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Theorem int2bits-add-high
⊦ j0 < 0 ∧ 0 < i ∧ 2 ^ (i - 1) < abs(j0) ∧ abs(j0) < 2 ^ i ∧ j < 0 → int2bits(j * 2 ^ i + j0) = int2bits(j - 1) + fillsgn(i→n(i), int2bits(j0).rest)
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: 30
Proof steps: 59
Used lemmas:
int2bits-truein
,
int2bits-neg-num
,
int2bits-exneg
,
uint2bits-2pot-02
,
uint2bits-falsein-01
,
uint2bits-truein
,
uint2bits-empty
,
uint2bits-zero
,
uint2bits-sgn-02
,
uint2bits-one
,
uint2bits-pos-num
,
uint2bits-2pot-01
,
uint2bits-2pot
,
int2bits-2pot
,
int2bits-2pot-02
,
int2bits-len-pos-suc
,
uint2bits-add-high-02
,
int2bits-lelen-07
,
int2bits-pos
,
int2bits-len-add
,
int2bits-neg-03
,
Used spec theorems:
int-mult
/
modzero-03
int-mult
/
modzero
int-mult
/
commutativity
int-pot
/
pot-dist-pos
list
/bitlista/
rest-01
bitopsaux
/
sgn-append-01
bitopsaux
/
sgn-append-05
bitopsaux
/
sgn-base-03
bitopsaux
/
fill-first
Used simplifier rules:
list
/bitlista/
e-01
list
/bitlista/
c-08
list
/bitlista/
in-13
list
/bitlista/
in-14
bitopsaux
/
invert-zero
bitopsaux
/
inv-one-01
list
/bitlista/
c
bitopsaux
/
succ-zero
bitopsaux
/
sgn-two-01
bitopsaux
/
fillsgn-empty
int-abs
/
mone-08
bitopsaux
/
fill-empty
int-abs
/
lels-02
bitlista
/
inmklist-01
list-last
/bitlista/
mk-empty
intnat
/
abs-zero
list-last
/bitlista/
mk-zero
bitopsaux
/
sgn-mklist-05
int-abs
/
numlelsdel-01
int-basic1
/
forward-pos
int-mult
/
one-01
list
/bitlista/
Nil
bitopsaux
/
sgn-empty
list
/bitlista/
rest
int-abs
/
sub-eq-01
int-abs
/
bet
list
/bitlista/
Two
list
/bitlista/
Last
bitopsaux
/
sgn-rec
bitopsaux
/
sgn-2pot
list
/bitlista/
app-01
int-mult
/
numsub
int-abs
/
zero-gels-04
int-mult
/
zero-ge
int-mult
/
numle-09
int-pot
/
succ
int-mult
/
pred-rmerge
int-abs
/
Sub-def
int-abs
/
minus-sub
int-pot
/
two-minus
list
/bitlista/
len
list
/bitlista/
len-02
list-last
/bitlista/
mk-len
list
/bitlista/
a
intnat
/
ini2-abs
int-abs
/
sub-sub
int-abs
/
sub-add-06
int-abs
/
sub-sub-04
int-abs
/
numsub
int-pot
/
pot2-pos-01
int-abs
/
abs-16
int-pot
/
pot2-succ-01
bitopsaux
/
sgn-base-02
list
/bitlista/
c-07
bitopsaux
/
sgn-true-mklist
list
/bitlista/
app-03
int-abs
/
succ-01
int-abs
/
sub-le
int-abs
/
sub-ls-01
int-abs
/
succ-02
int-basic1
/
lst
int-abs
/
numle-02
int-pot
/
ls-pos-2pot-01
int-basic2
/
ls
int-abs
/
sub-eq
int-abs
/
negle-07
int-basic2
/
add-zero
int-abs
/
forward-le-04
int-abs
/
leone
int-abs
/
sub-le-01
int-abs
/
zero-gels-03
int-abs
/
sub-add-01
int-abs
/
neg-15
int-abs
/
minus-02
int-abs
/
sub-ls
int-abs
/
lsone
int-abs
/
zero-gels-01
int-abs
/
mone-06
int-abs
/
numls-02
int-basic2
/
zero-01
bitopsaux
/
fill-zero
int-mult
/
one
int-abs
/
negle-13
int-abs
/
anti
int-mult
/
commutativity
int-mult
/
associativity
int-mult
/
dist-rmerge
intnat
/
nat2int
int-abs
/
lenls
nat-basic2
/
c
nat-basic2
/
a
intnat
/
i2i-pos
intnat
/
n2i-add
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-basic2
/
add-c
int-basic2
/
add-a
int-abs
/
forward-le-02
int-abs
/
forward-le-05
int-abs
/
neg-13
int-abs
/
neg-07
int-abs
/
abs-08