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Theorem uint2bits-mod2pot
0 ≤ i, 2 ^ i < j ⊦ uint2bits(j % 2 ^ i) = sgn(false ' + lastn(i→n(i), uint2bits(j).rest))
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
uint2bits-2potrec
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 30
Proof steps: 64
Used lemmas:
uint2bits-zero-01
,
uint2bits-len-min
,
uint2bits-pos-num
,
uint2bits-2pot-01
,
uint2bits-2pot
,
uint2bits-zero
,
uint2bits-empty
,
uint2bits-one
,
uint2bits-rec-01
,
Used spec theorems:
list-del
/bitlista/
num-lastN
int-pot
/
le-2pot-01
int-div
/
mod-succ
int-div
/
mod-twoeven
int-div
/
mod-twoodd-01
int-div
/
mod-zero-01
int-div
/
div-two
bitopsaux
/
sgn-last-01
list
/bitlista/
rest-01
bitopsaux
/
sgn-last
bitlista
/
mklist-intro
list-del
/bitlista/
lastn-length-01
list-data
/bitlista/
length-rest
Used simplifier rules:
intnat
/
abs-succ-03
nat
/
fle
nat-basic2
/
l-02
nat
/
lels
nat-basic2
/
s
nat
/
ls-01
nat-basic1
/
one-01
list-data
/bitlista/
l
nat-basic1
/
f
nat
/
lels-01
list
/bitlista/
app-05
bitopsaux
/
sgn-two
bitopsaux
/
sgn-append
list
/bitlista/
app-03
int-div
/
mod-two-02
int-div
/
div-mult-03
list-last
/bitlista/
mk-last
bitopsaux
/
sgn-rec
int-abs
/
anti
int-abs
/
numlsf-01
int-mult
/
ls-same-01
int-pot
/
mod2-2pot-05
int-mult
/
ls-pos
int-mult
/
neq-two
int-mult
/
eq-one
bitopsaux
/
sgn-mklist-01
int-mult
/
le-same-01
int-mult
/
zero-gr
int-mult
/
zero-eq
int-basic2
/
add-zero
int-div
/
div-elim
int-mult
/
le-pos
int-abs
/
succ-02
int-div
/
div-elim-pos
int-div
/
mod-less-01
int-basic2
/
succ-01
int-basic1
/
trans
int-basic1
/
lf-01
int-div
/
mod-two
list
/bitlista/
app-01
int-div
/
nummult-ls-02
int-pot
/
grz
int-mult
/
zero-ge-add
bitopsaux
/
sgn-two-02
bitopsaux
/
sgn-mklist-02
int-div
/
mod-two-04
list-del
/bitlista/
lastn-mklist-01
int-div
/
div-two
int-mult
/
zero-ge
int-mult
/
Mult-zero
int-mult
/
numls-01
int-mult
/
associativity
int-pot
/
two-zero
int-mult
/
two-zero
int-basic1
/
lf-02
int-abs
/
les
int-mult
/
commutativity
int-pot
/
succ
int-abs
/
mone-06
int-abs
/
numls-02
int-abs
/
numadd-01
nat-basic2
/
c
nat-basic2
/
a
nat-basic2
/
z
nat
/
add-01
intnat
/
rax
int-basic2
/
add-c
int-basic2
/
add-a
int-abs
/
elim-sub
int-basic1
/
ls-01
int-abs
/
leone
int-abs
/
sub-le-01
intnat
/
labs
int-div
/
abs
int-abs
/
abs-16
int-div
/
div2-nle
int-abs
/
lels-02
nat
/
pred-03
list
/bitlista/
c-04
bitopsaux
/
sgn-one
list
/bitlista/
app
list-del
/bitlista/
lastN-zero
int-div
/
mod-one
int-basic1
/
lf-03
intnat
/
abs-zero
nat-basic1
/
z
int-basic1
/
lst
int-div
/
div-two-zero-01
list
/bitlista/
Last
int-abs
/
lels
list
/bitlista/
Two
list
/bitlista/
c-07
list
/bitlista/
a
int-pot
/
2pot-leone
int-abs
/
lels-04
int-abs
/
lels-01
int-abs
/
forward-lsle
int-abs
/
forward-lele
int-pot
/
two-lsz