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Theorem int2bytes-rec-neg-05
j < ~(2 ^ (i * 8 - 1)), 0 < i, j % 2 ^ (i * 8) ≠ 0 ⊦ int2bytes(j) = int2bytes(j / 2 ^ (i * 8) - 1) + fix(i→n(i + 1), int2bytes(j % 2 ^ (i * 8))).rest
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
int2bytes-rec-neg-06
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 89
Proof steps: 168
Used lemmas:
bits2bytes-mklist-02
,
fix-bits2bytes-01
,
bits2bits-inj
,
bytes2int
,
fix-neg
,
bits2bytes-empty
,
bits2bytes-app
,
bits2bytes-len-02
,
bits2bytes-rec-02
,
bits2bytes-len-01
,
bits2bytes-base
,
bits2bytes-rec-01
,
fix-longer
,
int2bytes-byte
,
int2bytes
,
Used spec theorems:
int2bits
/
int2bits-rec-2pot-neg-02
int-div
/
div-zero-01
nat-div
/
modex
int2bits
/
int2bits-len-neg
intnat
/
rax-04
int-pot
/
zero
int2bits
/
int2bits-rest
nat-mult
/
zero-01
int2bits
/
int2bits-lslen-05
int-abs
/
mone-08
int-div
/
mod-grz
int-div
/
mod-lsz
list
/bitlista/
rest-01
list-data
/bitlista/
length-rest
list-del
/bytelist/
lastN-all
list-del
/bitlista/
rest-rec
list-del
/bitlista/
firstn-one-01
intnat
/
i2np
nat
/
prop-07
bitopsaux
/
fill-fill
nat
/
prop-01
list-del
/bitlista/
first-append
list-del
/bitlista/
first-mklist
nat
/
shift
int-div
/
mod-grz-01
int-pot
/
two-zero
Used simplifier rules:
list-del
/bitlista/
rest-mklist
list-del
/bitlista/
restN-append
nat
/
ls-02
nat-basic1
/
ls-02
nat
/
add-num-03
nat
/
eq-02
nat
/
le
nat
/
le-ls-simp
nat-basic1
/
trans
nat-basic1
/
trans-1
nat-basic2
/
succ
list-last
/bytelist/
mk-empty
list
/bytelist/
app-05
list-last
/bytelist/
mk-last
list-last
/bytelist/
mklist-one
list-last
/bytelist/
mk-plus
nat
/
ler
list-data
/bitlista/
length-rest
nat
/
l-num-04
nat-mult
/
ls-01
nat
/
not-zero
nat
/
let
int2bits
/
int2bits-zero
list
/bitlista/
rest
nat
/
le-num-05
list-data
/bytelist/
l
int-basic1
/
irref
list
/bytelist/
app-01
int-mult
/
zero-eq
nat
/
lels-03
int-mult
/
le-pos
intnat
/
labs-01
nat-basic2
/
eq
nat
/
anti
list
/bitlista/
app-02-ant
list-last
/bitlista/
mk-len
list
/bitlista/
len
nat
/
lels-02
int-div
/
mod-one
int-abs
/
zero-gels-04
nat
/
add-01
nat
/
pred-03
nat
/
lep-02
list
/bitlista/
Nil
nat
/
zero
nat
/
cancel-01
nat
/
zero-02
list-last
/bitlista/
mk-empty
int-div
/
mod-grz-01
int-abs
/
zero-gels-03
int2bits
/
int2bits-first-02
int-basic1
/
numlsf
int-basic2
/
add-zero
int-mult
/
abs-eqall
intnat
/
ini2-abs
intnat
/
n2i-add
int-abs
/
forward-lele
int-abs
/
lep-01
int-pot
/
two-lez-01
int-mult
/
zero-ls
list-data
/bitlista/
size-01
list
/bytelist/
app-04
int-basic1
/
lst-01
int2bits
/
int2bits-neg-num
int2bits
/
uint2bits-one
list
/bitlista/
Two
bitopsaux
/
invert-zero
bitopsaux
/
inv-one-01
bitopsaux
/
succ-zero
list
/bitlista/
Last
bitopsaux
/
sgn-two-01
list
/bitlista/
len-02
bitopsaux
/
fill-one-01
list-last
/bitlista/
mk-plus
bitlista
/
mklist-num-01
list-last
/bitlista/
mk-zero
list-last
/bitlista/
mk-last
list
/bitlista/
c-07
nat-basic2
/
l-02
nat
/
lels-01
int-abs
/
forward-le-04
int-abs
/
forward-lels
nat-div
/
mult
nat-basic2
/
z
intnat
/
abs-eq
list-del
/bitlista/
restN-zero
list-del
/bitlista/
firstN-zero
list
/bitlista/
app
list
/bitlista/
a
int2bits
/
bits2int-one
list
/bitlista/
c
int2bits
/
int2bits-first-01
list-del
/bitlista/
firstN-rec
list-del
/bitlista/
restN-rec
nat-div
/
mod-succ-06
nat-basic2
/
eq-01
nat-div
/
mod-le-02
list
/bytelist/
len
nat-mult
/
modeq-01
nat
/
add-num-01
int-pot
/
pot2-ls-pred
int-basic2
/
ls-01
int-div
/
nummult-ls-02
intnat
/
num-i2n-ls-02
int-mult
/
zero-ge-add
int-abs
/
zero-gels-01
int-abs
/
numsub
int-abs
/
sub-add-01
int-abs
/
sub-le-01
int-abs
/
leone
int-abs
/
Sub-def
int-abs
/
negle-13
list
/bytelist/
app-03
list
/bytelist/
c-07
list-del
/bitlista/
first-length
nat-mult
/
zero-01
nat-basic2
/
l-01
list-data
/bitlista/
l
nat
/
lep-01
nat-div
/
mod-mult
nat-mult
/
rsucc-02
nat-div
/
mult-01
int2bits
/
int2bits-not-empty
nat-div
/
mod-mult-01
nat-mult
/
mult-a
nat-mult
/
mult-c
int2bits
/
int2int-inj
list
/bytelist/
len-02
nat-basic2
/
one-03
intnat
/
abs-zero
list
/bytelist/
rest
list
/bytelist/
app
list
/bytelist/
a
list
/bytelist/
c-04
byte
/
i2b-noteq
int-abs
/
numls-02
int-abs
/
mone-06
int-abs
/
lels-02
int-basic1
/
ls-01
int-abs
/
ler
int-abs
/
abs-16
intnat
/
labs
nat-basic2
/
s
nat
/
les
nat-basic2
/
oz
nat-basic1
/
f
nat-basic1
/
lf-01
nat
/
eqle-one
list-del
/bytelist/
lastN-all
nat
/
ge
nat
/
succ-01
nat
/
lels
nat-basic2
/
a
nat-basic2
/
c
nat
/
eq
int-abs
/
neg-13
int-div
/
mod-zero-05
int-pot
/
pot2-pos
int-mult
/
zero-ge
int-abs
/
lels
int-abs
/
forward-lsle
int-abs
/
forward-le-01
int-basic2
/
ls
int-pot
/
two-lsz
int-abs
/
abs-08
int-abs
/
lels-03
int-mult
/
commutativity
int-mult
/
associativity
int-mult
/
zero-gr
int-abs
/
lels-01
int-abs
/
negle-07
int-abs
/
forward-le-05
int-abs
/
forward-le-02
int-abs
/
neg-07
int-basic2
/
add-c
int-basic2
/
add-a
intnat
/
abs-succ-03