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Theorem int2bits-restsgn
¬(∃ i. 2 ^ i = j), 0 ≤ j ⊦ sgn(int2bits(2 ^ n→i(# int2bits(j)) - j).rest) = int2bits(2 ^ n→i(# int2bits(j)) - j).rest
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
int2bits-neg-02
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 7
Proof steps: 15
Used lemmas:
uint2bits-restsgn
,
int2bits-len-pos
,
uint2bits-one
,
uint2bits-pos-num
,
int2bits-zero
,
int2bits-less-2pot-02
,
int2bits-pos
,
Used spec theorems:
int-pot
/
exin2pot
Used simplifier rules:
int-abs
/
leone
int-basic1
/
two-ls
int-basic1
/
lf-02
bitopsaux
/
sgn-two-01
list
/bitlista/
app-04
list
/bitlista/
e
int-pot
/
eq-one
int-abs
/
numlsf-01
int-mult
/
ls-same-01
int-abs
/
ler
int-basic2
/
ls-02
int-pot
/
ls-pos
int-pot
/
two-zero
int-basic1
/
ls-01
int-abs
/
lep
int-abs
/
absle
int-abs
/
abs-12
intnat
/
ini2-abs
int-abs
/
lels-04
int-abs
/
lels-03
intnat
/
nat2int
int-mult
/
zero-gr
int-div
/
nummult-ls-02
int-mult
/
commutativity
int-mult
/
associativity
int-mult
/
one
int-mult
/
numls-09
int-pot
/
two-le
int-basic1
/
trans
int-basic1
/
lf-01
int-abs
/
forward-lsle
int-abs
/
forward-lels
int-pot
/
succ
int-abs
/
lels-02
list
/bitlista/
app-01
bitopsaux
/
sgn-two-03
list
/bitlista/
a
list
/bitlista/
c-07
list
/bitlista/
Last
list
/bitlista/
Two
list
/bitlista/
len-02
int-abs
/
anti
int-abs
/
lels
int-abs
/
forward-lele
int-abs
/
lels-01
int-basic2
/
add-c
int-basic2
/
add-a
int-basic2
/
add-zero
int-abs
/
sub-le-01