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Theorem uint2bits-add-low-01
⊦ j0 < 0 ∧ 0 < i ∧ abs(j0) ≤ 2 ^ (i - 1) ∧ 0 < j → uint2bits(j * 2 ^ i + j0) = uint2bits(j - 1) + fillsgn(i→n(i), int2bits(j0))
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
int2bits-add-low
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 10
Proof steps: 17
Used lemmas:
uint2bits-one
,
int2bits-neg-num
,
int2bits-lslen-05
,
int2bits-not-empty
,
uint2bits-mod2pot-01
,
uint2bits-add-low
,
uint2bits-zero
,
Used spec theorems:
int-abs
/
zero-gels-03
int-pot
/
two-le
Used simplifier rules:
intnat
/
i2i-pos
list
/bitlista/
Two
bitopsaux
/
invert-zero
bitopsaux
/
inv-one-01
list
/bitlista/
c
bitopsaux
/
succ-zero
list
/bitlista/
Last
bitopsaux
/
sgn-two-01
bitopsaux
/
fill-one-02
int-abs
/
minus-add
int-abs
/
leone
int-pot
/
pot2-pos
list
/bitlista/
len-02
intnat
/
num-i2n-ls
int-abs
/
bet-01
list-last
/bitlista/
mk-zero
list
/bitlista/
app
bitopsaux
/
fill-one
list
/bitlista/
rest
list-data
/bitlista/
l
nat-basic1
/
f
nat
/
lels-01
bitopsaux
/
fill-refill
nat-basic2
/
a
nat-basic2
/
c
int-abs
/
anti
bitopsaux
/
fill-zero
int-abs
/
numle-02
int-abs
/
mone-08
int-basic2
/
add-zero
int-abs
/
zero-gels-02
int-basic1
/
forward-pos
list
/bitlista/
a
list
/bitlista/
app-01
int-abs
/
sub-le-01
int-abs
/
lep-01
int-abs
/
lep-02
int-basic2
/
ls
int-abs
/
bet
int-abs
/
sub-ls-01
int-basic1
/
ls-01
int-abs
/
lels-01
int-mult
/
succ-rmerge
int-abs
/
Sub-def
int-basic2
/
add-a
int-basic2
/
add-in
int-abs
/
zero-gels-01
int-abs
/
lels
int-abs
/
lels-03
int-abs
/
zero-gels-04
int-basic2
/
add-c
int-mult
/
commutativity
int-mult
/
associativity
int-mult
/
one
int-abs
/
forward-le-02
int-abs
/
forward-le-05
int-abs
/
forward-le-01
int-abs
/
negle-13
int-abs
/
abs-08