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Theorem sis-pos-low
⊦ 0 ≤ i ∧ i % 65536 ≤ 32767 → s2i(i2s(i)) = i % 65536
Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by:
short-in
,
short-larger
,
short-law-div-not
,
sis-ls-same
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 14
Proof steps: 24
Used lemmas:
sis-06
,
num-i2s-pos
,
num-issi
,
Used spec theorems:
int2bits
/
int2bits-mod2pot
list-del
/bitlista/
lastN-append
list-data
/bitlista/
length-rest
bitopsaux
/
fill-length
int2bits
/
int2bits-lslen-06
bitopsaux
/
fill-rec
int2bits
/
int2bits-lelen-06
int-div
/
mod-zero-05
Used simplifier rules:
int-abs
/
absle
int-abs
/
numleledel
int2bits
/
int2int-inj
int2bits
/
bits2int-fill
int-abs
/
zero-gels-04
int2bits
/
int2bits-first-02
list
/bitlista/
rest
list-data
/bitlista/
size-01
nat
/
not-zero
bitopsaux
/
fillsgn-longer
nat
/
lels
int2bits
/
int2bits-zero
bitopsaux
/
fill-rec-one
bitlista
/
mklist-num
list-last
/bitlista/
mk-zero
list
/bitlista/
app
list
/bitlista/
a
list
/bitlista/
c-07
list-del
/bitlista/
num-lastN
list-del
/bitlista/
lastn-one
list-last
/bitlista/
last-def
int2bits
/
bits2int-pos
int2bits
/
bits2uint-zero
int2bits
/
bits2uint-one-02
list-data
/bitlista/
l
nat-basic1
/
f
nat
/
lels-01
nat
/
pred-03
bitopsaux
/
fill-empty
int2bits
/
int2bits-not-empty
int-abs
/
lels
int-abs
/
anti
int-abs
/
lels-04
int-basic2
/
add-zero
int-abs
/
forward-lele
int-mult
/
zero-ge-add-01
int-basic2
/
add-c
int-basic2
/
add-a
int-mult
/
commutativity
int-mult
/
associativity
int-mult
/
zero-gr
int-basic2
/
ls-02
int-abs
/
numlsledel
int-basic1
/
ls-01
int-div
/
div-elim-pospos
int-basic1
/
numlslsdel-01
int-abs
/
forward-lels
int-basic1
/
forward-pos
int-abs
/
forward-le-05
int-abs
/
lels-01
int-abs
/
numleledel-01
int-abs
/
forward-le-01