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Theorem int2bits-add-low
⊦ j < 0 ∧ j0 < 0 ∧ abs(j0) < 2 ^ (i - 1) ∧ 0 < i → int2bits(j * 2 ^ i + j0) = int2bits(j - 1) + fillsgn(i→n(i), int2bits(j0))
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
Used by units in proved state:
byte
,
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 36
Proof steps: 60
Used lemmas:
int2bits-lelen
,
int2bits-neg-num
,
int2bits-sgn-02
,
int2bits-len-pos-pred
,
int2bits-2pot
,
int2bits-2pot-01
,
int2bits-2pot-02
,
int2bits-neg-02
,
uint2bits-empty
,
int2bits-lelen-04
,
int2bits-len-add
,
int2bits-zero
,
uint2bits-add-low-01
,
int2bits-eq
,
int2bits-first-02
,
int2bits-lslen-09
,
int2bits-len-neg-01
,
int2bits-not-empty
,
uint2bits-pos-num
,
uint2bits-one
,
int2bits-pos-num
,
int2bits-lelen-02
,
int2bits-pos
,
int2bits-neg-03
,
Used spec theorems:
int-mult
/
modzero-03
nat-basic2
/
c
int-abs
/
forward-lels
list
/bitlista/
rest-01
int-abs
/
forward-lele
int-pot
/
two-le
int-abs
/
sub-add-01
int-pot
/
pot-dist-pos
intnat
/
num-n2i-ls-04
int-pot
/
Pot-pos
int-mult
/
zero-gr-add-01
Used simplifier rules:
int-mult
/
modzero-01
int-mult
/
succ-rmerge
int-abs
/
sub-pred
int-abs
/
neg
int-mult
/
eq-dist
int-basic2
/
add-in
bitopsaux
/
invert-zero
bitopsaux
/
inv-one-01
bitopsaux
/
succ-zero
int-abs
/
zero-gels-01
int-abs
/
zero-gels-03
int-abs
/
sub-sub-04
int-abs
/
numsub
list
/bitlista/
e
list
/bitlista/
c-03
int-basic1
/
lst
int-abs
/
Sub-def
int-abs
/
minus-sub
int-pot
/
two-minus
int-mult
/
one
list-last
/bitlista/
mk-len
intnat
/
ini2-abs
int-abs
/
sub-add-06
int-pot
/
pot2-pos-01
int-abs
/
abs-16
int-pot
/
pot2-succ-01
bitopsaux
/
sgn-true-mklist
list
/bitlista/
app-01
int-abs
/
sub-eq
int-abs
/
lsone
int-abs
/
sub-ls
int-abs
/
sub-add-01
int-abs
/
minus-02
int-abs
/
neg-15
int-abs
/
sub-sub
int-abs
/
sub-add-09
int-abs
/
neg-12
int-abs
/
lep-02
int-abs
/
negeq
int-mult
/
Mult-zero
int-basic2
/
ls-02
int-abs
/
sub-add
nat-basic2
/
c
nat-basic2
/
a
intnat
/
i2i-pos
intnat
/
n2i-add
int-abs
/
lep-01
int-mult
/
zero-le-03
int-abs
/
lels-04
int-abs
/
lels-02
int-basic2
/
add-zero
bitopsaux
/
fill-one-02
int-mult
/
zero-eq
int-pot
/
zero
int-mult
/
associativity
int-abs
/
sub-le-01
int-abs
/
leone
int-abs
/
forward-le-04
int-abs
/
negle-13
int-abs
/
neg-10
list
/bitlista/
app
list
/bitlista/
c
int-mult
/
commutativity
int-abs
/
neg-05
list-data
/bitlista/
lf-01
nat-basic1
/
one
nat-basic1
/
z
intnat
/
num-n2i-ls-02
int-basic1
/
forward-pos
int-abs
/
subsub
list-data
/bitlista/
l
nat-basic1
/
f
nat
/
lels-01
intnat
/
n2n
int-abs
/
mone-08
intnat
/
nat2int
list
/bitlista/
Two
list
/bitlista/
len
list
/bitlista/
len-02
list
/bitlista/
a
list
/bitlista/
Last
list
/bitlista/
c-07
bitopsaux
/
sgn-two-01
int-basic2
/
add-a
int-basic2
/
add-c
int-abs
/
lels-03
int-pot
/
pot2-pos
int-abs
/
lels-01
int-basic1
/
ls-01
int-abs
/
forward-le-03
int-pot
/
two-lsz
int-abs
/
forward-le-01
int-abs
/
lels
int-abs
/
forward-le-02
int-abs
/
forward-le-05
int-abs
/
neg-13
int-abs
/
abs-08