[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 next-proper-permutation
ar = ar0 ⊦ ⟨next#(; ar; hasNext)⟩ (hasNext ⊃ nextperm(ar0, ar);ar = ar0 ∧ max(ar))
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
permut-correct
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 52
Proof steps: 167
Used lemmas:
ordered-all-rev
,
minimum-permutation
,
ascending-order-is-min-permuted
,
array-neg-le-eq-2
,
lexicographic-rec1
,
subarray-inc-offset0
,
array-le-kill-prefix
,
array-le-trans
,
array-le-one-diffrent-position
,
next-permutation
,
rev-subarray-split-last-swap
,
rev-subarray-split-step
,
get-rev
,
subarray-write-above
,
remains-ordered-by-swap
,
array-le-swap
,
descending-order-is-max-permuted
,
ordered-step-down
,
ordered-size-smaller-one
,
lexicographic-base1
,
maximum-permutation
,
next
,
Used spec theorems:
array
/natarray/
Extension
array-listops
/natarray/
nil
list-perm
/natarray-oarray-sort/
perm-switch
array
/natarray/
cputput-reverse
list-perm
/natarray-oarray-sort/
l
list-perm
/natarray-oarray-sort/
trans
list-perm
/natarray-oarray-sort/
sym
list-perm
/natarray-oarray-sort/
del
list-del
/natarray-oarray-sort/
in-get
list-perm
/natarray-oarray-sort/
del-01
nat-basic
/
addex
Used simplifier rules:
list-data
/natarray-oarray-sort/
l
nat
/
lez-01
nat-basic
/
succ
nat-basic
/
zero
nat
/
gr-def
list-perm
/natarray-oarray-sort/
empty-01
nat
/
pred-03
nat
/
le-def
nat-basic
/
one-01
nat
/
ls-01
nat-basic
/
s-04
nat-basic
/
ls-02
nat-basic
/
a
nat-basic
/
c
oelem
/natarray/
irreflexivity
nat
/
elim-pred-c
nat
/
eq-03
list-last
/natarray-oarray-sort/
rev-length
array-copy
/natarray/
size-subarray
nat-basic
/
f
oelem
/natarray/
ls-le
nat
/
ge
nat-basic
/
oz
nat
/
succ-01
nat
/
lels
nat
/
fle
nat-basic
/
l-02
nat
/
elim-sub
nat-basic
/
one-06
nat-basic
/
one
nat-basic
/
l
nat-basic
/
lf-01
nat
/
lels-03
nat-basic
/
eq-01
nat-basic
/
l-01
nat-basic
/
one-03
nat
/
sub-base
array-copy
/natarray/
subarray-elim-simp
oelem
/natarray/
transitivity
nat-basic
/
lf
nat
/
fle-01
nat
/
ls-02
nat
/
ls-le-simp
nat
/
les
nat
/
eqle-one
oelem
/natarray/
lel
nat
/
lep-02
nat
/
le-ls-simp
nat
/
let
nat
/
anti
array
/natarray/
Size-put
array
/natarray/
cgetput
array
/natarray/
ngp-07
array
/natarray/
put-same-content
array
/natarray/
ngp-08
nat
/
ler
list-del
/natarray-oarray-sort/
put-length
nat
/
l-num-04
nat-basic
/
l-06
array
/natarray/
ngp-06
nat
/
lels-02
array
/natarray/
Put-same
nat
/
ls-03
list
/natarray-oarray-sort/
a
array-copy
/natarray/
subarray-write-below
nat
/
cancel-01
array-copy
/natarray/
subarray-zero
nat
/
zero
nat
/
ls
nat-basic
/
add-base
nat
/
add-01
nat
/
le-num-01
nat
/
l-num-02
list-last
/natarray-oarray-sort/
revert-equal
list
/natarray-oarray-sort/
app
list
/natarray-oarray-sort/
Nil
list-perm
/natarray-oarray-sort/
ref
nat
/
eq
array-copy
/natarray/
subarray-at
list-del
/natarray-oarray-sort/
get-zero-01
nat-basic
/
less-zero
array
/natarray/
ngp-09
nat
/
prop-07
nat
/
l-num-06
nat
/
sub-add
nat
/
eq-01
nat
/
lep
nat
/
le-num-05
nat-basic
/
l-08
nat
/
l-num-01
nat
/
add-num-03
nat
/
l-num-03
nat
/
add-num-01
nat-basic
/
eqs
list-perm
/natarray-oarray-sort/
trans
list
/natarray-oarray-sort/
c
array
/natarray/
eq-write-left
list-perm
/natarray-oarray-sort/
cons
list
/natarray-oarray-sort/
c-06
list-del
/natarray-oarray-sort/
del1-n
list
/natarray-oarray-sort/
in-01
nat-basic
/
nls-fst
array
/natarray/
Put-other
nat-basic
/
eq-02
nat-basic
/
z-01