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Theorem sis-neg-low
⊦ i < 0 ∧ i % 65536 < ~32768 → s2i(i2s(i)) = i % 65536 + 65536
Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by:
sis-ls-same
,
sis-ls-same-01
,
sis-neg-lower
,
ushort-pos-02
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 18
Proof steps: 31
Used lemmas:
sis-pos-high
,
num-i2s-neg
,
num-issi
,
Used spec theorems:
int2bits
/
int2bits-add-high
list-del
/bitlista/
lastN-rest-01
bitopsaux
/
fillsgn-longer
list-del
/bitlista/
lastN-all
list-data
/bitlista/
length-rest
int2bits
/
int2int-rest-01
int-basic1
/
lsrec
int2bits
/
int2bits-len-neg
Used simplifier rules:
int-basic1
/
numlslsdel-01
nat
/
ls
nat
/
lels-02
list-data
/bitlista/
l
nat
/
not-zero
list
/bitlista/
a
list-del
/bitlista/
lastN-append-01
int2bits
/
int2bits-not-empty
nat
/
pred-03
nat
/
ls-01
nat-basic1
/
lf-02
nat-basic1
/
lf-01
nat-basic1
/
ls-02
nat-basic1
/
f
nat
/
lels-01
int-abs
/
numle-02
int-abs
/
numle-03
int-basic2
/
num-between
int-basic1
/
lst
int-basic1
/
numlslsdel
int-abs
/
mone-08
int2bits
/
int2bits-mone-02
list
/bitlista/
len-02
nat-basic2
/
a
nat-basic2
/
c
int-basic2
/
add-zero
int-mult
/
associativity
int-abs
/
anti
int-abs
/
lels
int-abs
/
numlelsdel-01
int-abs
/
numls-03
int-abs
/
neg-07
int-mult
/
commutativity
int2bits
/
int2bits-leneq-neg
int-abs
/
numlelsdel
int-abs
/
forward-le-04
int-basic2
/
add-c
int-basic2
/
add-a
int-abs
/
numls-02
int-abs
/
neg-13
int-abs
/
abs-08
int-abs
/
lels-02
int-div
/
div-elim-negpos
int-abs
/
lels-01
int-abs
/
zero-gels-01
int-div
/
mod-ls-zero
int-abs
/
forward-le-02
int-basic1
/
numlsf
int-abs
/
zero-gels-03
int-abs
/
forward-lsle
int-abs
/
forward-lels
int-div
/
mod-ls-same-01
int-basic1
/
ls-01