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Theorem int2bits-lslen-05
⊦ i < ~1 → (m < # int2bits(i) ↔ ¬ 0 ≤ i + 2 ^ (n→i(m) - 1))
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
int2bits-fill-rest
,
uint2bits-add-high-01
,
uint2bits-add-low-01
,
Used by units in proved state:
intops
,
bytes
,
byte
,
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 3
Proof steps: 10
Used lemmas:
int2bits-first-01
,
int2bits-not-empty
,
uint2bits-one
,
int2bits-neg-num
,
int2bits-lslen-02
,
Used spec theorems:
intnat
/
rax-01
Used simplifier rules:
nat
/
lez-01
nat-basic2
/
one
nat-basic2
/
oz
nat-basic2
/
l
nat-basic1
/
ref-1
nat
/
elim-pred-c
nat-basic1
/
lf-01
nat
/
lels-01
list
/bitlista/
app
list-data
/bitlista/
lf-01
nat-basic1
/
lf-02
nat-basic1
/
one
intnat
/
n2n
nat
/
pred-03
nat
/
lels-02
nat
/
ls-02
nat
/
lep-01
nat-basic2
/
c
nat-basic2
/
a
nat-basic2
/
s
nat-basic1
/
f
nat
/
fle
int-basic1
/
numlsf
nat
/
lels
int-abs
/
lels-01
int-abs
/
lels
int-abs
/
mone-08
int-abs
/
sub-le-01
int-abs
/
leone
intnat
/
num-n2i-ls-02
nat-basic1
/
z
list
/bitlista/
Two
bitopsaux
/
invert-zero
bitopsaux
/
inv-one-01
list
/bitlista/
c
list
/bitlista/
a
bitopsaux
/
succ-zero
list
/bitlista/
Last
bitopsaux
/
sgn-two-01
list
/bitlista/
len-02
nat-basic1
/
one-01
int-abs
/
mone-01
int-basic2
/
add-a
int-pot
/
grz
list-data
/bitlista/
l
int-basic2
/
add-zero
int-abs
/
lels-03
int-basic2
/
add-c