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Theorem int2bits-lelen
⊦ 0 < i → (# int2bits(i) ≤ m ↔ i < 2 ^ (n→i(m) - 1))
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
int2bits-add-low
,
int2bits-lelen-01
,
int2bits-lelen-03
,
int2bits-lslen
,
int2bits-lslen-01
,
Used by units in proved state:
intops
,
bytes
,
byte
,
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 7
Proof steps: 12
Used lemmas:
int2bits-len-pos
,
int2bits-zero
,
Used spec theorems:
int-pot
/
exin2pot
intnat
/
num-i2n-le
int-pot
/
succ
int-pot
/
ls-pos
Used simplifier rules:
int-basic1
/
ls-01
int-abs
/
succ-01
int-abs
/
sub-le-01
int-abs
/
mone-01
int-abs
/
numle-01
int-basic1
/
lf-03
int-pot
/
ls-pos
int-abs
/
numls-01
int-abs
/
succ-02
nat
/
lels-01
int-abs
/
numle-02
int-basic1
/
numlsf
nat-basic1
/
f
int-abs
/
numleledel-01
int-abs
/
lels-01
int-abs
/
lels-04
list
/bitlista/
len-02
int-pot
/
two-lez-01
int-pot
/
two-lez
int-abs
/
forward-lsle
int-mult
/
zero-gr
int-div
/
nummult-ls-02
int-mult
/
commutativity
int-mult
/
associativity
int-mult
/
one
int-mult
/
numls-09
int-basic1
/
trans
int-basic1
/
lf-01
int-abs
/
forward-lels
int-basic2
/
add-c
int-basic2
/
add-a
int-pot
/
succ
int-abs
/
lels-03
int-abs
/
lels
int-abs
/
elim-sub