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Theorem band-011x-pos
⊦ 0 ≤ j ∧ 0 ≤ i → band(j, 2 ^ i - 1) = j % 2 ^ i
Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by:
band-011x-is-unsigned
,
band-011x-pos-01
,
band-255-pos
,
band-65535-pos
,
band-mod256-pos
,
intshiftleft-is-mult
,
Used by units in proved state:
bytes
,
byte
,
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 25
Proof steps: 60
Used lemmas:
and-notempty
,
and-notempty-06
,
and-pos
,
and-rec-02
,
and-rec
,
and-rec-04
,
band-associativity
,
band-def
,
Used spec theorems:
int2bits
/
int2bits-pos
int2bits
/
uint2bits-rec-01
int-div
/
one-03
list-last
/bitlista/
mk-last-01-01
int2bits
/
bits2int-rec-false
int2bits
/
bits2int-rec
int2bits
/
uint2bits-first-01
int-div
/
mod-twoodd
Used simplifier rules:
int-basic2
/
add-zero
int-mult
/
neq-two
int-pot
/
two-zero
int-div
/
mod-mult-02
int-div
/
mod-two
int-pot
/
grz
int-basic2
/
add-in
int-mult
/
eq-pos
int-mult
/
zero-ge
int-mult
/
zero-ge-add
int-mult
/
two-zero
int-div
/
div-elim-pos
int2bits
/
bits2int-one
list
/bitlista/
Nil
int-basic1
/
lf-03
int2bits
/
bits2uint-zeros-03
int2bits
/
bits2uint-one
bitopsaux
/
succ-zero
bitopsaux
/
inv-one-01
bitopsaux
/
inv-append
int-abs
/
negeq
bitopsaux
/
invert-one
int2bits
/
bits2int-neg
list
/bitlista/
in-17
list
/bitlista/
in-append
list
/bitlista/
in-14
list-data
/bitlista/
elim-list-c
list
/bitlista/
c-08
int-pot
/
succ
int-abs
/
mone-06
int-abs
/
numls-02
nat-basic2
/
z
nat
/
add-01
intnat
/
rax
int-basic2
/
add-c
int-basic2
/
add-a
int-abs
/
numadd-01
int-abs
/
elim-sub
int-mult
/
commutativity
int-mult
/
associativity
int-mult
/
le-same
int-div
/
num-ls
int-abs
/
abs-16
int-div
/
abs
intnat
/
labs
int-abs
/
sub-le-01
int-abs
/
leone
list
/bitlista/
c
list-data
/bitlista/
lf-01
list-data
/bitlista/
l
int-basic1
/
lst
int-div
/
div-two-zero-01
int-div
/
mod-zero-04
int-pot
/
zero
int-pot
/
two-leone
int-abs
/
lsone
list
/bitlista/
e-01
int2bits
/
bits2uint-one-03
int2bits
/
bits2int-pos
list
/bitlista/
app-02-ant
list
/bitlista/
e
list-last
/bitlista/
mk-butlast
list-last
/bitlista/
mk-empty
intnat
/
num-i2n-eq
int-basic1
/
ls-01
nat-basic2
/
one
list
/bitlista/
Last
list-last
/bitlista/
last-def
list-last
/bitlista/
butlast-def
list
/bitlista/
len
list
/bitlista/
len-02
list-last
/bitlista/
mk-len
nat-basic1
/
one
nat-basic2
/
oz
nat-basic2
/
a
nat-basic2
/
c
nat-basic2
/
one-03
intnat
/
abs-zero
int2bits
/
uint2bits-zero
list
/bitlista/
Two
int2bits
/
uint2bits-one
int-abs
/
anti
int-abs
/
lels
int-abs
/
lels-02
int2bits
/
uint2bits-empty
int2bits
/
bits2int-zero
int-div
/
mod-one
list
/bitlista/
a
list
/bitlista/
app
list-last
/bitlista/
mk-zero
int2bits
/
int2bits-2pot-02
int-abs
/
lels-01
int-abs
/
lels-04