[Imprint]
[Data Privacy Statement]
[E-Mail]
View
long theorem info
. View
the proof
. Back to
main index
. View
the specification
. View
theorem base summary
, View
theorem base listing
, the
used properties by spec
, the
dependency list
, the
symbol table
,
Theorem array-le-swap
⊦ i < # ar ∧ j < # ar ∧ i < j → (ar ≤ ar[i, ar[j]][j, ar[i]] ↔ ar[i] ≤ ar[j])
Type: A user defined theorem
Validity: The proof is valid.
Features: s, ls,
Comment:
Used by:
next-proper-permutation
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 5
Proof steps: 11
Used lemmas:
array-le-refl
,
lexicographic-rec1
,
Used spec theorems:
Used simplifier rules:
nat-basic
/
succ
nat-basic
/
f
list-data
/natarray-oarray-sort/
l
nat-basic
/
lf
oelem
/natarray/
transitivity
nat
/
fle
oelem
/natarray/
ls-le
nat
/
lels
nat-basic
/
c
nat-basic
/
a
nat-basic
/
l
list
/natarray-oarray-sort/
a
list
/natarray-oarray-sort/
len-05
list
/natarray-oarray-sort/
c
nat-basic
/
s-04
list
/natarray-oarray-sort/
e-01
nat-basic
/
zero
list-del
/natarray-oarray-sort/
get-zero
list-del
/natarray-oarray-sort/
put-zero
list-del
/natarray-oarray-sort/
get-succ
list-del
/natarray-oarray-sort/
put-succ
array
/natarray/
put-same-content
nat
/
lels-02
nat-basic
/
oz
nat
/
succ-01
nat
/
le-def
nat-basic
/
ls-02
nat
/
lez
nat
/
l-num-06