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Theorem rev-subarray-split-last-swap
3 + n0 + k + n + m ≤ # ar ⊦ k ≤ 1 → subarray(ar, m + 1, n) + rev(subarray(ar, m + n + 1, k + 2)) + subarray(ar, m + n + 3 + k, n0) = subarray(ar[m + n + 1, ar[m + n + k + 2]][m + n + k + 2, ar[m + n + 1]], m + 1, n + k + 2 + n0)
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: 15
Proof steps: 50
Used lemmas:
get-rev
,
Used spec theorems:
array
/natarray/
Extension
list-del
/natarray-oarray-sort/
get-append-less
array-copy
/natarray/
at-subarray
array
/natarray/
Put-other
Used simplifier rules:
nat-basic
/
c
nat-basic
/
a
nat
/
add-num-03
nat-basic
/
f
array-copy
/natarray/
subarray-at
list
/natarray-oarray-sort/
a
array-copy
/natarray/
size-subarray
list-last
/natarray-oarray-sort/
rev-length
list
/natarray-oarray-sort/
len
nat-basic
/
eq-01
nat-basic
/
one
nat-basic
/
l
array
/natarray/
cgetput
nat
/
le-num-06
nat
/
lep-02
nat
/
let
nat
/
lels
array
/natarray/
Size-put
oelem
/natarray/
lel
nat
/
add-num-01
nat-basic
/
l-02
nat
/
eq-01
list-del
/natarray-oarray-sort/
get-append-grt
nat
/
cancel-01
nat
/
zero
nat-basic
/
zero
nat
/
le-def
nat
/
fle-01
nat-basic
/
l-01
nat
/
elim-sub
nat
/
lep
nat-basic
/
one-03
nat
/
ls-le-simp
nat
/
le-num-01
nat
/
lels-02
nat-basic
/
s-04
nat-basic
/
between
nat
/
lez
nat-basic
/
oz
nat-basic
/
add-base
nat-basic
/
eq-02
nat-basic
/
one-04
nat
/
one-02
nat
/
anti
nat-basic
/
lf-01
nat-basic
/
ls-02