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Theorem uint2bits-2potrec
0 ≤ i, 2 ^ i ≤ j ⊦ uint2bits(j) = uint2bits(j / 2 ^ i) + fillsgn(i→n(i + 1), uint2bits(j % 2 ^ i)).rest
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
int2bits-mod2pot
,
int2bits-rec-2pot-neg-02
,
uint2bits-mod2pot-01
,
Used by units in proved state:
bytes
,
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 9
Proof steps: 18
Used lemmas:
uint2bits-empty
,
uint2bits-len-min
,
uint2bits-div2pot
,
uint2bits-zero
,
uint2bits-one
,
uint2bits-2pot
,
uint2bits-mod2pot
,
Used spec theorems:
list-del
/bitlista/
lastN-rest
bitopsaux
/
fill-sgn-01
bitopsaux
/
fillsgn-longer
list-del
/bitlista/
lastn-length-01
list-del
/bitlista/
lastN-blastN
Used simplifier rules:
int-abs
/
ler
intnat
/
labs-01
int-abs
/
lels-02
nat-basic2
/
succ
intnat
/
abs-zero
nat-basic1
/
trans
nat
/
lels-02
nat
/
anti
nat
/
fle-01
nat-basic1
/
ls-02
nat
/
lels-03
intnat
/
labs
int-abs
/
absle
int-basic1
/
irref
nat
/
lels-01
nat
/
lep-02
list
/bitlista/
len-02
list
/bitlista/
len
nat
/
lels
nat
/
fle
nat-basic2
/
l-02
int-basic1
/
trans
int-basic2
/
succ-01
int-abs
/
numls-03
list-data
/bitlista/
l
nat-basic1
/
f
int-abs
/
forward-lsle
int-abs
/
forward-lels
int-basic1
/
lf-01
int-pot
/
two-lsz
int-basic1
/
ls-01
list
/bitlista/
app-01
list
/bitlista/
c-07
nat-basic2
/
c
nat-basic2
/
a
list
/bitlista/
a
list-last
/bitlista/
mk-last
list-last
/bitlista/
mklist-one
list-last
/bitlista/
mk-plus
bitopsaux
/
fill-one-01
int-div
/
mod-same
list
/bitlista/
Two
int-div
/
div-same
int-pot
/
two-zero
int-abs
/
anti
int-abs
/
lels
int-abs
/
lels-04
int-abs
/
lels-01
int-basic2
/
add-c
int-basic2
/
add-a
intnat
/
rax-04