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Theorem int2bytes-len-neg-01
~(2 ^ (8 * (i + 1))) < j, j < ~(2 ^ (8 * (i + 1) - 1)), 0 ≤ i ⊦ # int2bytes(j) = i→n(i + 2)
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: 34
Proof steps: 56
Used lemmas:
int2bytes-len-fits
,
int2bytes-len-adjust
,
Used spec theorems:
nat-div
/
modex
nat-mult
/
eq
int-abs
/
forward-lsle
int-mult
/
modlsp
intnat
/
num-n2i-ls-04
intnat
/
num-n2i-ls-02
int2bits
/
int2bits-lslen-04
int2bits
/
int2bits-leneq-neg
int2bits
/
int2bits-rec-neg
intnat
/
i2n-mult
int-pot
/
ls-pos-2pot
int-mult
/
modlsp-03
intnat
/
add-01
nat-mult
/
mult-c
nat-mult
/
mod-nle
intnat
/
num-i2n-le-02
Used simplifier rules:
nat-basic2
/
s
nat-basic1
/
neq-01
nat-basic2
/
eq-01
nat
/
add-num-01
intnat
/
abs-02
int-abs
/
forward-le
nat
/
ls-le-simp
nat
/
lels
int-abs
/
numlelsdel
intnat
/
nat2int-10
nat-basic1
/
lstwo
nat
/
lels-01
intnat
/
num-n2i-ls-06
intnat
/
le
nat
/
ler
nat-basic2
/
z
intnat
/
num-n2i-ls
intnat
/
nat2int
int-pot
/
pot2-ls-pred
int-basic2
/
add-zero
int-abs
/
succ-01
int-mult
/
le-pos
int-abs
/
succ-02
nat-mult
/
coef-20
nat
/
le-num-01
intnat
/
nat2int-14
nat-basic2
/
oz
nat-mult
/
rsucc-02
intnat
/
n2i-add
nat-basic2
/
one
nat-basic2
/
one-03
list
/bitlista/
a
list
/bitlista/
len-02
list
/bitlista/
len
int-pot
/
eq-one
int-mult
/
zero-eq
int-pot
/
2pot-leone
int-div
/
nummult-ls
int-abs
/
numls-03
nat
/
lep
int-abs
/
numadd-01
intnat
/
num-i2n-eq
nat-basic1
/
lf-02
nat-basic2
/
one-01
nat-basic2
/
z-01
int-abs
/
lels-03
nat-div
/
div-elim
int-abs
/
negeq
intnat
/
rax-04
nat-basic1
/
trans
nat-basic1
/
trans-1
nat-basic2
/
succ
nat-basic2
/
l
intnat
/
labs
int-abs
/
absle
int-basic1
/
irref
nat
/
add-num-03
nat-basic1
/
f
nat
/
lels-02
int-basic2
/
lst-02
intnat
/
le-int-le-nat
nat
/
le-add
nat-basic2
/
a
nat-basic2
/
c
int-abs
/
le-add
int-abs
/
sub-eq
intnat
/
inj
int-abs
/
forward-lels
int-abs
/
forward-lele
int-abs
/
forward-le-04
int-basic1
/
ls-01
int-abs
/
minus-add
int-abs
/
numleledel-01
int-abs
/
numle-02
int-mult
/
zero-ge
int-abs
/
sub-ls-01
int-basic2
/
lst-03
int-abs
/
lels-01
int-abs
/
lels-04
int-mult
/
ls-pos
int-abs
/
Sub-def
int-mult
/
zero-gr
int-abs
/
numls-02
int-abs
/
mone-06
int-abs
/
zero-gels-04
int-mult
/
Mult-zero
int-mult
/
numls-01
int-abs
/
numsub
int-abs
/
sub-add-01
int-abs
/
sub-ls
int-pot
/
ls-pos-2pot-01
int-abs
/
sub-le-01
int-div
/
nummult-le-02
int-abs
/
leone
intnat
/
num-n2i-ls-02
nat-basic1
/
z
int-mult
/
associativity
int-basic2
/
ls-01
int-mult
/
commutativity
int-abs
/
negle-13
intnat
/
n2i-mult
nat-mult
/
zero-01
int-abs
/
lels
nat-basic1
/
one
nat-mult
/
zero-num
nat-mult
/
one-01
int-basic2
/
ls
int-pot
/
two-lsz
list-data
/bitlista/
l
int2bits
/
int2bits-not-empty
nat-mult
/
mult-c
nat-mult
/
mult-a
nat-div
/
mult-01
int-abs
/
zero-gels-01
int-basic2
/
add-c
int-basic2
/
add-a
int-abs
/
forward-le-01
int-abs
/
forward-le-05
int-abs
/
forward-le-02
int-abs
/
forward-lsle
int-abs
/
neg-07
int-abs
/
neg-13