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Theorem int2bytes-first-zerobyte-01
⊦ 0 ≤ j → (int2bytes(j).first = i2b(0) ↔ (∃ i. 0 ≤ i ∧ 2 ^ (8 * i - 1) ≤ j ∧ j < 2 ^ (8 * i)))
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: 22
Proof steps: 41
Used lemmas:
int2bytes-first-zerobyte
,
Used spec theorems:
intnat
/
num-n2i-eq
intnat
/
add-01
intnat
/
i2n-mult
int2bits
/
int2bits-leneq-pos
nat-mult
/
modeq
nat-mult
/
mult-base
int-basic1
/
lsrec
int-pot
/
ls-pos-2pot
int-mult
/
modeqp-copied
int-mult
/
modlsp
int-mult
/
modlsp-03
Used simplifier rules:
int-basic2
/
lst-02
int-abs
/
numleledel-01
int-abs
/
numle-02
int-basic2
/
ls-01
int-pot
/
2pot-leone
int-abs
/
sub-eq-01
int-abs
/
minus-add
nat-basic2
/
oz
int-basic2
/
succ-01
int-abs
/
numadd
int-abs
/
numls-01
int-abs
/
lels-03
int-abs
/
numadd-01
int-mult
/
zero-eq
int-mult
/
numls-01
int-mult
/
Mult-zero
int-abs
/
numls-03
int-div
/
nummult-ls
int-abs
/
lsone
int-basic1
/
ls-01
int-abs
/
Sub-def
int-abs
/
anti
int-abs
/
bet-01
int-abs
/
mone-06
int-div
/
nummult-ls-03
int-abs
/
numls-02
int-pot
/
pot2-ls-pred
int-abs
/
ler
int-abs
/
succ-02
int-abs
/
numsub
int-abs
/
sub-add-01
int-abs
/
sub-ls
int-pot
/
ls-pos-2pot-01
int-basic1
/
two-ls
int-basic2
/
add-zero
nat-mult
/
one-01
intnat
/
n2i-mult
intnat
/
i2i-pos-01
intnat
/
n2i-add
nat-mult
/
zero-01
nat-basic2
/
one
intnat
/
num-i2n-eq
nat-basic2
/
z
nat-basic2
/
eq-01
intnat
/
num-i2n-ls
int-abs
/
numlelsdel
int-mult
/
zero-ls
int-pot
/
two-lez-01
int-mult
/
zero-gr
int-abs
/
leone
int-abs
/
sub-le-01
int-pot
/
pot2-pos
list
/bitlista/
len-02
int2bits
/
int2bits-zero
int-abs
/
lels-02
int-abs
/
forward-lels
int-basic1
/
forward-pos
int2bits
/
int2bits-len-one
nat-basic2
/
c
nat-basic2
/
a
nat-mult
/
mult-c
nat-mult
/
mult-a
nat-mult
/
zero-num
intnat
/
abs-zero
nat-basic2
/
z-01
nat-basic1
/
one
int-abs
/
zero-gels-04
int-mult
/
zero-ge
int-abs
/
lels-04
intnat
/
nat2int-08
int-abs
/
gr-def
int-mult
/
modzero-01
int-abs
/
zero-gels-01
int-abs
/
forward-le-02
int-abs
/
forward-lsle
int-basic2
/
add-c
int-basic2
/
add-a
int-mult
/
commutativity
int-mult
/
associativity
int-mult
/
zero-ge-add
int-abs
/
forward-le-05
intnat
/
num-n2i-ls-02
nat-basic1
/
z
list-data
/bitlista/
l
int2bits
/
int2bits-not-empty
int-div
/
div-elim
int-abs
/
forward-le-01
int-abs
/
lels
int-abs
/
lels-01