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Theorem cast-mod-neg-low
j < 0, j % 2 ^ i < ~(2 ^ (i - 1)), 0 < i ⊦ cast(i, j) = j % 2 ^ i + 2 ^ i
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
cast-add-2pot-h
,
cast-if
,
cast-mult-neg
,
Used by units in proved state:
byte
,
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 34
Proof steps: 64
Used lemmas:
cast-def
,
cast-mod-in
,
Used spec theorems:
int2bits
/
int2bits-lslen-03
int2bits
/
int2bits-rec-neg-03
int2bits
/
int2bits-rec-2pot-neg-02
list-del
/bitlista/
lastN-rest-01
list-del
/bitlista/
lastN-append
int-div
/
mod-grz
bitopsaux
/
fill-length
int2bits
/
int2bits-lslen-05
int-div
/
mod-lsz
bitopsaux
/
fillsgn-longer
int2bits
/
int2bits-lelen-03
int2bits
/
int2int-rest-01
int-abs
/
mone-07
int-div
/
mod-grz-01
int2bits
/
int2bits-len-neg
list-data
/bitlista/
length-rest
nat
/
elim-pred-c
int-div
/
mod-zero-05
Used simplifier rules:
int-pot
/
pred-le
int-abs
/
le-add
int-abs
/
forward-lele
int-basic2
/
eq
nat
/
eqle-one
nat-basic1
/
lf-01
nat-basic2
/
oz
nat
/
ler
nat-basic2
/
s
nat
/
ls-01
nat-basic1
/
one-01
list-data
/bitlista/
lr-04
nat-basic1
/
lf-02
int-pot
/
zero
nat
/
lels
nat
/
succ-01
int-pot
/
pot2-pos
nat
/
add-01
nat-basic2
/
z
intnat
/
abs-eq
nat
/
pred-03
bitopsaux
/
fill-empty
int-basic2
/
add-in
intnat
/
n2i-add
nat-basic2
/
eq-01
intnat
/
abs-succ-03
int-abs
/
Sub-def
int-basic1
/
ls-01
int-abs
/
lels-04
int-basic2
/
add-zero
int-abs
/
negle-07
int-abs
/
lels-02
int-abs
/
abs-08
int-abs
/
neg-13
int-abs
/
numls-02
int-basic1
/
minus-one
int-abs
/
forward-le-04
int-abs
/
sub-eq
int-mult
/
two-zero
int-mult
/
associativity
int-mult
/
commutativity
int-div
/
nummult-ls
int-div
/
div-elim-negpos
nat-basic2
/
c
nat-basic2
/
a
nat
/
lep
list
/bitlista/
len-02
list
/bitlista/
len
int-abs
/
numadd-01
int2bits
/
bits2int-one
list
/bitlista/
a
list-last
/bitlista/
last-def
int-abs
/
mone-08
int2bits
/
int2bits-not-empty
list-data
/bitlista/
l
nat
/
not-zero
int-basic1
/
numlsf
int-abs
/
zero-gels-03
int-abs
/
numls-03
list-del
/bitlista/
lastn-one
int-basic1
/
lst-01
intnat
/
i2i-pos
int-abs
/
forward-le-01
int-abs
/
forward-lsle
int-abs
/
zero-gels-01
int-basic2
/
ls-01
int-abs
/
leone
int-abs
/
sub-le-01
int-pot
/
ls-pos-2pot-01
int-abs
/
sub-add-01
int-abs
/
numsub
int-abs
/
sub-ls-01
int-basic2
/
ls
intnat
/
abs-zero
nat-basic1
/
f
nat
/
lels-01
int-abs
/
mone-06
int-abs
/
minus-add
int-abs
/
sub-ls
int-pot
/
2pot-leone
int-abs
/
lsone
int-pot
/
two-lsz
int-abs
/
forward-lels
int-basic2
/
add-c
int-basic2
/
add-a
int-abs
/
lels-01
int-abs
/
negle-13
int-abs
/
lels-03
int-abs
/
lels
int-abs
/
forward-le-05
int-abs
/
forward-le-02
int-abs
/
neg-07