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Theorem int2bytes-rec-pos-any
2 ^ (i * 8) ≤ j, 0 < i ⊦ int2bytes(j) = int2bytes(j / 2 ^ (i * 8)) + 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:
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 138
Proof steps: 261
Used lemmas:
bits2bytes-mklist
,
bytes2int-one
,
bits2bytes-rec-02
,
bits2bits-inj
,
bytes2bits-empty-01
,
bits2int-zero-ls
,
bytes2int
,
bits2bytes-len-01
,
fix-neg
,
fix-pos
,
bits2bytes-base
,
bits2bytes-rec-01
,
bits2bytes-empty
,
bits2bytes-len-02
,
fix-longer
,
bits2bytes-app
,
int2bytes
,
Used spec theorems:
int2bits
/
int2bits-rec-2pot-pos
int2bits
/
int2bits-len-mod2pot
int2bits
/
int2bits-rest
intnat
/
rax
bitopsaux
/
fill-fill
int2bits
/
int2bits-lslen-06
int-pot
/
mod2-2pot-05
int-div
/
mod-les
list-last
/bitlista/
mk-rest-01
list-del
/bytelist/
lastN-all
list-data
/bitlista/
length-rest
nat
/
prop-01
int2bits
/
int2bits-lelen
list
/bytelist/
first-01
byte
/
num-ibbi
int2bits
/
bits2int-le8-01
list-del
/bitlista/
first-num
nat-div
/
modex
int2bits
/
bits2int-lez
list-last
/bitlista/
mk-plus
list
/bitlista/
a
nat
/
zero-02
nat
/
num-02
nat
/
prop
nat-mult
/
zero-01
int2bits
/
int2bits-pos
nat-mult
/
numeral-32
list-del
/bitlista/
rest-app
list-del
/bitlista/
firstn-app-02
nat
/
sub-succ
int2bits
/
bits2int-zeros
int2bits
/
bits2int-pos-02
list-del
/bitlista/
firstn-first
intnat
/
i2np
nat-mult
/
mult-c
nat-mult
/
dist-sub
int-pot
/
mod2-pos
Used simplifier rules:
list-last
/bytelist/
mk-inj-01
nat-mult
/
mod-neq-01
nat-mult
/
ls-01
nat-basic1
/
z
list
/bytelist/
app-03
nat
/
lep
nat-basic1
/
one
nat-basic2
/
z-01
nat-div
/
nummult-eq
nat-div
/
mod-eq
nat-basic2
/
l-01
nat
/
l-num-01
nat-basic2
/
succ
nat
/
add-num-03
int2bits
/
uint2uint-pos
byte
/
i2b-noteq
list
/bytelist/
c-04
int-div
/
mod-zero
int-abs
/
forward-le
int-mult
/
one-01
nat
/
elim-pred-c
nat
/
lep-01
nat
/
le
nat
/
lels-03
list
/bytelist/
Nil
list-last
/bytelist/
mk-zero
nat
/
ls-01
nat
/
eq-02
nat
/
ls-03
int-abs
/
leone
intnat
/
num-i2n-le-02
nat
/
ls-02
nat
/
ls-le-simp
nat-basic1
/
ls-02
nat-mult
/
ls
nat-mult
/
zero-02
list-del
/bitlista/
firstN-empty
int2bits
/
bits2int-pos
int2bits
/
bits2uint-not-neg-01
int-basic1
/
numlsf
list-del
/bitlista/
first-length
nat-div
/
mod-le-02
int-abs
/
numlelsdel-01
nat-basic1
/
trans-1
nat-basic1
/
trans
int-basic2
/
num-between
int-basic1
/
numlslsdel-01
int-basic1
/
forward-pos
int-abs
/
numleledel-01
int-abs
/
zero-gels-03
list
/bytelist/
first
int2bits
/
int2int-inj
nat-basic1
/
lf-02
nat-mult
/
modls
nat-div
/
div-elim
nat-div
/
mult-01
list-last
/bytelist/
mk-empty
list
/bytelist/
app-05
list-last
/bytelist/
mk-last
list-last
/bytelist/
mklist-one
list-last
/bytelist/
mk-plus
int-abs
/
forward-lsle
nat-basic2
/
eq
list-last
/bitlista/
mk-rest-01
int-abs
/
zero-gels-01
int2bits
/
bits2int-zero
list
/bytelist/
len-02
list
/bytelist/
c-07
list-del
/bitlista/
firstN-zero
list-del
/bitlista/
restN-zero
int-div
/
nummult-ls-02
intnat
/
num-i2n-ls-02
nat
/
l-num-04
list-del
/bitlista/
firstN-rec
list-del
/bitlista/
restN-rec
nat-div
/
mod-succ-06
list
/bytelist/
len
nat-div
/
mod-succ-02
int-abs
/
lels-03
int-div
/
nummult-le
intnat
/
num-i2n-le
nat
/
le-num-05
int-abs
/
ler
nat
/
les
nat-basic2
/
oz
nat-basic1
/
lf-01
nat
/
eqle-one
intnat
/
abs-eq
nat-basic2
/
neq-01
nat-basic2
/
eq-01
nat-basic2
/
succ-03
list-data
/bytelist/
l
nat-div
/
mult
intnat
/
labs
int-basic1
/
irref
nat-div
/
mod-mult
nat
/
ge
int-pot
/
pot2-pos
int-basic2
/
add-zero
int-abs
/
numsub
int-abs
/
abs-16
int-mult
/
abs-eqall
intnat
/
ini2-abs
intnat
/
n2i-add
int-pot
/
two-lsz
int-abs
/
forward-le-02
bitopsaux
/
fill-one-01
bitlista
/
mklist-num
list
/bitlista/
app
list
/bitlista/
c-07
int-mult
/
zero-eq
nat-basic2
/
l-02
list
/bytelist/
a
list
/bytelist/
app-01
list
/bitlista/
e-01
list-last
/bitlista/
mk-last
list-last
/bitlista/
mklist-one
list-last
/bitlista/
mk-plus
nat
/
prop-07
list-last
/bitlista/
mk-len
list
/bitlista/
len
nat
/
zero-01
list-last
/bitlista/
mk-empty
list
/bitlista/
app-02-ant
nat
/
lels-02
int2bits
/
int2bits-zero
int2bits
/
int2bits-neg-num
int2bits
/
uint2bits-one
list
/bitlista/
Two
bitopsaux
/
invert-zero
bitopsaux
/
inv-one-01
list
/bitlista/
c
bitopsaux
/
succ-zero
list
/bitlista/
Last
bitopsaux
/
sgn-two-01
list
/bitlista/
len-02
int-abs
/
zero-gels-04
int-mult
/
zero-ge-add
intnat
/
num-i2n-eq
int-abs
/
numadd-01
int-mult
/
zero-neq-01
nat-div
/
mod-mult-01
nat
/
lep-02
nat-basic2
/
z
nat
/
add-01
nat
/
cancel-01
nat
/
pred-03
list
/bitlista/
a
list
/bitlista/
Nil
list-last
/bitlista/
mk-zero
nat
/
zero
int-mult
/
le-pos
int-abs
/
le-add
int-mult
/
numabs
intnat
/
labs-01
nat
/
let
nat
/
zero-02
int2bits
/
int2bits-first-02
bitopsaux
/
fill-fill
nat
/
le-ls-simp
int-abs
/
lels-02
nat-basic2
/
l
nat-mult
/
mult-a
intnat
/
abs-zero
nat-mult
/
zero-01
nat
/
succ-01
int-abs
/
numls-02
int-abs
/
mone-06
int-mult
/
zero-ge
nat-basic2
/
a
nat-basic2
/
s
list-data
/bitlista/
l
nat-basic1
/
f
nat
/
fle
nat
/
lels-01
int-abs
/
forward-le-01
nat-mult
/
mult-c
int-basic1
/
ls-01
nat-basic2
/
c
int-mult
/
zero-ls
int-pot
/
two-lez-01
int-abs
/
forward-le-04
int-abs
/
forward-lels
int-abs
/
forward-lele
nat
/
lels
int-abs
/
lels
int-abs
/
forward-le-05
int2bits
/
int2bits-not-empty
intnat
/
abs-succ-03
int-basic2
/
add-a
int-basic2
/
add-c
int-abs
/
lels-01
int-abs
/
lels-04
int-mult
/
zero-gr
int-mult
/
associativity
int-mult
/
commutativity