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Theorem uint2bits-add-low
⊦ j < 0 ∧ 0 < i ∧ abs(j) ≤ 2 ^ (i - 1) → uint2bits(j + 2 ^ i) = false ' + fillsgn(i→n(i), int2bits(j))
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
uint2bits-add-low-01
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 23
Proof steps: 42
Used lemmas:
int2bits-zero
,
int2bits-not-empty
,
uint2bits-2pot-02
,
int2bits-rec-neg
,
int2bits-neg-num
,
uint2bits-one
,
uint2bits-pos-num
,
Used spec theorems:
int-pot
/
Pot-pos
int-div
/
div2-add-neg
int-div
/
mod2-add-neg
bitopsaux
/
fill-rec-one
list-last
/bitlista/
mk-last-02
bitopsaux
/
fill-last
int-abs
/
Abs-neg
int-basic2
/
add-c
int-abs
/
numadd-01
int-pot
/
succ
int-mult
/
modlep-03
Used simplifier rules:
int-mult
/
zero-ge
int-abs
/
numlsledel-01
int-mult
/
dist-rmerge
int-pot
/
two-minus
int-basic2
/
lst-03
int-mult
/
succ-rmerge
int-abs
/
numsub
int-abs
/
elim-sub
int-basic2
/
lst-01
int-mult
/
zero-ge-add-01
int-basic2
/
zero-02
int-div
/
mult
int-mult
/
zero-ge-add
int-abs
/
succ-02
int-basic1
/
numlslsdel-01
int-div
/
neg-01
int-abs
/
sub-add-09
int-abs
/
numlelsdel-01
int-basic1
/
numlslsdel
int-abs
/
forward-lels
int-div
/
div-elim-pos
int-abs
/
neg-15
int-abs
/
minus-02
int-abs
/
neg-06
int-abs
/
Abs-pos
int-abs
/
mone-08
int-basic1
/
minus-one
int-abs
/
numls-02
int-abs
/
numle-02
intnat
/
abs-zero
list-last
/bitlista/
mk-last
nat-basic1
/
z
list-last
/bitlista/
mk-zero
bitopsaux
/
fill-zero
list
/bitlista/
e
int-abs
/
numleledel-01
int-pot
/
two-ls
int-abs
/
mone-06
int-basic1
/
lst-01
int-abs
/
mone-01
list
/bitlista/
in-17
list
/bitlista/
in-append
list
/bitlista/
in-14
nat
/
pred-03
intnat
/
abs-succ-02
int-abs
/
sub-sub
int-div
/
abs
int-abs
/
sub-ls-01
int-abs
/
anti
int-div
/
div-two-zero-01
intnat
/
abs-pred
int-abs
/
lels-03
int-abs
/
numadd-01
int-abs
/
negeq
int-div
/
mod-neg-01
int-abs
/
numlsf-01
int-pot
/
pot2-div2
int-basic1
/
lst
int-basic1
/
ls-01
int-pot
/
pot2-mod2-zero
int-abs
/
sub-eq
int-abs
/
Sub-def
int-abs
/
sub-le
int-basic2
/
add-zero
int-abs
/
leone
int-abs
/
sub-add-01
int-abs
/
sub-ls
int-mult
/
numsucc
int-div
/
nummult-ls-02
int-abs
/
sub-le-01
int-mult
/
numle-05
int-pot
/
two-leone
int-basic1
/
two-ls
int-abs
/
sub-eq-01
bitopsaux
/
invert-zero
bitopsaux
/
inv-one-01
list
/bitlista/
c
bitopsaux
/
succ-zero
list
/bitlista/
Last
bitopsaux
/
sgn-two-01
bitopsaux
/
fill-one-02
list-last
/bitlista/
mk-one-01
intnat
/
num-i2n-eq
int-abs
/
lep
int-abs
/
lsone
int-abs
/
numls-03
list
/bitlista/
a
list
/bitlista/
app-01
list
/bitlista/
Two
int-basic1
/
lf-02
int-abs
/
bet
int-abs
/
bet-01
int-abs
/
lels-02
int-abs
/
lels-04
int-mult
/
one
int-mult
/
numls-13
int-basic1
/
lf-03
int-mult
/
zero-gr
int-abs
/
forward-lele
int-abs
/
zeroone
int-mult
/
commutativity
int-abs
/
lels-01
int-basic2
/
ls-01
int-mult
/
ls-same
int-mult
/
associativity
int-abs
/
sub-pred
int-abs
/
lels
int-basic2
/
succ-01
int-basic2
/
add-c
int-basic2
/
add-a
int-basic2
/
ls-02
int-basic1
/
trans
int-basic1
/
lf-01
int-abs
/
forward-lsle
int-abs
/
negle-13
int-abs
/
abs-08