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Theorem int2bytes-len-pos
0 ≤ i, 2 ^ (8 * i) ≤ j, j < 2 ^ (8 * (i + 1) - 1) ⊦ # int2bytes(j) = i→n(i + 1)
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: 16
Proof steps: 30
Used lemmas:
int2bytes-len-fits
,
int2bytes-len-adjust
,
Used spec theorems:
int2bits
/
int2bits-lslen-01
nat-div
/
modex
intnat
/
sub
intnat
/
i2n-mult
int2bits
/
int2bits-lelen-01
int2bits
/
int2bits-lslen-06
int2bits
/
int2bits-leneq-pos
int2bits
/
int2bits-len-one
int-mult
/
modlsp-03
Used simplifier rules:
nat-basic2
/
eq
intnat
/
nat2int-05
intnat
/
n2n
int-abs
/
anti
int-abs
/
le-add-02
int-mult
/
ls-add-03
intnat
/
num-n2i-ls-03
int-abs
/
numle-03
intnat
/
nat2int-10
int-mult
/
le-dist-01
intnat
/
nat2int
int-basic2
/
lst-03
intnat
/
abs-02
intnat
/
num-n2i-ls
nat
/
lels
nat
/
ls-le-simp
int-abs
/
forward-le
int-abs
/
forward-lsle
int-abs
/
succ-01
int-mult
/
ls-pos
nat-basic2
/
oz
nat
/
ler
intnat
/
le
int-abs
/
succ-02
int-basic2
/
ls-01
int-abs
/
sub-add-01
int-abs
/
sub-ls
int-basic1
/
two-ls
int-abs
/
sub-eq-01
int-pot
/
2pot-leone
intnat
/
n2i-mult
nat-basic2
/
one
int-abs
/
lels-02
intnat
/
abs-zero
nat-basic1
/
lf-02
nat-basic2
/
one-01
nat-mult
/
zero-num
nat-basic2
/
z-01
nat-basic1
/
one
int-basic1
/
ls-01
nat-div
/
div-elim
int-basic2
/
add-zero
int-abs
/
numsub
intnat
/
ini2-abs
intnat
/
n2i-add
nat-basic2
/
eq-01
int-abs
/
numle-02
int-abs
/
numleledel-01
nat-mult
/
rsucc-02
nat
/
add-01
nat-mult
/
coef-20
nat
/
les
nat-basic2
/
succ-03
nat-mult
/
modls
nat-div
/
mult-01
nat-mult
/
mult-c
nat-mult
/
mult-a
nat-mult
/
zero-01
nat-basic1
/
lf-01
nat-basic2
/
c
nat-basic2
/
a
int-abs
/
absle
int-mult
/
abs-eqall
intnat
/
labs
nat-basic2
/
l
nat
/
fle
int-abs
/
lels-03
int-div
/
nummult-ls-02
int-pot
/
pot2-pos-01
int-abs
/
mone-06
int-abs
/
numls-02
int-mult
/
zero-gr
int-abs
/
leone
int-abs
/
sub-le-01
int-pot
/
pot2-pos
int2bits
/
int2bits-not-empty
list-data
/bitlista/
l
int-abs
/
forward-le-05
int-basic1
/
forward-pos
nat-basic1
/
f
nat
/
lels-01
int-abs
/
lels
int-abs
/
lels-01
int-abs
/
lels-04
int-abs
/
forward-lele
int-abs
/
forward-le-04
int-pot
/
two-lez-01
int-mult
/
zero-ls
int-abs
/
sub-ls-01
int-pot
/
ls-pos-2pot-01
int-mult
/
zero-ge
int-abs
/
zero-gels-04
int-mult
/
associativity
int-mult
/
commutativity
int-abs
/
forward-le-01
int-abs
/
forward-lels
int-basic2
/
add-c
int-basic2
/
add-a
intnat
/
rax-04