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Theorem shiftzero-rec-neg-shorter
⊦ i < ~1 ∧ # int2bits(i) ≤ n ∧ 1 < j → >>>(n, i, j) = >>>(n -1, (i - 1) / 2, j - 1)
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
shiftzero-max-neg
,
shiftzero-max-neg-01
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 15
Proof steps: 28
Used lemmas:
shiftrzero-def-01
,
Used spec theorems:
list-del
/bitlista/
sublist-def
bitopsaux
/
fill-length
int2bits
/
int2bits-rec-neg-01
list-last
/bitlista/
mk-rec
int2bits
/
int2bits-rec-neg
bitopsaux
/
fill-last
list-del
/bitlista/
firstn-butlast-intro
int2bits
/
bits2int-pos-02
list-del
/bitlista/
firstn-first
Used simplifier rules:
list-last
/bitlista/
mk-first
list
/bitlista/
app-02-ant
list-last
/bitlista/
mk-empty
int2bits
/
bits2uint-base
list-del
/bitlista/
firstN-empty
int-abs
/
lels-02
intnat
/
num-i2n-eq
list-last
/bitlista/
butlast-def
list-last
/bitlista/
mk-len
nat
/
sub-add
nat-basic2
/
s
nat-basic2
/
l-02
list
/bitlista/
Last
int-abs
/
mone-05
int-abs
/
numle-03
int-basic2
/
add-c
int-basic2
/
add-a
int-abs
/
numsub
int-abs
/
sub-add-01
int-div
/
div-ls-zero
int2bits
/
int2bits-first-02
bitopsaux
/
fill-fill
nat-basic2
/
pred
nat
/
le-sum
list
/bitlista/
len-02
int-div
/
mod2-neg-odd
int-abs
/
lels
int-abs
/
lels-03
int2bits
/
bits2int-pos
list-del
/bitlista/
weak-firstN-rec
list
/bitlista/
c
nat-basic2
/
z
nat
/
add-01
intnat
/
abs-zero
list-last
/bitlista/
mk-zero
list
/bitlista/
Nil
nat-basic2
/
oz
nat
/
elim-pred-c
list
/bitlista/
len
list
/bitlista/
a
nat
/
le-add
nat
/
let
nat-basic2
/
c
nat-basic2
/
a
nat
/
lels
nat
/
succ-01
nat
/
ls-02
nat
/
lels-01
nat-basic1
/
one-01
list-del
/bitlista/
firstN-zero
bitopsaux
/
fill-zero
nat
/
lez-01
list-data
/bitlista/
l
int2bits
/
int2bits-not-empty
list-del
/bitlista/
restN-zero
bitopsaux
/
fill-length
intnat
/
rax-01
int-basic1
/
numlsf
int-basic1
/
forward-pos
int-abs
/
forward-le-05
nat
/
pred-03