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Theorem uint2bits-add-high-01
⊦ j0 < 0 ∧ 0 < i ∧ 2 ^ (i - 1) < abs(j0) ∧ abs(j0) ≤ 2 ^ i ∧ 1 < j → uint2bits(j * 2 ^ i + j0) = uint2bits(j - 1) + fillsgn(i→n(i), int2bits(j0).rest)
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
uint2bits-add-high-02
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 7
Proof steps: 11
Used lemmas:
uint2bits-one
,
int2bits-neg-num
,
int2bits-lslen-05
,
int2bits-not-empty
,
uint2bits-add-high
,
uint2bits-zero
,
uint2bits-mod2pot-01
,
Used spec theorems:
bitopsaux
/
fill-sgn-03
Used simplifier rules:
int-abs
/
numsub
intnat
/
i2i-pos
intnat
/
n2i-add
list
/bitlista/
Two
bitopsaux
/
invert-zero
bitopsaux
/
inv-one-01
list
/bitlista/
c
bitopsaux
/
succ-zero
list
/bitlista/
Last
bitopsaux
/
sgn-two-01
list
/bitlista/
rest
bitopsaux
/
sgn-empty
bitopsaux
/
fillsgn-empty
list-last
/bitlista/
mk-plus
list-last
/bitlista/
mklist-one
list-last
/bitlista/
mk-last
list
/bitlista/
c-07
list-last
/bitlista/
mk-inj-01
nat-basic2
/
a
nat-basic2
/
c
nat
/
lels-01
nat
/
fle
nat-basic1
/
f
nat
/
fle-01
list-data
/bitlista/
l
nat-basic2
/
l
int-abs
/
anti
bitopsaux
/
fill-zero
int-abs
/
numle-02
int-abs
/
mone-08
int-basic2
/
add-zero
int-abs
/
zero-gels-01
int-abs
/
zero-gels-04
int-abs
/
numlelsdel-01
list
/bitlista/
a
list
/bitlista/
app-01
int-abs
/
lels-01
int-basic1
/
ls-01
int-abs
/
sub-ls-01
int-abs
/
lels
int-abs
/
bet
int-abs
/
lels-04
int-basic2
/
ls
int-abs
/
lels-03
int-mult
/
one-01
int-abs
/
sub-eq-01
int-basic1
/
forward-pos
int-abs
/
forward-le-05
int-abs
/
forward-le-02
int-abs
/
forward-le-01
int-abs
/
negle-13
int-abs
/
neg-07
int-abs
/
abs-08
int-mult
/
commutativity
int-mult
/
succ-rmerge
int-abs
/
Sub-def
int-basic2
/
add-a
int-basic2
/
add-c
int-mult
/
associativity
int-basic2
/
add-in