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Theorem longshiftzero-carry-01
⊦ 0 ≤ i ∧ i ≤ 1 → ¬ 1 < (i + band(4294967295, j) + band(4294967295, j0)) l>>> 32
Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by:
Used by units in proved state:
byte
,
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 11
Proof steps: 18
Used lemmas:
band-max-05
,
band-max-02
,
shiftright-pos-div
,
band-32-not-neg
,
shiftzero-pos
,
band-commutativity
,
band-associativity
,
band-63-pos-02
,
longshiftzero-def-unbounded
,
Used spec theorems:
int-div
/
div-rec
int-div
/
div-zero
int-abs
/
forward-lels
Used simplifier rules:
int-abs
/
numlelsdel
int-basic2
/
add-zero
int-abs
/
anti
int-abs
/
bet
int-abs
/
mone-06
int-abs
/
numle-02
int-basic2
/
num-between
int-basic1
/
numlslsdel-01
int-basic2
/
ls-01
int-abs
/
sub-le-01
int-abs
/
sub-ls
int-div
/
sub-ls-01
int-basic2
/
zero-02
int-abs
/
numls-02
int-abs
/
succ-02
int-abs
/
numleledel-01
int-abs
/
forward-le
int-abs
/
lels
int-abs
/
zero-gels-03
int-abs
/
lels-03
int-abs
/
lels-04
int-abs
/
lels-01
int-abs
/
forward-lsle
int-abs
/
forward-le-02
int-basic2
/
ls
int-basic2
/
add-a
int-basic2
/
add-c
int-basic1
/
forward-pos
int-abs
/
forward-le-05
int-abs
/
forward-le-01
int-abs
/
forward-lels