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Theorem cast-mod-pos-low
0 ≤ j, j % 2 ^ i ≤ 2 ^ (i - 1) - 1, 0 < i ⊦ cast(i, j) = j % 2 ^ i
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
cast-add-2pot-h
,
cast-if
,
cast-law-add-pos
,
cast-law-add-pos-01
,
cast-law-mult-pos
,
cast-law-neg-pos
,
cast-mult-2pot
,
cast-mult-pos
,
Used by units in proved state:
byte
,
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 16
Proof steps: 31
Used lemmas:
cast-def
,
cast-mod-in
,
Used spec theorems:
int2bits
/
int2bits-lslen
int2bits
/
int2bits-rec-2pot-pos
list-del
/bitlista/
lastN-append
list-data
/bitlista/
length-rest
bitopsaux
/
fill-length
bitopsaux
/
fillsgn-longer
int-div
/
mod-zero-02
bitopsaux
/
fill-rec
int2bits
/
int2bits-lslen-06
int-div
/
mod-zero-05
Used simplifier rules:
intnat
/
num-i2n-ls
list-last
/bitlista/
mk-len
list-last
/bitlista/
mk-last
list-last
/bitlista/
mk-zero
bitlista
/
mklist-num
list-last
/bitlista/
mk-plus
bitopsaux
/
fill-one-01
int-pot
/
mod-lez
nat-basic1
/
lf-02
nat-basic2
/
s
int2bits
/
int2bits-first-02
nat-basic2
/
pred
list
/bitlista/
c-07
int2bits
/
bits2int-fill
int2bits
/
int2int-inj
nat
/
lep
list
/bitlista/
len-02
list
/bitlista/
rest
list
/bitlista/
app
nat-basic1
/
one-01
int-abs
/
lels-04
nat
/
succ-01
nat
/
lels
nat
/
let
nat
/
fle
nat-basic2
/
l-02
int-abs
/
forward-le-04
int-abs
/
forward-lele
intnat
/
n2i-add
int-basic2
/
add-zero
list-data
/bitlista/
l
nat-basic2
/
c
nat
/
add-01
nat-basic2
/
z
nat-basic2
/
a
intnat
/
abs-eq
nat
/
pred-03
bitopsaux
/
fill-empty
int2bits
/
int2bits-not-empty
list
/bitlista/
a
list
/bitlista/
len
intnat
/
abs-succ-03
int-basic1
/
irref
int-abs
/
absle
int-abs
/
zero-gels-04
int-pot
/
pot2-ls-pred
int-basic1
/
ls-01
int-abs
/
lels-02
int-abs
/
lsone
int-pot
/
two-lez-01
int-div
/
mod-zero-04
int-pot
/
zero
list-del
/bitlista/
lastn-mklist-03
bitopsaux
/
fill-one-02
int2bits
/
int2bits-zero
int-abs
/
anti
intnat
/
i2i-pos
int-basic1
/
forward-pos
int-abs
/
forward-lels
int-pot
/
pot2-pos
int-pot
/
pot2-pos-01
int-abs
/
sub-ls-01
int-abs
/
leone
int-pot
/
ls-pos-2pot-01
int-abs
/
sub-ls
int-abs
/
sub-add-01
int-abs
/
numsub
int-abs
/
minus-add
intnat
/
abs-zero
nat-basic1
/
f
nat
/
lels-01
int-pot
/
two-lsz
int-basic2
/
ls
int-abs
/
forward-le-02
int-abs
/
forward-lsle
int-abs
/
lels-01
int-abs
/
negle-13
int-abs
/
lels-03
int-abs
/
lels
int-abs
/
forward-le-05
int-abs
/
forward-le-01
int-basic2
/
add-c
int-basic2
/
add-a
int-abs
/
succ-01
int-abs
/
sub-le-01