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Theorem int2bytes-len-le
⊦ 0 ≤ i ∧ int2bytes(i).first ≠ i2b(0) → (n ≤ # int2bytes(i) ↔ 2 ^ ((n→i(n) - 1) * 8) ≤ i)
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
int2bytes-len-ls
,
int2bytes-len-ls-03
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 14
Proof steps: 26
Used lemmas:
bytes2int-size-02
,
int2int
,
int2bytes-empty
,
bytes2int-first-lez
,
bytes2int-size-03
,
Used spec theorems:
int-abs
/
lels-02
list
/bytelist/
fr
list-data
/bytelist/
length-rest
intnat
/
n2i-sub
int-mult
/
modlsp-02
intnat
/
num-n2i-ls-04
Used simplifier rules:
int-abs
/
numle-02
intnat
/
num-n2i-ls-07
intnat
/
add-nonneg-int-to-nat
nat
/
les
nat
/
eqle-one
nat-basic1
/
lf-01
nat-basic2
/
one
nat
/
lep-02
nat-basic2
/
s
nat
/
lels
nat
/
ler
intnat
/
n2i-add
int-abs
/
numsub
int-basic2
/
add-zero
int-mult
/
numls-02
int-mult
/
Mult-zero
int-abs
/
sub-le
nat-basic1
/
one
nat
/
fle-01
nat
/
not-zero
int-abs
/
Sub-def
nat-basic1
/
one-01
list-data
/bytelist/
l
int-basic2
/
lst-03
int-abs
/
mone-06
int-abs
/
numls-02
int-mult
/
zero-gr
int-abs
/
forward-le-05
nat
/
lels-01
int-abs
/
forward-lels
int-mult
/
commutativity
int-mult
/
associativity
intnat
/
nat2int
int-mult
/
zero-ge
int-pot
/
ls-pos-2pot-01
int-mult
/
ls-pos
int-abs
/
sub-ls-01
intnat
/
ls-int-ls-nat
int-basic2
/
add-a
int-basic2
/
add-c
int-pot
/
pot2-pos
int-abs
/
sub-le-01
int-abs
/
leone
intnat
/
num-n2i-ls-02
nat-basic1
/
z
nat
/
fle
nat-basic1
/
f
nat
/
sub-ls
nat-basic2
/
a
nat-basic2
/
c
nat
/
pred-03
byte
/
byte-equal-01
int-abs
/
lels-04
int-abs
/
zero-gels-04
int-abs
/
forward-le-04
int-abs
/
forward-lele
int-abs
/
lels
int-abs
/
forward-le-01
int-abs
/
lels-01