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Theorem int2bytes-len-eq-pos
⊦ 0 ≤ i ∧ int2bytes(i).first = i2b(0) → (# int2bytes(i) = n ↔ 2 ^ ((n→i(n) - 1) * 8 - 1) ≤ i ∧ i < 2 ^ ((n→i(n) - 1) * 8) ∧ 0 < n)
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: 31
Proof steps: 56
Used lemmas:
bytes2int-size-01
,
int2int
,
no-leading-zero-01
,
int2bytes-byte
,
int2bytes-zero
,
int2bytes-empty
,
bytes2int-size
,
Used spec theorems:
nat-basic1
/
lstwo
list-data
/bytelist/
length-rest
intnat
/
n2i-sub
Used simplifier rules:
nat-basic1
/
trans-1
nat-basic1
/
trans
nat-basic1
/
lf-01
nat-basic1
/
ls-02
nat
/
le-ls-simp
int-abs
/
succ-01
int-abs
/
sub-le
int-pot
/
2pot-leone
int-div
/
nummult-ls
int-abs
/
numls-03
intnat
/
nat2int-08
nat-basic1
/
ref-1
intnat
/
nat2int-04
nat
/
sub-ls
int-pot
/
pot2-ls-pred
nat-basic1
/
lstwo
nat
/
lels-02
intnat
/
ls-int-ls-nat
int-mult
/
ls-pos
intnat
/
le
nat
/
leprf
nat
/
let
nat-basic2
/
c
nat-basic2
/
a
list-data
/bytelist/
lr-04
nat
/
succ-01
nat
/
lep-02
nat
/
le
intnat
/
le-int-le-nat
int-mult
/
le-pos
int-abs
/
succ-02
int-abs
/
sub-ls
int-pot
/
ls-pos-2pot-01
int-abs
/
numls-02
int-abs
/
mone-06
list
/bytelist/
fr
list-data
/bytelist/
length-rest
intnat
/
nat2int
nat
/
not-zero
int-abs
/
Sub-def
list
/bytelist/
onein
nat-basic1
/
lf-02
list
/bytelist/
c-03
int-abs
/
zero-gels-04
int-abs
/
lels-04
nat-basic1
/
f
nat
/
ls-02
nat
/
lels-01
nat-basic1
/
one-01
list-data
/bytelist/
l
nat
/
pred-03
int-abs
/
forward-lels
int-basic2
/
add-c
int-basic2
/
add-a
intnat
/
num-n2i-ls-07
int-abs
/
numle-02
int-mult
/
zero-ge
int-abs
/
forward-le-05
list
/bytelist/
app
list
/bytelist/
len-02
int-pot
/
pot2-pos
int-abs
/
sub-le-01
int-abs
/
leone
int-mult
/
zero-gr
int-abs
/
sub-ls-01
intnat
/
num-n2i-ls-02
nat-basic1
/
one
int-mult
/
associativity
int-mult
/
commutativity
list
/bytelist/
a
list
/bytelist/
in-14
list
/bytelist/
c
list-data
/bytelist/
elim-list
int-abs
/
forward-le-01
nat-basic1
/
z
int-abs
/
lels
int-abs
/
lels-01