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Theorem int2bytes-len-ls-01
⊦ 0 ≤ i ∧ int2bytes(i).first = i2b(0) → (n < # int2bytes(i) ↔ 2 ^ (n→i(n) * 8)-1 ≤ i)
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
fillsgn-len-short
,
int2bytes-len-le-01
,
int2bytes-len-le-upper
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 34
Proof steps: 66
Used lemmas:
int2bytes-len-adjust
,
int2bytes-first-zerobyte
,
int2bytes-byte
,
Used spec theorems:
nat-div
/
modex
intnat
/
num-n2i-eq
intnat
/
Int2nat-pos
int2bits
/
int2bits-len-one
int2bits
/
int2bits-lelen-01
intnat
/
num-i2n-le-02
intnat
/
num-n2i-ls-04
int2bits
/
int2bits-lslen-01
intnat
/
sub
nat-basic2
/
c
nat
/
num-02
intnat
/
i2n-mult
int2bits
/
int2bits-lslen-06
int2bits
/
int2bits-leneq-pos
Used simplifier rules:
intnat
/
abs-eq
nat-basic2
/
z
nat-div
/
mult
int-pot
/
ls-pos-2pot-01
int-abs
/
sub-ls
int-abs
/
succ-02
int-mult
/
le-pos
int-abs
/
lels-03
intnat
/
i2i-pos
intnat
/
n2n
nat-mult
/
ls
intnat
/
nat2int-02
int-mult
/
zero-eq
nat
/
succ-01
nat
/
ls-02
nat-basic1
/
ls-02
nat-basic2
/
l-06
nat-basic2
/
succ
nat
/
ler
nat-basic1
/
trans-1
nat-basic1
/
trans
nat-basic1
/
lf-01
nat
/
eqle-one
nat
/
les
int-abs
/
ler
int-abs
/
abs-16
intnat
/
labs-01
nat-mult
/
le-num
nat
/
le-ls-simp
nat
/
ls-01
intnat
/
num-i2n-le-02
int-div
/
nummult-ls-02
int-abs
/
sub-ls-01
intnat
/
abs-pred
nat-basic2
/
l
nat
/
fle
int2bits
/
int2bits-not-empty
list-data
/bitlista/
l
nat-basic1
/
f
int-pot
/
pot2-ls-pred
int-pot
/
pot2-pos-01
int-abs
/
forward-lels
int-basic1
/
forward-pos
int-abs
/
minus-add
intnat
/
i2i-pos-01
intnat
/
n2i-add
nat-mult
/
zero-01
nat-basic2
/
one
nat
/
lez-01
intnat
/
abs-zero
nat-mult
/
zero-num
nat-basic2
/
one-03
nat-basic2
/
oz
nat-basic1
/
one
int-basic2
/
add-zero
int-abs
/
numsub
int-abs
/
numls-02
int-abs
/
mone-06
int-mult
/
zero-ge
int-abs
/
zero-gels-04
nat
/
lels-01
int-mult
/
zero-ge-add
int-abs
/
lels-04
int-basic2
/
add-a
int-basic2
/
add-c
intnat
/
nat2int
int-div
/
div-elim-pospos
nat-basic2
/
c
nat-basic2
/
a
nat-basic2
/
s
intnat
/
n2i-mult
nat-mult
/
mult-a
nat-mult
/
mult-c
int-div
/
mod-zero-num
nat
/
lels
int-basic1
/
ls-01
int-abs
/
lels
int-abs
/
forward-le-05
int-abs
/
lels-02
int-abs
/
forward-le-01
int-abs
/
lels-01
int-abs
/
sub-pred
list
/bytelist/
first
byte
/
num-i2b-equal
list
/bytelist/
len-02
nat-basic1
/
one-01
int-pot
/
pot2-pos
int-abs
/
sub-le-01
int-abs
/
leone
int-mult
/
zero-gr
intnat
/
num-n2i-ls-02
nat-basic1
/
z
int-mult
/
associativity
int-mult
/
commutativity