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Theorem shiftzero-max-neg-01
⊦ i < 0 ∧ # int2bits(i) ≤ n ∧ j ≤ n→i(n) ∧ 0 < j ∧ n ≠ 0 → >>>(n, i, j) < 2 ^ (n→i(n) - j)
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 15
Proof steps: 30
Used lemmas:
shiftzero-by-one-01
,
shiftright-pos-div
,
shiftzero-minus-one
,
shiftzero-rec-neg-shorter
,
shiftzero-rec-neg-longer
,
Used spec theorems:
int2bits
/
int2bits-mone
int-pot
/
twopot-mone-div
int-pot
/
pot-sub-dist
intnat
/
n2i-sub
int2bits
/
int2bits-rec-neg-01
Used simplifier rules:
nat
/
elim-pred-c
list
/bitlista/
len
list
/bitlista/
a
list-data
/bitlista/
l
int2bits
/
int2bits-not-empty
nat
/
let
nat
/
ls-le-simp
nat-basic1
/
f
int-abs
/
forward-lels
int-basic2
/
add-zero
int-pot
/
ls-pos-2pot-01
int-abs
/
sub-ls
int-abs
/
Sub-def
int-abs
/
succ-02
intnat
/
le
nat
/
lels-02
nat
/
le-add
int-abs
/
mone-06
int-abs
/
numls-02
int-abs
/
forward-le
nat
/
sub-ls
intnat
/
ls-int-ls-nat
nat
/
lels
nat
/
succ-01
nat
/
ls-02
int-abs
/
sub-le
int-abs
/
sub-sub-04
int-abs
/
mone-05
int-abs
/
numle-03
int-abs
/
numsub
int-abs
/
sub-add-01
int-div
/
div-ls-zero
int-abs
/
numlelsdel-01
int-abs
/
sub-ls-01
intnat
/
rax-01
intnat
/
num-i2n-le-02
nat
/
ls-01
nat-basic2
/
s
intnat
/
labs
int-abs
/
abs
nat-basic2
/
a
nat-basic2
/
c
nat-basic1
/
one
int-basic1
/
forward-pos
nat-basic1
/
one-01
int-abs
/
lep
int-div
/
div-two-zero-01
int-abs
/
lels-03
nat
/
pred-03
bitopsaux
/
fill-length
int-basic1
/
irref
int-basic2
/
add-c
int-basic2
/
add-a
int-abs
/
succ-01
int-abs
/
lels-04
int-abs
/
lels-02
int-abs
/
sub-le-01
int-abs
/
leone
int-pot
/
pot2-pos
intnat
/
nat2int
int-abs
/
lels-01
int-basic1
/
ls-01
nat
/
not-zero
list
/bitlista/
len-02
int-abs
/
bet
nat
/
lels-01
int-abs
/
mone-08
nat
/
le-ls-simp
nat-basic1
/
z
intnat
/
num-n2i-ls-02
int-abs
/
forward-le-02
int-abs
/
forward-le-05
int-abs
/
forward-lsle
int-abs
/
lels