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Theorem shiftzero-rec-neg-longer
⊦ i < ~1 ∧ n < # int2bits(i) ∧ 1 < j → >>>(n, i, j) = >>>(n, (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: 12
Proof steps: 21
Used lemmas:
shiftrzero-def-01
,
Used spec theorems:
int2bits
/
int2bits-rec-neg
list-del
/bitlista/
sublist-def
bitopsaux
/
fillsgn-longer
list-last
/bitlista/
mk-rec
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
list-del
/bitlista/
firstN-empty
int-abs
/
lels-02
intnat
/
num-i2n-eq
list-last
/bitlista/
butlast-def
list-last
/bitlista/
mk-len
int2bits
/
bits2int-pos
list-del
/bitlista/
weak-firstN-rec
list
/bitlista/
c
nat-basic2
/
z
nat
/
add-01
nat-basic2
/
oz
intnat
/
abs-zero
list-last
/bitlista/
mk-zero
list
/bitlista/
Nil
list-del
/bitlista/
firstn-app
list-del
/bitlista/
first-all
int2bits
/
int2int-inj
nat
/
elim-pred-c
nat
/
lels-01
nat
/
fle
nat-basic2
/
l-02
list-del
/bitlista/
restN-zero
bitopsaux
/
fillsgn-longer
nat-basic2
/
c
nat-basic2
/
a
nat
/
lels
nat-basic2
/
s
list
/bitlista/
a
list
/bitlista/
len-02
list
/bitlista/
len
int-div
/
mod2-neg-odd
intnat
/
rax-01
nat
/
pred-03
int-abs
/
lels
int-abs
/
lels-03
int2bits
/
int2bits-not-empty
list-data
/bitlista/
l
int-basic1
/
numlsf
nat-basic1
/
f
int-basic1
/
forward-pos
int-abs
/
forward-le-05