
(
l2
:
Z
)
(
u2
:
Z
),
(
u1
<=
l2
)
%
Z
->
((
permut_sub
a1
a2
l1
u1
)
->
((
permut_sub
a2
a3
l2
u2
)
->
(
permut_sub
a1
a3
l1
u2
))).
Axiom
permut_all_refl
:
forall
{
a
:
Type
}
{
a_WT
:
WhyType
a
}
,
forall
(
a1
:
(
@
array
a
a_WT
)),
(
permut_all
a1
a1
).
Axiom
permut_all_trans
:
forall
{
a
:
Type
}
{
a_WT
:
WhyType
a
}
,
forall
(
a1
:
(
@
array
a
a_WT
))
(
a2
:
(
@
array
a
a_WT
))
(
a3
:
(
@
array
a
a_WT
)),
(
permut_all
a1
a2
)
->
((
permut_all
a2
a3
)
->
(
permut_all
a1
a3
)).
Axiom
exchange_permut_all
:
forall
{
a
:
Type
}
{
a_WT
:
WhyType
a
}
,
forall
(
a1
:
(
@
array
a
a_WT
))
(
a2
:
(
@
array
a
a_WT
))
(
i
:
Z
)
(
j
:
Z
),
(
exchange
a1
a2
i
j
)
->
(
permut_all
a1
a2
).
Axiom
array_eq_permut_all
:
forall
{
a
:
Type
}
{
a_WT
:
WhyType
a
}
,
forall
(
a1
:
(
@
array
a
a_WT
))
(
a2
:
(
@
array
a
a_WT
)),
(
array_eq
a1
a2
)
->
(
permut_all
a1
a2
).
Axiom
permut_sub_weakening
:
forall
{
a
:
Type
}
{
a_WT
:
WhyType
a
}
,
forall
(
a1
:
(
@
array
a
a_WT
))
(
a2
:
(
@
array
a
a_WT
))
(
l1
:
Z
)
(
u1
:
Z
)
(
l2
:
Z
)
(
u2
:
Z
),
(
permut_sub
a1
a2
l1
u1
)
->
(((
0
%
Z
<=
l2
)
%
Z
/
\
(
l2
<=
l1
)
%
Z
)
->
(((
u1
<=
u2
)
%
Z
/
\
(
u2
<=
(
length
a1
))
%
Z
)
->
(
permut_sub
a1
a2
l2
u2
))).
Axiom
permut_sub_permut_all
:
forall
{
a
:
Type
}
{
a_WT
:
WhyType
a
}
,
forall
(
a1
:
(
@
array
a
a_WT
))
(
a2
:
(
@
array
a
a_WT
))
(
l
:
Z
)
(
u
:
Z
),
(
permut_sub
a1
a2
l
u
)
->
(
permut_all
a1
a2
).
...
...
@@ -246,7 +264,7 @@ apply permut2_sym; auto.
apply
permut2_sym
;
auto
.
eapply
permut2_exchange
with
i
j
.
apply
H
.
a
pply
H0
.
a
e
.
ae
.
Qed
.
...
...
examples/verifythis_fm2012_LRS/why3session.xml
View file @
4cf56aa6
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