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Theorem uint2bits-add-high-02
⊦ j0 < 0 ∧ 0 < i ∧ 2 ^ (i - 1) < abs(j0) ∧ abs(j0) ≤ 2 ^ i ∧ 0 < j → uint2bits(j * 2 ^ i + j0) = sgn(uint2bits(j - 1) + fillsgn(i→n(i), int2bits(j0).rest))
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
int2bits-add-high
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 11
Proof steps: 25
Used lemmas:
uint2bits-sgn-02
,
int2bits-eq
,
int2bits-first
,
int2bits-truetrue-01
,
int2bits-true
,
int2bits-truein
,
int2bits-not-empty
,
uint2bits-add-high
,
uint2bits-zero
,
uint2bits-add-high-01
,
Used spec theorems:
bitopsaux
/
sgn-rec-01
bitopsaux
/
sgn-fill
Used simplifier rules:
int-abs
/
sub-ls-01
int-basic1
/
forward-pos
int-pot
/
two-lsz
bitopsaux
/
sgn-mklist-05
bitopsaux
/
fill-first
int-basic1
/
ls-01
int-abs
/
lsone
int-pot
/
2pot-leone
int-abs
/
sub-ls
int-abs
/
lels-02
int-pot
/
pot2-pos
int-abs
/
leone
int-abs
/
sub-le-01
int-abs
/
minus-add
int-basic2
/
add-zero
int-abs
/
mone-08
int-abs
/
numle-02
list
/bitlista/
e
bitopsaux
/
sgn-mklist-01
bitopsaux
/
fillsgn-empty
bitopsaux
/
sgn-empty
list
/bitlista/
app
list
/bitlista/
a
list
/bitlista/
in-14
list
/bitlista/
c
list-data
/bitlista/
elim-list
intnat
/
abs-zero
bitopsaux
/
fill-empty
int-abs
/
zero-gels-04
int-abs
/
zero-gels-01
int-abs
/
sub-eq-01
int-mult
/
commutativity
int-mult
/
associativity
int-mult
/
one-01
int-abs
/
bet
int-abs
/
lels-04
int-abs
/
lels-01
int-basic2
/
add-c
int-basic2
/
add-a
int-abs
/
lels-03
int-abs
/
lels
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