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Theorem int2int-lastn-negpos
⊦ i < 0 ∧ ¬ lastn(m, int2bits(i)).first ∧ m ≤ # int2bits(i) ∧ m ≠ 0 ∧ i % 2 ^ n→i(m) ≠ 0 → bits2int(lastn(m, int2bits(i))) = i % 2 ^ n→i(m) + 2 ^ n→i(m)
Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by:
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 14
Proof steps: 26
Used lemmas:
bits2bits-def
,
int2bits-lelen-01
,
bits2int-first
,
bits2int-first-01
,
bits2uint-inv-neg
,
bits2uint-inv-pos
,
int2bits-first
,
bits2int-split-01
,
int2bits-first-01
,
int2int-inj
,
int2bits-not-empty
,
Used spec theorems:
list-del
/bitlista/
lastN-ex
int-mult
/
commutativity
int-div
/
modeq-neg-02
int-div
/
modex
int-div
/
mod-zero-05
bitopsaux
/
sgn-nls
Used simplifier rules:
nat-basic2
/
l-02
nat-basic2
/
a
nat-basic2
/
c
bitopsaux
/
sgn-empty-01
nat-basic1
/
f
nat
/
lels-01
intnat
/
n2n
int-abs
/
anti
int-basic1
/
numlsf
int-abs
/
forward-lele
int-abs
/
forward-lels
int-abs
/
numlsf-01
int-abs
/
zeroone
int-basic2
/
lst-03
int-abs
/
absle
int-mult
/
zero-ls
int-basic2
/
ls
int-basic2
/
succ-01
int-basic1
/
trans
int-basic1
/
lf-01
int-abs
/
forward-lsle
int-abs
/
Sub-def
int-pot
/
two-zero-01
int-mult
/
dist-rmerge
int-div
/
mod-mult-04
int-basic2
/
add-zero
int-mult
/
eq-same
int-basic1
/
lf-02
int-abs
/
lels-03
int-abs
/
lels-01
intnat
/
nat2int
int-pot
/
grz
int-abs
/
lels
int-mult
/
eq-succ
int-abs
/
sub-add-06
int-abs
/
sub-sub
list-del
/bitlista/
lastN-empty
int-abs
/
mone-01
int-abs
/
sub-eq
int-abs
/
sub-add-01
int-abs
/
neg-15
int-mult
/
commutativity
int-mult
/
associativity
int-mult
/
minus-left
int-basic2
/
add-c
int-basic2
/
add-a
int-abs
/
numadd-01
int-abs
/
negeq
int-abs
/
subsub
list
/bitlista/
c
list-data
/bitlista/
elim-list-c
int-basic1
/
lf-03
list-del
/bitlista/
lastn-length-01
list-data
/bitlista/
size-01
nat
/
zero-02
list
/bitlista/
Nil
list
/bitlista/
a
list-data
/bitlista/
l
nat
/
ler