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Theorem int2bytes-len-le-neg
⊦ i < 0 ∧ int2bytes(i).first ≠ i2b(~1) → (n ≤ # int2bytes(i) ↔ i < ~(2 ^ (8 * (n→i(n) - 1))))
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
int2bytes-len-eq-neg
,
int2bytes-len-ls-neg-02
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 10
Proof steps: 20
Used lemmas:
bytes2int-size-04
,
int2int
,
int2bytes-empty
,
bytes2int-first-lez
,
bytes2int-size-06
,
Used spec theorems:
intnat
/
n2i-sub
list
/bytelist/
fr
list-data
/bytelist/
length-rest
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-basic2
/
a
nat-basic2
/
c
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
int-basic2
/
lst-03
intnat
/
n2i-sub
int-abs
/
sub-ls-01
int-abs
/
negle-13
nat-basic1
/
one
nat
/
fle-01
nat-basic1
/
f
int-abs
/
forward-lsle
int-abs
/
forward-le-01
int-abs
/
zero-gels-01
int-basic2
/
ls-01
int-mult
/
commutativity
int-mult
/
associativity
nat-basic1
/
z
intnat
/
num-n2i-ls-02
int-abs
/
leone
int-abs
/
sub-le-01
int-mult
/
zero-ge
int-pot
/
ls-pos-2pot-01
int-mult
/
ls-pos
int-abs
/
sub-ls
int-abs
/
Sub-def
intnat
/
nat2int-04
nat
/
le-ls-simp
nat
/
not-zero
nat
/
lels-01
nat-basic1
/
one-01
list-data
/bytelist/
l
int-abs
/
lels-01
int-basic2
/
add-a
int-basic2
/
add-c
nat
/
pred-03
byte
/
byte-equal-01
int-abs
/
lels-03
int-abs
/
forward-le-02
int-abs
/
lels
int-abs
/
neg-07